1 Introduction

Since the discovery of radioactivity, nuclear reactions, the neutron and nuclear fission, a considerable knowledge-base was developed in nuclear physics about these processes and their characteristics. This evolved from many sophisticated experiments and the development of advanced models based on phenomenology and theoretical insight. Early on, applications of nuclear science developed that have had and will have an important impact on society – nuclear energy, medicine, security, material characterization, geological exploration, radiation safety and protection, the promise of fusion energy.

Developments are increasingly facilitated and stimulated by better quantitative modeling of physics processes through improved engineering tools and computing power. This allows a reduction in the requirement to use assumptions and approximations in the interpretation, testing and validation of data.

To profit from these advances, physics models have to be coded better and the required input data, in particular the nuclear data, have to be more accurate and complete. In addition, they are required in forms that are compatible with the software that is used for modeling. The input should include full covariance information such that uncertainties can be propagated to derive uncertainty margins of design and operational parameters at a desired confidence level.

In nuclear physics and engineering there is a long tradition to provide nuclear data libraries in response to evolving needs in the field. In this paper the Joint Evaluated Fission and Fusion nuclear data library version 3.3 (JEFF-3.3) is described. It is the last of a series of libraries developed over the past 35 years through a collaborative effort of nuclear laboratories coordinated by the Databank of the OECD Nuclear Energy Agency (NEA). JEFF-3.3 was released on 20 November 2017. The library consists of reaction data files for incident neutrons, protons, deuterons, tritons, helions, alphas and photons, a decay data file, a fission yields file, a thermal neutron scattering file, an activation file, and a displacements per atom (dpa) file. Although the JEFF-3.3 library builds on earlier releases (3.0 [1], 3.1 [2], 3.1.1 [3, 4], 3.1.2 and 3.2), it includes substantial changes. For completeness, in particular for neutron activation applications and decay heat estimations, many files were adopted from TENDL [5]. This includes files for charged-particle and photon induced reactions which are of interest for accelerator applications.

1.1 Purpose

JEFF-3.3 is a general purpose library serving a wide field of nuclear technology applications, both nuclear energy and non-energy applications. The main effort is directed at improving the data for neutron transport calculations. This part of the library, i.e. the neutron transport sublibrary, is used for the design, performance and safety assessment of industrial and experimental nuclear reactors, criticality safety analyses of spent nuclear fuel, nuclear safeguards and security and basic science.

JEFF-3.3 developments targeted the needs for the following reactor development programmes: ASTRID, a French fast reactor concept with enhanced sustainability and safety and reduced production of high level nuclear waste [6], MYRRHA, a research reactor developed in Belgium, advancing and promoting the development of accelerator driven systems and lead or lead-bismuth cooled fast reactors [7, 8], and the ITER and DEMO [9, 10] reactors and the IFMIF-DONES material irradiation facility [11] in support to nuclear fusion technology. JEFF-3.3 also aims at maintaining or improving performance for present and prospective pressurised water reactors (PWR) and boiling water reactors (BWR) for which JEFF-3.1.1 and JEFF-3.2 demonstrated excellent performance. Of particular interest are the concerns for safe, economic and ecologic transport, intermediate storage and final disposal of spent fuel. This requires accurate neutron transport and depletion calculations for criticality safety analyses and the prediction of decay heat and radiation source terms.

1.1.1 MYRRHA

MYRRHA, a Multi-purpose Research Reactor for High-tech Applications is being designed at SCK•CEN, Belgium [7, 8]. It is envisaged to operate both in critical and sub-critical mode. The reactor has a pool design with Lead-Bismuth Eutectic (LBE) coolant ensuring a fast neutron spectrum. This positions MYRRHA in the class of heavy liquid metal cooled fast reactors. In case the sub-critical operation mode is chosen, the central sub-assembly hosts a spallation neutron source. High energetic protons, with an energy of 600 MeV, are produced by a high-power linear accelerator with a max. beam current of 4 mA. The protons produce neutrons by interacting with the LBE coolant.

The two operation modes have their specific energy and neutron fluence distributions that permit a wide range of applications, from transmutation research to radionuclide production for medical and industrial applications. A flexible core design envisages many positions for experimental rigs to test new types of fuel and materials for e.g. fusion reactors. A sensitivity and uncertainty analysis revealed the noticeable contribution of lead and bismuth cross sections to the \(k_{\text {eff}}\) uncertainty [12]. In addition, neutron capture on \(^{209}\hbox {Bi}\) leads through the decay of \(^{210g}\hbox {Bi}\) to the formation of \(^{210}\hbox {Po}\), a highly radiotoxic nuclide determining the radioactive source term of LBE coolant.

1.1.2 ASTRID

ASTRID, the Advanced Sodium Technological Reactor for Industrial Demonstration, is a Generation-IV sodium-cooled fast reactor project, proposed by the Commissariat à l’Énergie Atomique (CEA) [6]. The main goals of ASTRID are multiple recycling of plutonium for the sustainability of natural uranium resources, minor actinide transmutation to reduce nuclear waste, and an enhanced safety compared to Generation-III reactors, such as the European Pressurized-water Reactor – EPR. Based on the experience with past Sodium-cooled Fast Reactors (SFR), ASTRID has the objective to demonstrate at an industrial scale the relevance and performance of innovations, in particular in the fields of safety and operability. ASTRID, with the related R&D facilities (hot labs, irradiation, technological platform, severe accidents, etc.) is designed to allow the:

  • testing and qualification of innovative safety design options towards a commercial reactor,

  • qualification of different fuels (transmutation, plutonium burner, etc.),

  • collection of the necessary data to justify a useful lifetime of 60 years for future SFR,

  • confirmation of the performance of innovative components and systems in order to optimise the design of future commercial reactors from a technical and economical point of view,

  • establishment of a reference for SFR cost assessment for construction and operation.

1.1.3 PWR and BWR and Spent Nuclear Fuel

Previous JEFF-3.1.1, JEFF-3.1.2 and JEFF-3.2 releases were tested broadly for pressurized and boiling water reactors. JEFF-3.1.1 was proven to perform well for these reactors in normal conditions [2]. JEFF-3.2 aimed at keeping this good behavior and fixed some issues for applications based on fast neutrons. For JEFF-3.3, the community chose to keep as much as possible this good behaviour and including results from recent studies carried out by WPECFootnote 1 subgroup 34 on the Coordinated evaluation of Plutonium-239 in the resonance region [13], subgroup 40, the Collaborative International Evaluated Library Organisation (CIELO) Pilot Project for major isotopes \(^{235,238}\hbox {U}\), \(^{239}\hbox {Pu}\), Iron, Oxygen and Hydrogen [14, 15]. In addition, recommendations resulting from the CHANDA (solving CHAllenges in Nuclear Data) project [16], a project supported by the European Commission within the 7th framework, were taken into account. For fission yields and thermal scattering data, additional collaboration through WPEC was co-ordinated under the WPEC subgroup 37 on Improved fission product yield evaluation methodologiesFootnote 2 and subgroup 42 on Thermal Scattering Kernel S(\(\alpha \),\(\beta \)): Measurement, Evaluation and Application2.

With the prospect of phasing out of PWR and BWR there is an increasing emphasis on spent nuclear fuel intermediate storage and final disposal, long term disposal of high level waste and the related encapsulation and transport problems. Therefore, considerable emphasis is placed on criticality safety, decay heat and radiation source term estimates for the proposed solutions and operations.

1.1.4 Fusion applications

The European strategy for the realisation of fusion energy, as expressed in the recent fusion roadmap [9], is built on three main pillars: the international ITER tokamak to demonstrate the scientific and technological feasibility of fusion as an energy source, an accelerator based neutron source, called IFMIF-DONES [11], for the development and qualification of fusion materials and a DEMOnstration power plant (DEMO) [10], which shall deliver a substantial amount of electricity to the grid and operate with a closed tritium fuel cycle. Neutronics simulations play a fundamental role for the design and optimisation of these facilities, including the evaluation and verification of their nuclear performance. Accurate nuclear data are required to predict the tritium breeding capability, assess the shielding efficiency, estimate the nuclear power generated in the system and produce activation and radiation damage data for the irradiated materials and components. This applies to the radiation dose fields after shut-down or during maintenance periods [17]. The availability of high quality nuclear data is thus a pre-requisite for reliable design calculations affecting the nuclear design and performance of the facilities, as well as safety, licensing, waste management and decommissioning issues.

A dedicated programme is conducted by the EUROfusion consortium on the development and qualification of nuclear data for fusion. This includes the evaluation of general purpose neutron cross-section data as required for design calculations using particle transport codes, the generation of new activation and displacement damage cross-section data libraries, and the evaluation of deuteron cross-sections as required for the IFMIF-DONES d-Li accelerator. This work is complemented by extensive benchmark, sensitivity and uncertainty analyses to check the performance of the evaluated cross-section data and libraries against integral experiments. Nuclear data evaluations of specific importance to fusion applications, such as those for Cr, Cu, W, and Zr stable isotopes, were contributed to the JEFF-3.3 general purpose neutron cross data library and benchmarked against fusion relevant integral experiments. Specific nuclear data libraries were provided as sub-libraries to JEFF-3.3 including a dedicated neutron activation data file (see Sect. 2.9) and a displacement damage data library (see Sect. 2.6).

2 Components

In this section the components of JEFF-3.3 are presented. We start with the neutron transport sublibrary consisting of data for actinides (Sect. 2.1), structural materials, coolants and fission products (Sects. 2.2 and 2.3) and thermal neutron scattering (Sect. 2.10). The neutron transport sublibrary includes modifications for improved delayed neutron and gamma-ray emission data. We then present covariances related with the neutron transport sublibrary, fission yields, decay data, neutron activation, and displacement damage data.

2.1 Actinide evaluations

2.1.1 \(^{235}\hbox {U}\) in the resonance range

In the late 1980s and early 1990s a \(^{235}\hbox {U}\) Reich–Moore resonance evaluation was performed from thermal energy to 2.25 keV  [18] using the SAMMY [19] code. This was the first attempt to use a more rigorous resonance formalism to account for interference effects in the fission channels. The evaluation represented a substantial improvement compared to previous \(^{235}\hbox {U}\) evaluations based on the Single-Level Breit-Wigner (SLBW) formalism combined with background cross-sections. Very little integral benchmark testing was carried out to assess the quality prior to its adoption in an evaluated library. Subsequent benchmark testing demonstrated shortcomings of this evaluation. In particular, these tests suggested that the capture cross-section in the energy region from 22.6 to 454 eV was underestimated [20]. No issues with the fission cross-section were found. It should be pointed out that at the time of the evaluation of Ref. [18] no reliable capture cross section data in the energy range above 100 eV were available. In addition, reported capture cross-section data for neutron energies above 100 eV suffered from bias effects due to normalisation and background corrections. Therefore, in the evaluation process no capture data were included.

The \(^{235}\hbox {U}\) evaluation of Ref. [18] was revised using results of integral benchmark and extensive sensitivity analysis studies [21]. The results were included in the ENDF, JEFF and JENDL libraries. The JENDL project adopted the evaluation up to 500 eV and used an unresolved resonance representation above 500 eV to improve consistency with results of a fast critical assembly benchmark (FCA) [22]. The revised evaluation produced a higher capture cross-section that is not supported by results of both the FCA and the ZEUS benchmark (hmi6 [23]).

The WPEC subgroup 29 [24] investigated this issue and recommended new measurements of the capture cross-section to be considered in future evaluations.

Therefore, capture cross-section measurements with the time-of-flight technique were performed independently at the Rensselaer Polytechnic Institute (RPI) [25] and at the Los Alamos National Laboratory (LANL) [26]. The results of these measurements were included in a resonance analysis to update the \(^{235}\hbox {U}\) resonance parameters in the energy range from thermal energy to 2.25 keV. Using the new resonance parameters the results of integral benchmarks could be better reproduced. Unfortunately, fission cross section data derived from these parameters showed marked differences with those recommended by the standards evaluation [27]. Recently, fission cross-section data resulting from measurements at the n_TOF facility provided strong support to the recommendations in the standards evaluation. Indeed, normalising the n_TOF fission data to the energy integral from 7.8 to 11.0 eV of Ref. [27] (Table 4) results in good agreement between the n_TOF data and the cross-sections from the standards evaluation in the low energy region, supporting the averaged fission cross-sections of Ref. [27] in the resonance region. Therefore, the 235U resonance parameter evaluation for JEFF-3.3 was revised based on results of a new analysis that included the n_TOF experimental fission data.

Table 1 Experimental data included in the SAMMY resonance analysis of \(^{235}\hbox {U}\) for JEFF-3.3; The references (Refs.) column mentions the lead author to identify the data set of the figures of this section. ER is the energy range (eV). L is the nominal flight-path length (m) of the time-of-flight measurement. n is the atom density times the sample thickness (atoms per barn), T is sample temperature (K)

\(^{235}\)U resolved resonance range Resonance parameters for neutron energies between \(10^{-5} \, \hbox {eV}\) and 2.25 keV were derived from a resonance analysis using the experimental data given in Table 1. These data include the high-resolution transmission, fission cross-section, and eta measurements that were included in previous evaluations and the data of LANL, n_TOF and RPI, which were not available before. The results of the capture cross section measurements carried out at LANL and RPI were important to unveil issues with the capture cross section above 100 eV. The fission cross-section measurements carried out at n_TOF supported the standard cross section values, which were used as a reference in the analysis.

The Reich–Moore approach implemented in SAMMY was used for fitting the data. Before fitting the data shown in Table 1, the experimental conditions were examined carefully. Experimental resolution, normalisation, background, multiple-scattering and data alignment were inspected to assure consistency between experimental input parameters and the experimental conditions. The experimental data were fitted with typical values for Chi-square between 0.94 and 1.8. An example of the associated residuals is given in Fig. 1 for the transmission data of Harvey et al. in a limited energy range.

Table 2 External levels for the \(^{235}\hbox {U}\) resonance analysis for JEFF-3.3
Fig. 1
figure 1

Top: comparison of the experimental and calculated \(\eta \)(E) for \(^{235}\hbox {U}\) in the thermal energy range. Middle: comparison of the SAMMY fit of the experimental data for \(^{235}\hbox {U}\). The bottom figure gives a flavor of typical residuals and highlights an unaccounted Ta impurity in the Harvey data. Chi-square varies between 0.94 and 1.8 over the range of the fits (see also the next figure)

Previous evaluations of the \(^{235}\hbox {U}\) resonance parameters made use of several external resonance energies: 14 bound levels and 14 levels above 2.25 keV. This proved not necessary to represent the interference effects in the resonance range from \(10^{-5}\, \hbox {eV}\) to 2.25 keV. Actually, it was found that the issue of fitting the standard fission cross-section was directly related to the contribution of the external energy levels. The long-range interference effects inherent in the R-matrix methodology precluded finding a good fit of the experimental fission data. It also had an impact on the elastic scattering cross section. The present evaluation contains five bound energy levels and five energy levels above 2.25 keV. The 10 external energy levels are listed in Table 2. For each resonance the resonance energy \(E_{\text {r}}\), gamma width \({\varGamma }_{\gamma }\), neutron width \({\varGamma }_{\text {n}}\), two fission widths \({\varGamma }_{\text {f1}}\) and \({\varGamma }_{\text {f2}}\) and the spin and parity \({\hbox {J}}^\pi \) are reported. A negative sign for a partial width reflects the sign of the reduced width. The bound level with an energy close to zero (\(-3.657 \times 10^{-5}\, \hbox {eV}\)) and a very small neutron width is responsible for the curved energy dependence of the \(\eta \)(E) at low energy [39]. Two experimental \(\eta \)(E) measurements (Table 1) were included in the fit (Fig. 1).

An accurate representation of the external resonance contribution provides the basis for the effective scattering radius. The analysis of high-resolution transmission data led to an effective scattering radius of 9.602 fm.

Having fixed the external levels, a sequential analysis of the data was carried out to achieve a reasonable fit of the data with an acceptable \(\chi ^2\). In the energy range a total of 3170 resonance levels were identified. Not only were the resonance parameters allowed to vary in the fit but also normalisation, resolution parameters, and others. The normalization correction ranges from \(-\) 1.8% to + 3.1%. These corrections are essential for the consistency of the fit and are achieved by a sequential fitting of the experimental data. The normalization of the fission data of Weston were 1.8% lower than that of Paradela fission data. Likewise, Gwin fission data normalization were about 1.4% lower compared to Paradela’s data. This feature has precluded in the past to obtain the 7.8–11.0 eV standard fission integral value. The capture data of Danon and Jandel were in agreement with a normalization correction of about 1.1%. Perez capture data below 200 eV were also consistent with the Danon and Jandel experimental data. However, the De Saussure capture data have a normalization correction of about 3.1%.

The results of a fit to the Harvey [29] (transmission), Spencer [28] (transmission), and the Paradela [33] (fission cross-section) data are shown in Fig. 1. An examination of the transmission data of Harvey revealed an inconsistency around the energy 4.25 eV. It was found that this is due to an impurity of \(^{181}\hbox {Ta}\) present in the transmission sample. Although the data reduction was suitably done it appears that the effect of the \(^{181}\hbox {Ta}\) impurity was not completely removed.

Fig. 2
figure 2

Top: SAMMY fitting of the \(^{235}\hbox {U}\) fission cross section in the 100–400 eV energy range for JEFF-3.3. Bottom: SAMMY fitting of the \(^{235}\hbox {U}\) capture cross section in the 100–200 eV energy range for JEFF-3.3

In the analysis an adjustable normalisation factor was included for each fission cross section data set. This normalisation factor was adjusted using the fission integral in the energy range between 7.8 and 11 eV recommended in Ref. [27]. Due to this procedure the Weston [31, 32] and Gwin [30] fission data were adjusted by about 2%. The results of a fit to the Weston [32] and Paradela [33] data is shown in Fig. 2 in the energy range 100–400 eV. The resolution of the n_TOF data is excellent, displaying the details of the Porter–Thomas like fluctuations not seen in the Weston data in this energy range. The results in Table 3 confirm that the averaged fission cross sections derived from the final resonance parameters are in very good agreement with those of the standards evaluation [27].

Table 3 JEFF-3.3 energy-averaged fission cross sections for \(^{235}\hbox {U}\) from the SAMMY resonance analysis compared with the standards [27, 40]. For the interval 7.8–11 eV the energy integrated cross section is given

The capture data of Perez et al. [37] were used below 200 eV together with the data of Danon et al. [25] obtained at RPI, which were used up to 2250 eV. The data of Jandel et al. obtained at LANL were used in the region above 100 eV. The three data sets in the energy range 100–200 eV are displayed in Fig. 2 together with the results of a fit. As can be seen, the resolution of the RPI data is excellent for resonance analysis. Since the flight path lengths for the three measurements are about the same, the main difference in resolution is due to the neutron burst width. In the energy range from 100 to 200 eV the results are based on the capture data obtained by Danon (RPI), Jandel (LANL) and Perez (ORNL).

Table 4 JEFF-3.3 fission \(\sigma _{\text {f}}\), capture \(\sigma _\gamma \) and scattering \(\sigma _{\text {s}}\) cross sections of \(^{235}\hbox {U}\) for the 0.0253 eV neutron energy compared with the standards [27, 40]. The JEFF-3.3 cross sections are obtained with the SAMMY resonance analysis

As previously indicated, the main motivation for revising the \(^{235}\hbox {U}\) resonance parameter was to address discrepancies with the \(^{235}\hbox {U(n,f)}\) cross section in the standards file [27]. The revision of the external resonance values, bound energy levels and energies above 2250 eV, allowed a quick convergence to the standard values at thermal energy and the average values for the fission cross section recommended in the 2009 standards evaluation [27]. The values at thermal energy calculated from the new resonance parameters are listed in Table 4 and compared with those of the 2009 [27] and 2018 standards evaluation [40]. The JEFF-3.3 evaluation is seen to be within one standard deviation of both evaluations for all but two energy groups (400–500 and 900–1000 eV).

To summarize, for neutron energies below 2.25 keV, a re-evaluation of the \(^{235}\hbox {U}\) resonance parameters was carried out to address discrepancies with cross section standards at thermal energy and average fission cross-section values and to include new capture cross section data above 100 eV. A new fission cross section measurement done at the n_TOF facility of CERN was the primary factor in obtaining good agreement between the results of the new evaluation and the standards evaluation. The new set of resonance parameters includes fewer external levels and provides a better way of calculating the interference effects of the fission channels. The values at thermal energy agree within uncertainties with those recommended in the 2009 standards evaluation. A normalization to the fission integral in the energy range from 7.8 to 11 eV resulted in good agreement with all average fission cross sections of the 2009 standards evaluation below 2 keV. Hence, the new set of resonance parameters presented in this paper are improved compared to those presented in previous JEFF versions.

\(^{235}\)U unresolved resonance range In JEFF-3.3 cross section data for neutron interactions with \(^{235}\hbox {U}\) in an URR representation is provided for energies between 2.25 and 46.2 keV. Average resonance parameters were derived with the model implemented in NJOY [41] to ensure full consistency between the evaluation and the files produced with NJOY for application codes (see Sect. 3.6). The Integral Data Assimilation (IDA) procedure of the CONRAD code [42] was used. This procedure allows to include in the analysis both microscopic and integral data. The option within TALYS [43] to run unresolved resonance calculation was used to calculate average parameters. This option, which is consistent with the model implemented in NJOY, allows an adjustment of s-wave parameters to a set of experimental data. For the fission cross section, the values recommended in the 2018 neutron standards file [40], were used. Capture cross section data in the EXFOR data base are characterised by a large spread. Therefore, it was preferred to use results of the PROFIL integral experiments carried out in the fast reactor PHENIX [44] to optimise the average parameters that are sensitive to the capture reaction. A set of (\(\ell \),J) dependent average parametersFootnote 3 (mean level spacings, reduced neutron widths and partial widths for the capture and fission reactions) was derived in order to calculate self-shielding factors between 2.25 and 46.2 keV. Results were tested on the integral benchmarks ZEUS and MASURCA-1B.

Fig. 3
figure 3

\(^{235}\hbox {U}\) fission and capture cross sections calculated for JEFF-3.3 with TALYS (\(E<100~\hbox {keV}\)), compared with fission cross sections reported in Refs [40] (IAEA 2006) and [33] (nTOF 2015) and with capture data retrieved from the EXFOR data base: [45] (Andreev), [46, 47] (Corvi) [48] (Hopkins), [49] (Kononov) [50] (Muradyan), [51] (Spivak)

The PROFIL and PROFIL-2 sample irradiation experiments were carried out in the PHENIX reactor of the CEA/DEN Marcoule. These experiments use rods with a large number of samples (130 samples) containing almost pure separated actinides and fission products. The experiments were designed to collect integral information to improve neutron-induced cross sections of interest for fast reactor applications. The PROFIL results were analysed using the ERANOS-2.2 code with the JEFF-3.1.1 nuclear data library. The analyses show that the capture-to-fission ratio \(\alpha \) for \(^{235}\hbox {U}\) can be derived from the (\(^{235}\hbox {U}/{}^{238}\hbox {U}\)) and (\(^{236}\hbox {U}/{}^{235}\hbox {U}\)) isotopic ratios. They characterize the fission and capture cross sections for \(^{235}\hbox {U}\), respectively. In this work, the IDA procedure was used to extract the \(\alpha (^{235}\hbox {U})\) ratio in the neutron energy range 500–150 keV.

Prior values and uncertainties for the s-wave average radiation width \(\langle {\varGamma }_{\gamma _{0}}\rangle \), mean level spacing \(D_0\) and neutron strength function \(S_0\) were determined from the statistical analysis of the resolved resonance parameters yielding:

$$\begin{aligned} \langle {\varGamma }_{\gamma _{0}}\rangle&= 38 (4) {\text { MeV}},\\ D_0&= 0.49 (2) ~{\text {eV}}, \\ S_0&= 0.98 (7) \times 10^{-4}. \end{aligned}$$

\(D_0\) and \(S_0\) were determined simultaneously by using the ESTIMA method [52]. ESTIMA provides the most probable neutron strength function and mean level spacing for s-wave levels. We decided to fix the the mean level spacing and to consider the neutron strength function as a free parameter. The posterior value provided by the CONRAD code is close to \(S_0= 1.02 \times 10^{-4}\). Final fission and capture cross sections are shown in Fig. 3. The theoretical curves are in good agreement with the microscopic experimental data. The calculated-to-experimental ratios for the (\(^{235}\hbox {U}/{}^{238}\hbox {U}\)) and (\(^{236}\hbox {U}/{}^{235}\hbox {U}\)) isotopic ratios for the PROFIL results [44] deviate by less than 3% from unity.

Fig. 4
figure 4

Integral trends for the calculated minus experimental (C-E) effective neutron multiplication factor JEFF-3.3 \(^{235}\hbox {U}\) obtained with the ZEUS (hmi6) and MASURCA-1B (MAS1B) benchmarks. The brown (grey) band corresponds to 1 (2) experimental standard uncertainty

To understand if for applications the resolved resonance range is best terminated at 0.5, 1 or 2 keV and whether the alpha-ratio extracted with the assistance of the PROFIL data is appropriate, calculations were made with the TRIPOLI-4® [53] Monte Carlo code to simulate the MASURCA-1B and ZEUS hmi6 experiments (See also Sect. 3.1). The ZEUS critical benchmarks consist of four configurations, which are characterised by increasing Energy of the Average Lethargy causing Fission (EALF: 4.44 keV, 9.45 keV, 22.80 keV, and 80.80 keV). For the results in Fig. 4 only JEFF-3.1.1 data were used besides the different options of \(^{235}\hbox {U}\) considered for JEFF-3.3. All three options improve the agreement with experiment, with discrepancies ranging between \(-\) 300 and + 300 pcm. The observed trend for increase with EALF of JEFF-3.1.1 between the three first ZEUS benchmarks vanishes. Contrary to the underprediction for the first three ZEUS cases, the fourth ZEUS configuration and MASURCA-1B show an overprediction. Although there is no clear optimum for the upper limit of the resolved resonance range a choice of 2.25 keV is very reasonable, as is the choice for \(\alpha ({}^{235}\hbox {U}).\)

2.1.2 \(^{238}\hbox {U}\) in the resonance range

\(^{238}\)U resolved resonance range The neutron transport sublibrary in the resolved resonance region for \(^{238}\hbox {U}\), which covers neutron energies from 0 to 20 keV, was constructed by replacing the JEFF-3.2 parameters for resonances below 1200 keV with the parameters reported by Kim et al. [54]. The parameters in JEFF-3.2 were primarily based on the work of Derrien et al. [55]. The parameters reported by Kim et al. [54] were obtained from a least squares fit to the experimental capture yields derived by Kim et al. [54] and the transmission data of Olsen et al. [56, 57]. The fission widths were adjusted to reproduce the fission areas of Difilippo et al. [58]. The resonance shape analysis code REFIT [59], which is based on the Reich–Moore [60] approximation of the R-matrix formalism [61], was used. The latest version of the code accounts for various experimental effects such as Doppler broadening, neutron self-shielding, multiple interaction events, the response function of the TOF-spectrometer, properties of the detection system, \(\gamma \)-ray attenuation in the sample and inhomogeneities of the sample [62].

The capture experiments of Kim et al. [54] were carried out at a 12.5 and 60 m measurement station of the time-of-flight facility GELINA [63]. The total energy detection principle in combination with the pulse height weighting technique was applied using \({\hbox {C}}_6 {\hbox {D}}_6\) liquid scintillators as prompt \(\gamma \)-ray detectors. The data were normalised to the isolated and saturated \(^{238}\hbox {U}\) resonance at 6.67 eV. The procedures recommended in Ref. [62] were applied to reduce bias effects due to the weighting function, normalisation, dead time and background corrections, and corrections related to the sample properties. Therefore, the options in REFIT [62] to correct for neutron and \(\gamma \)-ray transport in the sample in case of capture data were used. The total uncertainty due to the weighting function, normalisation, neutron fluence and sample characteristics was \(\sim \) 1.5%. The transmission data of Olsen et al. [56, 57] resulted from time-of-flight experiments at a 42 m and 150 m station of ORELA using 7 samples of different areal density (from 0.0002 at/b to 0.175 at/b). Both the transmission and capture data were analysed without applying any additional background or normalisation correction.

Fig. 5
figure 5

Comparison of experimental and theoretical observables. The experimental yield \({Y}_{exp}\) obtained at 60 m with a \(9.55 \times 10^{-4}\) at/b sample is compared with the theoretical yield \({Y}_M\). The experimental transmission \(T_{exp}\) from measurements with a \(3.76 \times 10^{-3}\) and \(1.24 \times 10^{-3}\) at/b sample at ORELA is compared with the theoretical transmission \(T_M\). The calculated observables were obtained from calculations with REFIT after adjusting the parameters to the experimental data as described in the text. The residuals are calculated considering only the uncorrelated uncertainties due to counting statistics

The free gas model with an effective temperature of 295 K was used to account for the Doppler effect. The initial resonance parameters, including parity and spin, and effective scattering radius R\(^\prime \) = 9.48 fm were taken from Derrien et al. [55]. Examples of the result of a simultaneous fit to the capture and transmission data are shown in Fig. 5. To fit the transmission data of Olsen et al. [56, 57], without applying a normalisation factor, the contribution of the two bound states at \(-\) 7 eV and \(-\) 33 eV were adjusted maintaining the capture cross section at thermal energy \(\sigma _{\gamma }~=~2.683~(12)~\hbox {b}\) recommended by Trkov et al. [64]. After this adjustment the elastic scattering cross section at thermal energy was reduced by about 0.5 % compared to the one in JEFF-3.2. The corresponding coherent scattering length \(b_{c}~=~8.57~(2)~\hbox {fm}\) is in agreement with the one \(b_c~=~8.63~(4)~\hbox {fm}\) recommended by Koester et al. [65]. The cross sections at thermal energy and resonance integrals derived from the recommended resonance parameters are listed in Table 5.

Table 5 \(^{238}\hbox {U}\) total, elastic and capture cross sections \(\sigma \) at thermal energy and resonance integrals (RI) between 0.5 eV and 100 keV calculated from the resonance parameter file of JEFF-3.3
Table 6 \(^{239}\hbox {Pu}\) resonances external to the resolved resonance range of 0–4 keV used for JEFF-3.3

\(^{238}\)U unresolved resonance range The unresolved resonance range extends from 20 to 150 keV. The so-called infinitely dilute cross sections for the unresolved resonance range was obtained from the statistical model approach presented in Sect. 2.1.4. However, for the sole purpose of calculating self-shielding factors the file retains the evaluation present in the JEFF-3.2 library, which dates from JEFF-2.2. The appropriate flags have been set in the evaluated file to ensure its proper use.

As may be noted from Fig. 9, the JEFF-3.3 evaluation for the neutron capture cross section of \(^{238}\hbox {U}\) is less than those of JENDL-4.0 and ENDF/B-VIII.0 in the energy range around 40 keV and from 150 to 500 keV. In this respect, the JEFF-3.3 evaluation does not follow the result from the evaluation of the standards [27, 40].

2.1.3 \(^{239}\hbox {Pu}\) in the resonance range

\(^{239}\)Pu resolved resonance range Resonance parameters for \(\hbox {n}+{}^{239}\mathrm{Pu}\) in the RRR, which covers the energy region from 0 to 4 keV, were obtained from a resonance shape analysis with SAMMY using the Reich–Moore approximation [19]. Long-range interference in the R-matrix formalism plays a major role in modeling fissile isotopes. For the present evaluation the first step consisted of finding pseudo resonances, resonances outside of the resolved resonance range of 0–4 keV, that mock-up the contribution and interference due to all resonances not treated explicitly. Five negative levels and three resonances above 4 keV were found that describe well the interference effect. The parameters of these bound states, i.e. resonance energy \(E_{\text {r}}\), gamma width \({\varGamma }_{\gamma }\), neutron width \({\varGamma }_{\text {n}}\), two fission widths \({\varGamma }_{\text {f1}}\) and \({\varGamma }_{\text {f2}}\) and the spin and parity \(J^{\pi }\), are listed in Table 6. Negative signs associated with the fission partial widths \({\varGamma }_{\text {f1}}\) and \({\varGamma }_{\text {f2}}\) reflect the sign of the reduced amplitude width \(\gamma _{\text {f1}}\) and \(\gamma _{\text {f2}}\). The ground state spin of the \(^{239}\hbox {Pu}\) is \(1/2^+\) which leads, for an s-wave (\(\ell = 0\)) to two J-values \(0^+\) and \(1^+\). Higher angular momenta (\(\ell > 0\)) show negligible contribution to the cross section below 4 keV due to the higher penetrability.

The experimental database used in the new evaluation is essentially the same as the one used in Ref. [66]. The high-resolution transmission data of Harvey et al. [29] allowed extending the resonance range from 2.5 to 4 keV. The results of the SAMMY fitting of the transmission data of Harvey et al. [29] and the fission and capture data of Gwin et al. [30] are shown in Fig. 6. The analysis of the high-resolution transmission data led to an effective scattering radius of 9.41 fm. The number of resonances used in the fit of the experimental data from 0 to 4 keV is 1572.

Fig. 6
figure 6

Comparison of the SAMMY fit for the resolved resonance range of \(^{239}\hbox {Pu}\) JEFF-3.3 to the experimental data

Table 7 \(^{239}\hbox {Pu}\) thermal cross section values (0.0253 eV) calculated with SAMMY and compared to the Atlas of Neutron Resonances (ANR) and the standards evaluations [27, 40]
Fig. 7
figure 7

Unresolved resonance range cross sections for \(^{239}\hbox {Pu}\) total (a), fission (b) and capture (c), with comparisons between JEFF-3.3, JEFF-3.1.1, ENDF/B-VIII.0, JENDL-4.0u and the IAEA 2018 Standards Reference Cross Section

The fission, capture and scattering cross sections at thermal energy are displayed in Table 7, together with the values of previous JEFF evaluations, the ones listed in the Atlas of Neutron Resonances [67] and those recommended in the 2009 and 2018 standards [27, 40]. The JEFF-3.3 values are within one standard uncertainty in agreement with the 2009 standards evaluation and the Atlas. The fission cross section of JEFF-3.3 differs by 1.5 standard uncertainty from the one in the 2018 standards evaluation.

\(^{239}\)Pu unresolved resonance range The URR for \(\hbox {n} + ^{239}\hbox {Pu}\) in JEFF-3.3 covers incident neutron energies from 4 to 30 keV. The \(\hbox {n} + {}^{239}\hbox {Pu}\) average cross sections in the URR were adapted to match the new analysis in the resolved resonance range and in the fast range (Sect. 2.1.4). To generate fluctuations necessary for self-shielding calculations the average resonance parameters for \(\hbox {n} + {}^{239}\hbox {Pu}\) in JEFF-3.3 are those of JEFF-3.1.1 [3].

The average total cross sections and those for neutron induced fission and capture in JEFF-3.3 and JEFF-3.1.1 are compared in Fig. 7. Also shown are the ENDF/B-VIII.0 and JENDL-4.0u evaluations and for the fission cross section the result from the IAEA standards evaluation. JEFF-3.3 differs from the standards evaluation by a small amount (few %) that is well within the fluctuations in this region, as partly evidenced by the ENDF/B-VIII.0 result. JENDL-4u shows similar differences.

The average fission cross section in JEFF-3.3 and the one recommended in IAEA 2009 and 2018 standard [27, 40] are listed in Table 8 for the range below 4 keV (resolved range). The differences vary between less than 1 and up to 8 standard uncertainties. Deviations greater than two standard deviations occur for the energy groups of 300–400, 600–700, 700–800, 800–900 and 1000–4000 eV.

Table 8 \(^{239}\hbox {Pu}\) average fission cross section from the SAMMY resonance fit for JEFF-3.3. The energy-range for the fit is given in column \({\hbox {E}}_{\text {n}}\). The standard evaluations are from Refs. [27, 40]

2.1.4 Major actinides beyond a few keV

For incident neutron energies above the URR, that is, beyond a few tens or hundreds of keV, the evaluation for the neutron transport library of the major actinides is performed within the statistical model framework for the continuum region. Results of this evaluation are also used as input for the evaluation process in the URR.

For modeling nuclear reaction cross sections and light particle emission in the continuum region, the “Full Model” approach is used, as described in detail in [68, 69]. This approach [69] relies on the use of the TALYS code [43] in which the main nuclear reaction models, the optical model for direct interaction mechanisms, the statistical model for compound nucleus decay and pre-equilibrium models are implemented in combination with nuclear structure models and databases. An important source of parameters for TALYS is the IAEA Reference Input Parameter Library (RIPL) [70]. For prompt fission neutron multiplicities and spectra, a modified version of the Madland–Nix model [71] is employed (Sect. 2.1.5).

The optical model is of major importance for the evaluation in the continuum region. It provides the total, elastic and reaction cross sections, as well as transmission coefficients. Together with nuclear level densities, transmission coefficients are the main ingredients of the statistical Hauser–Feshbach model. They distribute the compound nucleus formation cross section into the different open channels at a given neutron incident energy. In the current approach an actinides-specific optical model has been adjusted both for proton and neutron induced reactions using all available experimental data. Since actinides are deformed targets, the coupled channel approach was used, selecting a large enough number of coupled levels to saturate coupling. This saturation is defined by the convergence of the reaction cross section. In practice, levels of the ground state band and of vibrational quadrupole and octupole rotational bands have been coupled. A total of 7, 19 and 9 levels have been coupled for \(^{235}\hbox {U}\), \(^{238}\hbox {U}\) and \(^{239}\hbox {Pu}\) respectively. As can be observed in Fig. 8, total cross sections have slightly changed from JEFF-3.1.2 to JEFF-3.3, in particular for \(^{235}\hbox {U}\) and \(^{239}\hbox {Pu}\). The difference between JEFF-3.2 and JEFF-3.3 for \(^{238}\hbox {U}\) is almost negligible.

We note that for the present evaluation the effect of the Engelbrecht–Weidenmüller transformation on the width fluctuation factor in the case of coupled channels calculations was not taken into account. This well-known effect was clarified recently by Kawano et al. [73], but is not widely used, yet. For instance, it leads to an increase of the inelastic scattering cross section by several percent. This may lead to some of the differences between evaluations (see total and inelastic cross sections in Figs. 8 and 9), although these use different optical potentials that already imply differences.

Once optical models are fixed, fission barrier heights and widths, nuclear level densities and gamma ray strength functions were adjusted by simultaneously fitting all available experimental data. The most important data are the total inelastic cross section, the capture cross section and the fission cross section. Evaluated total cross sections and cross sections for some reaction channels that play a key role in neutron transport simulations, i.e. (n,f), (n,\(\gamma \)), (n,n’), are compared with experimental data in Figs. 8 and  9.

Fig. 8
figure 8

Comparison between experimental data and the last 3 versions of the JEFF library for \(^{235}\hbox {U}\) (top), \(^{238}\hbox {U}\) (middle) and \(^{239}\hbox {Pu}\) (bottom) total (left) and fission (right) cross sections as function of the incident neutron energy

Fig. 9
figure 9

Comparison between experimental data and the last three versions of the JEFF library (left) and with other evaluations (right) for the \(^{235}\hbox {U}\) capture cross section (top), \(^{238}\hbox {U}\) capture (middle) and \(^{238}\hbox {U}\) inelastic (bottom) cross sections as function of the incident neutron energy

An important feature of the “Full model” approach is the coherent analysis of all available data for a given nuclide. This means, for instance, that the set of parameters used to describe photo-fission of \(^{238}\hbox {U}\) is also used for the second chance fission of neutron induced fission of \(^{238}\hbox {U}\) since, in both cases, the same compound nucleus is involved. The price to pay is a more tedious parameter adjustment. The added value of this larger number of constraints is a much better consistency, ensuring a better confidence in model calculations.

The calculated fission cross sections were substituted by those taken from the 2009 IAEA neutron standards project [27]. This choice can be observed in Fig. 8, which illustrates that below a few tens of keV, the evaluation shows sharp oscillations which can hardly be described by a pure model calculation. A comparison between different evaluation libraries reveals that the JEFF-3.3 evaluation is globally closer to the ENDF/B-VIII.0 than the JENDL-4.0 evaluation.

Often microscopic experimental data do not provide enough constraints to obtain satisfactory evaluations from the user point of view. This can be compensated by including results of integral experiments in the evaluation process, as long as the original differential constraints are also respected, as illustrated by the data in Figs. 10 and 11. Figure 10 shows the fission cross section \(\sigma _f\) and average total number of prompt fission neutrons \({\bar{\nu }}_p\) as a function of incident neutron energy. Experimental data are compared with the values recommended in JEFF-3.3 together with a reduction of 0.15% in the recommended \(\sigma _f\) and an increase of 1% in the recommended \({\bar{\nu }}_p\). Figure 10 shows that such changes produce recommended data that are within uncertainties in agreement with experimental microscopic data. Combining the variations in \(\sigma _f\) and \({\bar{\nu }}_p\) simultaneously provides results (blue dots in Fig. 11) that are again very close to those obtained with the JEFF-3.3 evaluation (red dots in Fig. 11). This confirms the study performed in Ref. [74], where strong correlations between the fission cross sections, prompt neutron multiplicities and prompt fission neutron spectra are created when results of integral benchmarks are used in the adjustment process.

In the current evaluation, it is important to mention that the use of standard fission cross sections has removed the possibility of adjusting the fission cross section. Therefore, the average prompt fission neutron multiplicity was adjusted to account for integral benchmark data. The adjustement involved an iterative procedure to achieve an overall good agreement with various benchmarks sensitive both to low and high energy multiplicities. Depending on the results obtained with respect to the selected benchmarks, a small re-normalisation was applied to the prompt neutron multiplicities with typical changes of the order of a few tenths of a percent. The delayed neutron multiplicity was of course not modified. This small adjustment is clearly not the same for each incident neutron energy since each benchmark has its own neutron spectrum sensitivity, but the final multiplicity remains compatible with the experimental uncertainties as shown in Fig. 10.

Fig. 10
figure 10

\(^{239}\hbox {Pu}\) fission cross section (top) and prompt neutron multiplicit \({\bar{\nu }}\) (bottom) as function of the incident neutron energy. The red curves correspond to the JEFF-3.3 evaluation and the blue curves to a reduction of 0.15% for the fission cross section (top) and an increase of 1% of \({\bar{\nu }}\) (bottom) of the JEFF-3.3 evaluation

Fig. 11
figure 11

Neutron multiplication factors (vertical) of ICSBEP Pu fast metallic critical assemblies [23]. Comparisons between experiments and simulations performed using MCNP5 [72] with several choices for the \(^{239}\hbox {Pu}\) evaluations. The red dots correspond to the results obtained with the JEFF-3.3 library. The green dots are obtained increasing by 1% the \(\bar{\nu }\) of \(^{239}\hbox {Pu}\) in the JEFF-3.3 library. The pink dots are obtained decreasing by 0.15% the \(^{239}\hbox {Pu}\) fission cross section in the JEFF-3.3 library. The blue dots are obtained by simultaneously increasing \({\bar{\nu }}\) by 1% and decreasing by 0.15% the fission cross section in the \(^{239}\hbox {Pu}\) evaluation of the JEFF-3.3 library

2.1.5 Prompt fission neutrons

Actinide evaluations require mean prompt fission neutron multiplicities \(\bar{\nu _p}\) and prompt fission neutron spectra \(\chi _\nu \) (PFNS). While the most satisfactory approach would consist in computing these spectra from each fission fragment decay, we adopted a more pragmatic and simple approach, the so-called “Los Alamos” or “Madland–Nix” model, which is extensively described in [71, 78]. With this model, the PFNS are calculated from the decay of two average fragments, a light and heavy one and \(\bar{\nu }\) is then deduced from an energy average involving the mean neutron energy of the modelled PFNS. The model parameters are those extracted from the systematics of Tudora [79] with a slight modification for some of them, in order to have a better agreement with experimental data. With increasing incident neutron energy, multiple fission channels open up and partial fission cross sections corresponding to each fission channel must also be accounted for to produce the final PFNS and \({\bar{\nu }}\). The latter are taken from the modeling of the continuum cross sections mentioned above. Moreover, whereas in the original work of Madland and Nix, the evaporation spectrum due to neutron emission prior to fission was obtained from a Weisskopf spectrum, in the current approach, this contribution was extracted from the aforementioned continuum cross section modeling, as done by Maslov [80].

As one of the difficulties is to account for the strong fission neutron energy dependence of the PFNS, an approach relying only on experimental data is not possible and was therefor not adopted JEFF-3.3. This is illustrated by the ratio of the experimental data to a reference Maxwellian. In Fig. 12, the ratio of the PFNS to a Maxwellian is shown for four different incident neutron energies inducing fission on \(^{235}\hbox {U}\). By default, in the Los Alamos model, the light and heavy fragment spectra (pink and blue curve) are averaged to produce the total PFNS. As can be observed, the shape of the calculated curve is rather different from the experimental one. The calculated spectrum is too hard and disagrees with the experiments below 500 keV and above 1.5 MeV. A simple way to get softer prompt fission neutron spectra is to assign a different weight to the light and heavy fragments spectra. This has been done for \(^{239}\hbox {Pu(n,f)}\) and \(^{235}\hbox {U(n,f)}\) in order to improve the agreement with experimental data. These predictions are shown in Fig. 12. More precisely, for the first chance fission of \(\hbox {n} + {}^{235}\hbox {U}\) and \(\hbox {n} + {}^{239}\hbox {Pu}\) we weighted the light spectrum with a 0.7 factor and the heavy spectrum with a factor of 1.3. For second and higher chance fission, the weights are set to 0.75 and 1.25, respectively. Even if clear differences remain, the agreement with the data is much better than expected when one sees the two component spectra of the light and heavy fragments.

Using the aforementioned weighting factors, the mean prompt fission neutron energy can be computed as a function of the energy of the neutron inducing fission. The resulting predictions are compared in Fig. 13 with experimental data and with other libraries. It can be noticed that, for \(^{235}\hbox {U}\) and \(^{239}\hbox {Pu}\) neutron induced fission, the mean prompt fission neutron energies are reduced compared to JEFF-3.2 and JEFF-3.3. For \(^{239}\hbox {Pu(n,f)}\), differences between libraries are larger than the differences for \(^{235}\hbox {U(n,f)}\) and \(^{238}\hbox {U(n,f)}\). However, these differences are small compared to the scatter and uncertainty of the experimental data (Fig. 14) so that all recommended values for \(\bar{\nu _p}\) are consistent with the experimental microscopic data.

At the time the JEFF-3.3 prompt fission neutron spectra and nu-bar evaluations were completed, the results of a new campaign at the Los Alamos Chi–Nu setup carried out for \(^{239}\hbox {Pu}\) were not yet available. The preliminary results obtained by a collaboration led by CEA show that the \(\hbox {n} + {}^{239}\hbox {Pu}\) are in similarly good agreement with the JEFF-3.3 evaluation. Tests were also made for the fast criticals of the Mosteller suite replacing the JEFF-3.3 PFNS with that of this experimental campaign above 1 MeV incident neutron energy. The resulting effective multiplication factor was in similar agreement with the benchmarks as the JEFF-3.3 evaluation. As these results are preliminary, details will be published elsewhere. A second campaign at Chi–Nu by the same collaboration is planned for \(\hbox {n} + {}^{235}\hbox {U}\).

2.1.6 \(^{241}\hbox {Am}\) in the resonance range

For \(\hbox {n} + {}^{241}\hbox {Am}\) the JEFF-3.2 library with some minor changes was adopted in JEFF-3.3. The RRR covers an energy region between 0 to 150 eV and the URR a region from 150 eV to 40 keV. For energies above 40 keV the evaluation produced for JEFF-3.2 was maintained applying the principles described in Sect. 2.1.4. This resulted in an excellent description of the \(^{241}\hbox {Am}\)(n,2n) cross section [81].

The re-evaluation of the resolved and unresolved resonance ranges was triggered by an overestimation of the \(k_{\text {eff}}\) values for MOX fuels identified with Monte-Carlo (TRIPOLI-4® [53]) and deterministic (APOLLO2 [82]) calculations based on JEFF-3.1.1. The overestimation becomes sizeable with plutonium ageing, reaching a reactivity change of \({\varDelta }\rho \simeq +700~\hbox {pcm}\) for integral measurements carried out with MOX fuel containing a large amount of americium (see also below).

The evaluation in the resolved and unresolved resonance ranges for \(\hbox {n} + {}^{241}\hbox {Am}\) is the result of a collaboration between JRC-Geel and CEA Cadarache. A detailed explanation of the evaluation work and the benchmark results can be found in Refs. [83, 84]. Resonance parameters for \(\hbox {n} + {}^{241}\hbox {Am}\) were derived by adjusting them in a least squares fit to experimental data that are reported in the EXFOR library together with the transmission and capture data obtained by Lampoudis et al. [85] at the GELINA facility. From a simultaneous analysis of the data sets, listed in Table 9, energies and partial widths of 211 resonances (\(l=0\)) up to 150 eV were determined. The REFIT code [59] was used for the analysis.

In the analysis, the transmission data of Lampoudis et al. [85] were considered as a reference. They were obtained from measurements at a 26.45 m station of GELINA with a homogeneous sample prepared by the sol-gel method. The sample, with an areal density of \(n=2.068(10) \times 10^{-4}\) at/b, was especially designed to derive accurate parameters for the strong s-wave resonances at 0.306, 0.574 and 1.270 eV.

Fig. 12
figure 12

PFNS for \(\hbox {n} + {}^{235}\hbox {U}\) as function of the energy of the outgoing neutron for 4 incident neutron energies (from 0.025eV up to 14.7 MeV). The pink (blue) curve shows the neutron spectrum of the light (heavy) fragment and the red curve shows the total PFNS. The data for 0.025 eV are from Ref. [75], those for 530 keV from Ref. [76] and those for 2.9 and 14.7 MeV from Ref. [77]. The two leftmost columns show the total PFNS according to the Madland–Nix weighting of the light and heavy fragment spectra, while the rightmost columns display the PFNS with the weights of the JEFF-3.3 evaluation

Fig. 13
figure 13

Mean prompt fission neutron energy as a function of the energy of the neutron inducing fission for \(\hbox {n} + {}^{235}\hbox {U}\) (left), \(\hbox {n} + {}^{238}\hbox {U}\) (middle) and \(\hbox {n} + {}^{239}\hbox {Pu}\) (right). Comparisons are made with experimental data, with JEFF-3.2 (top) and other libraries (bottom). For \(\hbox {n} + {}^{238}\hbox {U}\) and \(\hbox {n} + {}^{239}\hbox {Pu}\) the mean energy is calculated over the range of prompt fission neutron energies measured by the mentioned experiment (The values in brackets following the label \({\bar{E}}\))

Fig. 14
figure 14

Prompt neutron multiplicity \(\bar{\nu _p}\) as a function of the energy of the neutron inducing fission for \(\hbox {n} + {}^{235}\hbox {U}\) (left), \(\hbox {n} + {}^{238}\hbox {U}\) (middle) and \(\hbox {n} + {}^{239}\hbox {Pu}\) (right). Comparisons are made with experimental data and with JEFF-3.2 (top) and other libraries (bottom)

The transmission data of Derrien and Lucas [88] were obtained from measurements at 17.9 m and 53.4 m stations using three \({\hbox {AmO}}_2\) powder samples with different areal density, i.e. 0.18, 0.63 and \(1.87 \, {\hbox {g/cm}}^2\). The results of the three data sets were merged into one single experimental total cross section from 0.8 eV to 1 keV so that the individual transmission factors are not reported in EXFOR. As noted in Ref. [62], parameters of strong resonances derived from measurements with powder samples will be biased, unless their particle size distributions are taken into account in the analysis. Unfortunately, not enough detail is provided to account for the particle size distribution by the procedure that has been implemented in REFIT [90, 91]. To reduce bias effects due to the sample properties an average areal density was determined from a fit to the data. In addition, transmission data involving the strong resonances with energies below 8 eV were not included in the fit.

Since the neutron widths for most of the low energy resonances are much smaller than their radiation widths, the neutron widths derived from the transmission data of Lampoudis et al. were used to normalize the capture yields of Refs. [85,86,87]. The capture data of Lampoudis et al. [85] were obtained from experiments with a detection system consisting of two \({\hbox {C}}_6 {\hbox {D}}_6\) detectors using the same sample as the one used for the transmission measurements. The energy dependence of the neutron fluence was derived in parallel from measurements with a detector placed one meter before the sample. The detector consisted of two ionisation chambers with a common cathode loaded with two layers of \(^{10}\hbox {B}\). Fixed background filters were used to reduce bias effects due to the background corrections. Given the low amount of \(^{241}\hbox {Am}\) in the sample the impact of the neutron flux attenuation in the sample was negligible and no correction due to the attenuation of the neutron beam was required.

Van Praet et al. [87] derived a capture yield from measurements with \({\hbox {C}}_6 {\hbox {D}}_6\) detectors at a 8.6 m station of GELINA. The energy distribution of the neutron fluence was measured with a \({\hbox {B}}_4\hbox {C}\) disc at the place of the capture sample. Although a relatively thick metallic \(^{241}\hbox {Am}\) sample (areal density of \(1.063 \times 10^{-3}\) at/b) was used, no special procedure was applied to correct for the neutron attenuation and related gamma-ray transport in the sample.

The capture yield of Jandel et al. [86] resulted from measurements at LANSCE with a \(4\pi \) total absorption detector placed at 20.2 m from the neutron producing target. A thin \(^{241}\hbox {Am}\) sample, prepared by electroplating was used.

Figure 15 shows the result of an adjustment with REFIT. The theoretical and experimental capture yield and transmission obtained at the JRC-Geel facility are compared. Compared to JEFF-3.1.1 the new evaluation results in an increase of the capture cross section at thermal energy and the capture resonance integral by 15% and 20%, respectively, while the fission resonance integral is decreased by 14% (Table 10).

The average resonance parameters of interest for a partial wave breakdown of the neutron cross sections in the resonance region are the mean level spacing, the neutron strength function and the average radiation and fission widths. Parameters for s-wave levels were determined from a statistical analysis of the resolved resonance parameters. For higher values of angular momentum \(\ell >0\), average resonance parameters are obtained from systematics and by means of optical and statistical model calculations.

For 14 resonances, both the neutron and radiation width were determined. From these data an average radiation width was derived (Table 10).

This average value is in good agreement with the average value reported by Derrien and Lucas [88] and Lampoudis et al. [85]. The ESTIMA method [52] was used to determine simultaneously the most probable neutron strength function \(S_0\) and mean level spacing \(D_0\) for s-wave levels from the properties of the cumulative Porter–Thomas distribution of reduced neutron widths [92]. Such a procedure also accounts for the number of missing levels. In the present analysis, we obtain for the neutron width

$$\begin{aligned} \langle {\varGamma }_{n_J}^0\rangle = 6.03 (70)\times 10^{-5}{\text { eV}}. \end{aligned}$$

The neutron strength function \(S_0\) is derived from the ratio of the reduced neutron width \(\langle {\varGamma }_{nJ}^0\rangle \) to the mean level spacing \(D_0\). The uncertainty of \(S_0\) is obtained from the quadratic sum of the variances of \(D_0\) and \(\langle {\varGamma }_{n_J}^0\rangle \) (Table 10).

ECIS calculations were performed on the basis of the rigid rotor model using the optical model established by Soukhovitskii [95] and \(^{241}\hbox {Am}\) file of the JENDL neutron library. As proposed in Ref. [96], five ground-state rotational band levels (\(5/2^-\), \(7/2^-\), \(9/2^-\), \(11/2^-\) and \(13/2^-\)) were included in the coupled-channel calculations. The deformation parameter \(\beta _2\) was slightly optimised to improve the agreement with the \(S_0\) value established with the ESTIMA method. Uncertainties and correlation matrix for the optical model parameters of interest for this work (geometrical parameters, depth of the potentials and deformation parameters) were determined by propagating the uncertainties of the experimental total cross section of Philips and Howe [93] and the s-wave neutron strength function provided by ESTIMA, using the conventional uncertainty propagation applied in least squares adjustments. In Fig. 16, the total cross section calculated with ECIS is compared with the EXFOR data.

In the unresolved resonance range, the \(^{241}\hbox {Am} (\hbox {n}, \gamma )\) reaction was calculated with the TALYS code [43], in which the partial cross sections are calculated by means of the Hauser–Feshbach formula with width fluctuation correction factor using Moldauer’s prescription. The \(^{241}\hbox {Am}\) capture cross section calculated with the TALYS code by using the mean level spacing \(D_0=0.6\, \hbox {eV}\) and the average radiation width \(\langle {\varGamma }_{\gamma _0}\rangle =43.3\, \hbox {meV}\) is compared in Fig. 16 with data available in the EXFOR data base. The option within TALYS to run unresolved resonance calculation was then used to automatically generate the average resonance parameters in ENDF-6 format.

To account for the uncertainties of systematic effects the Monte Carlo procedure proposed by De Saint Jean [97] was applied. This procedure was used to propagate the uncertainties of the equivalent distance (\({\varDelta }L = 1~\hbox {cm}\)), time offset (\({\varDelta }t_0= 1~\hbox {ns}\)), sample temperature (\({\varDelta }T = 5~\hbox {K}\)), the normalizaton factors and areal densities. The resulting relative uncertainties and correlations on the capture cross section calculated over a broad energy mesh (15 groups) are shown in Fig. 17.

Table 9 List of capture, fission and transmission data used in the evaluation for \(\hbox {n} + {}^{241}\hbox {Am}\) in the resolved resonance range
Fig. 15
figure 15

Comparison of the REFIT curves with experimental capture yield and transmission measured at the JRC-Geel facility for \(^{241}\hbox {Am}\) up to 3 eV

To understand the impact of the new evaluation, the above mentioned integral experiments performed at the zero power reactor EOLE in Cadarache were revisited. Material buckling \({B}_m^2\) was analysed with APOLLO2 and \(k_{\text {eff}}\) measurements with TRIPOLI-4\(^{\textregistered }\) (Fig. 17). As the JEFF-3.2 and JEFF-3.3 evaluations for \(\hbox {n} + {}^{241}\hbox {Am}\) are the same the conclusions are valid for both (see also Sect. 3.1.6). The results are shown as a function of plutonium ageing from MH1.2 (no ageing) to MISTRAL-2, -3 and -4 (20 years old Pu for MISTRAL-4). The observed trend confirms the increasing discrepancies with Pu ageing between calculation and experiment. The worst result reaches a maximum close to \({\varDelta }\rho \approx +800~ \hbox {pcm}\) for the reference configuration of the MISTRAL-4 program carried out in 1999. The Japanese code MVP confirms the \(k_{\text {eff}}\) estimates. The increase of the \(^{241}\hbox {Am}(\hbox {n}, \gamma )\) cross section in the new evaluation (\(+20\%\) compared to JEFF-3.1.1 and the Atlas and 9% compared to ENDF/B-VIII and JENDL-4, see Table 10) improves significantly the reactivity calculations of the MOX configurations over a wide range of moderation ratios. The mean value \(\langle {\varDelta }\rho \rangle \) calculated over the five reference configurations of the FUBILA, MH1.2 and MISTRAL-2-3-4 programs is now:

$$\begin{aligned} \langle {\varDelta }\rho \rangle = 50 (180){\text { pcm}}. \end{aligned}$$
Table 10 \(^{241}\hbox {Am}\) thermal capture cross section, capture (fission) resonance integral and average parameters of JEFF-3.3 compared to ENDF/B-VIII, JENDL-4 and Atlas values
Fig. 16
figure 16

Top: \(^{241}\hbox {Am}\) total cross section calculated with the ECIS code and compared with EXFOR data [88, 93]. Bottom: Comparison of the theoretical \(^{241}\hbox {Am}\) capture cross section (TALYS) with data retrieved from the EXFOR data base [86, 87, 94] multiplied by the square root of the incident neutron energy

Fig. 17
figure 17

Top: relative uncertainties and correlation matrix for the \(^{241}\hbox {Am}(\hbox {n}, \gamma )\) reaction up to 150 eV. Bottom: integral trends obtained with the JEFF-3.1.1, JENDL-3.2 and JEFF-3.2 libraries for material buckling \({B}_m^2\) (APOLLO2 calculations) and critical \(k_{\text {eff}}\) measurements (TRIPOLI-4® and MVP calculations)

Resonance parameter uncertainties of \(^{241}\hbox {Am}\) were propagated to \(k_{\text {eff}}\) [98] and contribute 131 pcm for MISTRAL-2 and 143 pcm for MISTRAL-3, a considerable fraction of the total uncertainty.

2.1.7 Curium

Neutron cross sections for curium isotopes, i.e. \(^{240-250} \hbox {Cm}\), were evaluated at KAERI. A more detailed description of this evaluation is given in Refs. [99, 100]. The upper boundaries of the RRR and URR, together with the half-lifes and the experimental data that are available in the EXFOR data library, are listed in Table 11. The data in the resonance region were adopted from JENDL-4 [101]. For neutron interactions above the resonance region, evaluated cross section and covariance data were derived from model calculations using the EMPIRE code [102]. Table 11 reveals that experimental data that can be used to adjust the model parameters and to validate the results are rather scarce. In addtion, for \(^{240,241,249}\hbox {Cm}\), which have a very short half-life, no resolved or average resonance parameters are available. For these isotopes only averaged cross sections derived by the EMPIRE code are given. The lower energy boundaries for these cross sections are at 3.0 eV, 1.1 eV and 3.1 eV for \(^{240}\hbox {Cm}\), \(^{241}\hbox {Cm}\) and \(^{249}\hbox {Cm}\), respectively. Given the limited number of experimental data a procedure similar to the one applied for Nd-isotopes was followed [103]. This procedure relies on model parameters, such as the parameters of the optical model potential and the asymptotic value of the level density parameter, that vary smoothly as a function of mass number.

Table 11 Experimental data for \(^{240-250}\hbox {Cm}\) reported in the EXFOR library, together with the half-lives (\({\hbox {T}}_{1/2}\)) and upper energy boundary of the resolved (RRR) and unresolved resonance region (URR). Only fission data (f) are available for \(^{242-248}\hbox {Cm}\). The half-lives are from the JEFF-3.3 radioactive decay data file (Sect. 2.8). 1 a(nnus) is 365.242198 d [4]
Fig. 18
figure 18

Top: total, elastic, inelastic, fission and capture cross sections for \(^{244}\hbox {Cm}\) compared to the Gianotti model calculations [106] and the measurements [107,108,109,110,111,112]. Bottom: fission and capture cross sections for \(^{244}\hbox {Cm}\) compared to the JENDL-4.0 and ENDF/B-VII.1 evaluations, the Gianotti model calculations [106] and the measurements [107,108,109,110,111,112]

Fig. 19
figure 19

Total, elastic, and fission cross sections for all Cm isotopes [106,107,108,109,110,111,112]

Fig. 20
figure 20

The correlation of total and fission cross sections for \(^{244}\hbox {Cm}\) and the uncertainties compared to the measurements [106,107,108,109,110,111,112,113,114,115,116,117,118,119]

The EMPIRE code calculates cross sections for all relevant reaction channels, angular distributions, exclusive and inclusive particle- and \(\gamma \)-ray emission spectra, double-differential cross sections, and spectra of recoils. Nuclear reaction models in the Empire code can be classified into three major classes: (i) optical model and direct reactions (Coupled-channels (CC) and Distorted-wave Born approximation (DWBA)), (ii) preequilibrium emission, and (iii) Hauser–Feshbach statistical decay. An isospin-dependent coupled-channel optical model potential containing a dispersive term (DCCOMP) as suggested by Capote et al. [104] was used. The model parameters were taken from the RIPL-2 data base [70]. The Empire-specific level density formulas were employed and their parameters adjusted by a fit to known nuclear discrete levels and available experimental data. The gamma strength function proposed by Plujko et al. [105] was used. Fission cross sections were derived in the WKB approximation supposing a double-humped fission barrier with free parameters that were adjusted to experimental cross section data [99]. Results of the evaluation are illustrated in Figs. 18 and 19. Figure 18 compares the evaluated and experimental total cross section for \(^{244}\hbox {Cm}\) together with those for the capture reaction and elasitic and inelasting scattering. A comparison of the evaluated fission cross section for \(^{244}\hbox {Cm}\) with experimental data reported in the EXFOR library is shown in Fig. 18. The results for the other isotopes are shown in Fig. 19. The total cross section and the cross section for elastic scattering are compared with an evaluation reported by Fernandez Gianotti [106]. Figure 19 also compares the fission cross sections reported in this work with the results of experiments of Refs. [107,108,109,110,111,112].

Covariance data were generated by the Kalman code implemented in the EMPIRE system supposing a 10% uncertainty on the model parameters. These uncertainties were complemented in a Bayesian updating procedure with the experimental fission cross section data listed in Table 11. Figure 20 shows the resulting uncertainties for total and fission cross sections together with their correlation matrix.

2.1.8 Other actinides

In the previous sections the three major actinides \(^{235,238}\hbox {U}\) and \(^{239}\hbox {Pu}\) and the minor actinides \(^{241}\hbox {Am}\) and \(^{240-250}\hbox {Cm}\) were presented. Evidently, this does not cover all actinide nuclear data of importance. For instance, the thorium-uranium fuel cycle takes interest in \(^{232}\hbox {Th}\), \(^{233}\hbox {U}\) and minor actinides such as \(^{231,233}\hbox {Pa}\) and \(^{232,234}\hbox {U}\). For use of MOX, high level waste management, spent nuclear fuel transport, storage and fuel disposal and in particular transmutation, data are needed for \(^{237}\hbox {Np}\), \(^{238,240-242,244}\hbox {Pu}\), \(^{242m,243}\hbox {Am}\). For JEFF-3.3 these are either taken from earlier JEFF releases or from other evaluations. Table 12 shows the primary source of the evaluations and the references providing further details.

Table 12 Some actinide evaluations in JEFF-3.3 adopted from other evaluations
Fig. 21
figure 21

Evolution of the JEFF library with respect to DN data

2.1.9 Delayed neutrons

Delayed neutrons (DN) are of great importance for a safe reactor operation. The uncertainty of DN production due to the quality of nuclear data resulted in a strong conservatism in the design and operation of reactor control systems. An international effort has been made by the NEA/WPEC Subgroup 6 to improve the nuclear data that is required to predict the DN production. This resulted in the recommendations for the major actinides that are specified in the Subgroup 6 report [123]. These recommendations, which are based on an 8-group structure with a fixed set of half-lifes, were already adopted in JEFF-3.1.1 and are restored in the official release of JEFF-3.3.

It is a common procedure to sort the approximately 300 delayed-neutron precursors into groups (typically 6 or 8) and to represent their aggregate behavior through group parameters [124]. The most important application of the group constants is the estimation of the reactivity (\(\rho \)) from the measurement of the reactor period (T), through the Inhour equation in which the average delayed neutron precursor half-life (\(\overline{T_{1/2}}\)) plays an important role [125].

The average precursor half-life can be computed by adding up the individual contributions (second expression in Eq. 1) or by using the group approximation (third expression in Eq. 1):

$$\begin{aligned} \overline{T_{1/2}} = \sum \limits ^n_i \frac{CY_i \; P_{n,i} \; T_{1/2,i}}{\overline{\nu _d}} = \frac{\sum \nolimits ^G_j a_j \; T_{1/2,j} }{\sum \nolimits ^G_j a_j}, \end{aligned}$$

where \(a_j\) is the abundance of group j and \(T_{1/2,j}\) its half-life [124].

Delayed-neutron parameters can be found by either a macroscopic approach, based on experiments carried out on irradiated samples, or by a microscopic approach by investigating the properties (i.e. cumulative fission product yield, half-life, neutron emission probability) of individual neutron precursors. The data from the NEA/WPEC-6 report published in 2002 [123] is based on an 8-group structure. The abundances \(a_i\) come from the expansion of a 6-groups data set that Keepin obtained in 1957 through results of an integral measurement [126]. The uncertainties of the 8-group abundances have been estimated to preserve the reactivity uncertainty based on a 6-group estimation [125]. The main feature of the new set is that the group decay-constants are valid for any fissioning system at any incident neutron energy, thus simplifying the modeling of multiple fissioning nuclides. The data recommended by Subgroup 6 were extensively validated for thermal and fast reactors (see Refs. [2, 3])

The JEF-2.2 library, released in 1992, only contained delayed-neutron data for the major nuclides, as shown in Fig. 21. Reliable estimates of the \(\beta _{\text {eff}}\) for fast reactor systems or for end-of-cycle-conditions could not be made since DN data for Am and Cm isotopes were missing. The time dependence of the DN production was reproduced by the 6-group parameters with a fitted set of decay constants (one set per fissioning nuclide). The effect of the incident neutron energy could not be represented.

The Subgroup 6 recommendations were adopted in JEFF-3.1.1 for most of the U, Np, Pu, Am and Cm isotopes. The data for minor isotopes were taken from other libraries. The incredible effort of delayed neutron data compilation done by the international community led to the marked improvement reflected in JEFF-3.1.1, as seen in Fig. 21.

In JEFF-3.2, which was released in 2014, the neutron transport sublibraries for \(^{242-246,248}\hbox {Cm}\), \(^{241}\hbox {Am}\), \(^{232,233}\hbox {U}\) and \(^{231}\hbox {Pa}\), including the DN data, were replaced by results of other evaluations. Since no new experimental data was produced or became available after the work of Subgroup 6 there was in principle no justification to replace the DN data. In the process of developing JEFF-3.3, it was demonstrated that for 235U the DN data taken from ENDF/B-VII.0 lead to a wrong evaluation of the average DN precursor’s half-life [127]. In addition, IPEN and SPERT benchmarks both concluded that JEFF-3.1.1 data provides the best C/E agreement on the dynamic reactivity from the Inhour equation, due to the better evaluation of the \(a_i\) and \(\lambda _i\) data.

The United States library ENDF/B-VII.1, on the other hand, is still relying on the 6-group \(a_i\) and \(\lambda _i\) from the Brady and England fit of the decay-curve computed by a summation method [128].

All the considerations mentioned above motivated the restoration of the 8-group data for \(^{227,229,232}\hbox {Th}\), \(^{231}\hbox {Pa}\), \(^{232-235}\hbox {U}\), \(^{237}\hbox {Np}\), \(^{238,241}\hbox {Pu}\), \(^{241,243}\hbox {Am}\), \(^{242-246,248}\hbox {Cm}\) and \(^{249}\hbox {Cf}\). For nuclides without DN data in JEFF-3.1.1, i.e. \(^{250}\hbox {Cf}\), \(^{241}\hbox {Cm}\) and \(^{239-241}\hbox {U}\), data coming from other libraries were adopted in JEFF-3.3. As the ENDF-6 format cannot handle uncertainties on DN group constants, the information in the Subgroup 6 report for \(^{235,238}\hbox {U}\) and \(^{239,241}\hbox {Pu}\) was summarised in the header of their files.

2.2 Structural materials and coolants

An overview of the origin of evaluations for coolants, moderators, structural and shielding materials is given in Table 13. As indicated in the table, below we describe the evaluations for JEFF-3.2 and JEFF-3.3.

Table 13 Origin of evaluations for structural materials, coolants and moderators in JEFF-3.3

2.2.1 Deuterium

In JEFF-3.2 a new evaluation for n+D reactions was introduced [132]. The elastic and breakup cross sections are computed by solving the three-body Faddeev equations with the semi-realistic MTI-III [133] and the realistic INOY [134] nucleon-nucleon potentials. The n-d reaction is considered as a three particle problem for nucleons interacting via pairwise potentials. The solution has been obtained numerically by means of standard methods used in few-body problems. They are based on a spline expansion of the Faddeev amplitudes which transform the set of partial differential equations into a homogeneous linear system [135].

For JEFF-3.3 the evaluation modifies the JEFF-3.2 evaluation by correcting for masses and Q-values and adding covariances for the total, elastic (n,2n) and (n,\(\gamma \)) reactions. The covariances were based on an analysis of the experimental data. Finally, decay data were added for tritium.

Fig. 22
figure 22

Low energy cross section for n+D scattering. The weighted average of the experimental data is 3.390(11) b in agreement with the most accurate value obtained by Dilg et al. [136]. The remaining data are from Rayburn et al. [137], Fermi and Marschall [138], Rainwater et al. [139] and Hanstein [140]

Fig. 23
figure 23

Total cross section data for n+D scattering compared to JEFF-3.3, ENDF/B-VIII.0 and JENDL-4u for 20 keV to 30 MeV (top), 20 keV to 2 MeV (middle) and 2 MeV to 30 MeV (bottom). The data labels refer to the following references: rpi73(b for filtered beam) [141, 142], lrl80 [143], rpi72 [144], wis71 [145], orl64 [146], lrl58-60 [147, 148], las01 [149], har65 [150]

Fig. 24
figure 24

Differential scattering data by Schwarz et al. [151] compared with model calculations using the AV-18 nucleon–nucleon potential (red line) and the INOY potential (dashed green line – JEFF-3.3, [132])

The cross sections calculated with the INOY potential (JEFF-3.3) are compared to the existing experimental data in Figs. 22, 23 and 24. Figure 22 shows the excellent agreement with the very accurate low energy scattering cross section. Similar agreement is obtained by ENDF/B-VIII.0 and JENDL-4u which is hidden by the other two evaluations in the figure. The total cross section data are well described by the three evaluations, as well. Slight differences are observed that are well within the experimental uncerainties. Even if the three evaluations show some distinct weak and different trends there is no conclusive answer as to which is best. At low energy the behaviour of JEFF-3.3 and ENDF/B-VIII.0 are smooth whereas JENDL-4u shows a stronger energy dependence. For the angular distributions a comparison is only made with the data of Schwarz et al. [151]. The comparison is similar to that of Ref. [132] but here we include the calculation that led to JEFF-3.3 which is based on the INOY potential. This calculation follows very closely that of the AV-18 potential and shows overall good agreement with the data that correspond to 20 neutron energies between 2.5 and 30 MeV. A recent measurement for n+d scattering by Pirovano et al. shows good agreement with JEFF-3.2 (and therefore JEFF-3.3) for the backward–forward scattering ratio for neutron energies between 0.2 and 2 MeV [152].

The multiplication factors \(k_{\text {eff}}\) of heavy water benchmarks obtained by Monte Carlo simulations including this evaluation can be found in [132]. Further comparisons may be found below.

2.2.2 Sodium

The JEFF-3.1.1 [3] sodium evaluation shows large discrepancies in the MeV range with the microscopic experimental data that is available in EXFOR , even though it behaves well in integral experiment benchmarking. Furthermore, cross section covariance matrices, which are of interest for fast reactor applications in sensitivity and uncertainty analysis, are not available. In the framework of the ASTRID project (French sodium fast reactor), a new evaluation for sodium from 0 to 20 MeV [153] was carried out using the CONRAD code [154]. The results are included in the JEFF-3.3 library. The file contains both re-evaluated nuclear data and covariances and is divided in two energy regions: the resolved resonance range and the continuum part.

The resonance range, which had an upper limit of 350 keV in previous versions, has been extended to 2 MeV. For the continuum region, a simultaneous analysis of total, inelastic, capture and charged particle cross section data was performed with the ECIS [155] and TALYS [43] codes, interfaced with CONRAD. An overall good agreement between experimental and theoretical cross sections was achieved. The covariance data were produced with a Monte Carlo marginalisation procedure which consists in propagating the uncertainties of the most important systematic effects to the uncertainties of the nuclear reaction model parameters.

The resolved resonance range for sodium in JEFF-3.1.1 was described up to 350 keV using the Multilevel Breit-Wigner approximation. With this R-Matrix approximation in the ENDF-6 format, the upper energy value cannot exceed the first inelastic threshold which is at 459.3 keV for \(^{23}\hbox {Na}\).

To produce improved resolved resonance parameters for JEFF-3.3, the high resolution experimental total cross section data of Rahn [156] and Larson [157] and the inelastic cross-section data of Rouki et al. [158] were used. These data show large and detailed resonant structures up to 5 MeV. This is the primary motivation to extend the resonance range up to 2 MeV, just before the opening of the second inelastic scattering channel. For a better representation of the elastic-inelastic scattering interferences the Reich–Moore approximation of the R-matrix formalism was used. An energy-dependent effective scattering radius (\(R_{\text {eff}}\)) was required in order to obtain a good agreement with the experimental data above 1 MeV. The energy dependence was derived from results of optical model calculations.

For the resonance analysis the starting parameters were mainly taken from the Atlas of Neutron Resonances [67]. The neutron widths for resonances below 450 keV were adjusted to the total cross section data of Rahn [156] and Larson [157]. Above this energy, the inelastic data of Rouki et al. [158], obtained at the GELINA facility of the JRC Geel, were used to derive the neutron elastic and inelastic scattering widths and total angular momentum. The good agreement between the results of the adjustment and experimental data is shown in Figs. 25 and 26.

Fig. 25
figure 25

Evaluated \(^{23}\hbox {Na}\) total cross-section (red) compared to Larson experimental data (blue dots [157])

Fig. 26
figure 26

Evaluated \(^{23}\hbox {Na}\) inelastic cross-section (red) compared to Rouki experimental data (blue dots [158])

In the continuum region, i.e. for neutron energies larger than 2 MeV, optical model and statistical model parameters (level density, giant dipole resonance, pre-equilibrium...) were derived with the ECIS [155] and TALYS [43] codes. We used a spherical dispersive parameterisation derived from the global optical model of Morillon and Romain [159] found in the RIPL-3 database [70].

In this energy range, we use the data from Rouki et al. [158] for the first six inelastic channels up to 3.5 MeV. Above this energy, we derived our parameters set from the Larson measurements and various experimental data available in EXFOR for the \((n,\gamma )\), (np), \((n,\alpha )\), (n, 2n) reactions. The agreement with respect to Larson data is excellent. Concerning the partial and total inelastic cross-sections, an overall good agreement has been achieved with the data obtained by Rouki et al. 

Experimental uncertainties, in particular a normalisation uncertainty of 3% for the data of Larson and 6% for those of Rouki et al. were propagated to the model parameters using a Monte-Carlo marginalisation technique [97] for both energy domains at the same time. This procedure creates correlations between resonance and statistical parameters and also between the resonance range and the continuum region.

2.2.3 Aluminum

The aluminum evaluation of ENDF/B-VI.8 was adopted in JEFF-3.0. For JEFF-3.3, it was modified to include inelastic scattering, in particular the emitted gamma rays (Sect. 2.4). In addition, covariances were generated for the resonance parameters and the cross sections using the TENDL method [5].

Fig. 27
figure 27

Left: The \(^{52}\hbox {Cr}(\hbox {n,2n}) {}^{51}\hbox {Cr}\) and \(^{52}\hbox {Cr}(\hbox {n,p}) {}^{52}\hbox {V}\) evaluations compared with the experimental data. Middle: The production of protons (left) and alphas (right) on natural chromium. Right: Examples of the modifications to the neutron inelastic scattering channels of \(^{52}\hbox {Cr}\) from JEFF-3.2 to JEFF-3.3. Left, inelastic scattering to the first excited level, right, inelastic scattering to the second excited level. The data are labeled by the first author of the reference

2.2.4 Chromium

New evaluated data files were prepared for \(\hbox {n} + {}^{50,52,53,54}\hbox {Cr}\) interactions for the JEFF-3.2 release [160]. With one modification to the evaluation of \(\hbox {n} + {}^{52}\hbox {Cr}\) data these were adopted for JEFF-3.3. The resonance range evaluations were performed at Oak Ridge National Laboratory, USA. The data were analysed using the SAMMY [19] resonance analysis code. The experimental data that were included and the quality of the fit are comprehensively summarized in Ref. [161]. In the fast energy range the data for \(\hbox {n} + {}^{52}\hbox {Cr}\) were evaluated up to 150 MeV using the GNASH code while the data for \(\hbox {n} + {}^{50,53,54}\hbox {Cr}\) were evaluated with TALYS-1.0 up to 200 MeV using the geometry dependent hybrid pre-equilibrium model [162]. Particular attention was paid to reproducing the available experimental data for the total cross section and the (n,xn), (n,xp) and (n,x\(\alpha \)) channels especially when these lead to radioactive residual nuclei [160]. Figure 27 shows the evaluation compared with data for the \(^{52}\hbox {C}\)(n,2n) [163,164,165,166,167,168,169,170,171,172] and \(^{52}\hbox {Cr}\)(n,p) [164, 169, 170, 172,173,174,175,176] reactions and for the production of protons and alphas on natural chromium. The latter are important for the effect of gas production on material damage.

For JEFF-3.3 this evaluation was modified to account for a change of normalization of the data for neutron inelastic scattering of Mihailescu et al. by 12.5% ([177, 178], see also Sects. 2.2.14, 2.2.15). The change implied replacing the data for inelastic scattering to the first level up to 4.5 MeV, to levels 2, 3, 4, 5 and 9 up to 4 MeV and to levels 6, 7 and 8 up to 3.9 MeV with the renormalized experimental data as available in EXFOR [179]. The cross sections above these energies were smoothly matched to the existing evaluated cross sections at 20 MeV by a multiplicative factor depending linearly on the energy (Fig. 27).

2.2.5 Iron

Recently, the CIELO project developed new evaluations for the stable iron isotopes, that were adopted in the ENDF/B-VIII.0 library [14, 180]. The evaluations in JEFF-3.3 for \(^{54,56,57,58}\hbox {Fe}\) are unchanged from those in JEFF-3.2. The files in JEFF-3.2 were modifications of those in JEFF-3.1. Besides a few corrections, new capture gamma data were included (Sect. 2.4). For \(^{56}\hbox {Fe}\) covariance data for the elastic, inelastic and capture cross sections were obtained by an adjustment to the PERLE experiment at the Eole zero power reactor and the gas-benchmark at the Masurca zero power reactor. These experiments were carried out in Cadarache, France, and featured iron reflectors for a typical Generation-III PWR configuration and a typical Generation-IV fast reactor (see also Sect. 3.1.6). An iterative non-linear regression was performed using the RDN code to arrive at the posterior covariance matrix [181].

For \(^{56}\hbox {Fe}\) in JEFF-3.1 the original JEFF-3.0 (EFF-3.1) file with an evaluation up to 20 MeV was extended up to 200 MeV using the TALYS code by Koning and Duijvestijn [1, 2, 43]. The evaluations for \(^{54,57,58}\hbox {Fe}\) were newly introduced by these authors in JEFF-3.1 and were left untouched, aside from the inclusion of capture gamma-ray emission for JEFF-3.2 (Sect. 2.4).

The decision to leave the iron files for JEFF-3.3 untouched was due to the fact that these files are competitive in terms of the description of available microscopic data, are performing well in criticality benchmarking and are better than the CIELO files in shielding benchmarks (Sects. 3.1 and 3.3). The choice has the unfortunate consequence that new insights in inelastic scattering are not included in the evaluation [182,183,184,185,186].

2.2.6 Nickel

From Table 13 it is clear that the stable isotopes for nickel were taken from either TENDL-2015 (\(^{62,63}\hbox {Ni}\)), from ENDF/B-VII.1 (\(^{61,64}\hbox {Ni}\)) or from EFF-3.1 (\(^{58,60}\hbox {Ni}\)). For JEFF-3.3 only the radioactive product data of the \(^{58}\hbox {Ni}\)(n,p) channel were added. For the unstable nuclides, evaluations were added for \(^{56,57,59}\hbox {Ni}\). For \(^{56,57}\hbox {Ni}\) these were taken wholesale from TENDL2015. For \(^{59}\hbox {Ni}\) a Talys based statistical method was pioneered that is of interest to evaluations for future libraries such as JEFF-4.

\(^{59}\hbox {Ni}\) is interesting because of its non-threshold (n,\(\alpha \)) and (n,p) reactions. The isotope is unstable, but has a half-life of 76,000 years and is produced in thermal neutron spectra from neutron capture in \(^{58}\hbox {Ni}\). For austenitic materials, including a wide range of common stainless steels, nickel may be sufficiently transmuted to reach as much as \(3\%\) of the nickel content and \(^{59}\hbox {Ni}\) reactions have been shown to contribute the vast majority of displacement damage in some heavily thermalised environments [187]. Since nickel is one of the constituents of many stainless steels, the (n,\(\alpha \)) and (n,p) reactions may also contribute a large fraction of the gas production reactor components [187].

The previous JEFF evaluation [188] did not contain any covariance data and only ranged up to 20 MeV. The new evaluation work is focused towards covariances, and contains, e.g., cross-channel correlations over the whole energy range, up to 200 MeV. The evaluation contains several novel features, e.g. a sampling of experimental errors merged with the sampling of resonance and model parameters; sampling from the latter two is similar to Total Monte Carlo [189]. A summary of the evaluation is presented below and further details are given in Ref.  [190].

Since the thermal cross sections of \(^{59}\hbox {Ni}\) are judged to be most important for applications, the evaluation is focused on these. Also, most available experiments are for thermal cross sections.

The publications (or, if not available, the EXFOR entries [179]) of thermal cross section experiments are studied in some detail, and the evaluators try to identify experimental uncertainty components which are not included in the experimenters’ analyses. Seemingly missing uncertainties are added using assumed default values, which are intended to be somewhat conservative. Uncertainty components which are in common for different experimental points are identified (even for different experiments, for example originating from the use of the same target or monitor cross section).

Table 14 Estimated expected values \(\left\langle \sigma \right\rangle \) and standard uncertainty u in barns for the thermal cross sections of the current \(^{59}\hbox {Ni}\) evaluation, compared to the values from Mughabghab [67] and the previous JEFF evaluation. The uncertainties of the standard deviations are determined using the method described in Ref. [191]
Fig. 28
figure 28

The cross sections of (n,\(\alpha \))for the \(^{59}\hbox {Ni}\) JEFF-3.3 evaluation (green with error bands) as functions of energy compared to JEFF-3.2 (blue, no error bands) and JENDL-4.0 (cyan no- error bands)

After this analysis, the error components are sampled. In this way, random realisations of the different experiments are obtained. For each set of realisations, estimates for each of the (n,\(\alpha \)), (n,p), (n,\(\gamma \)), and (n,tot) thermal cross sections are obtained using generalized least squares. In this way, a sample from the full joint distribution of the thermal cross sections is obtained. Physical constraints (a non-negative (n,el) cross section and the matching to other data) are included by redrawing and thus discarding “unphysical” results. This procedure impacts the distribution of the thermal cross sections. The resulting mean values and uncertainties are presented and compared to the previous JEFF evaluation and the Mughabghab Atlas of Neutron Resonances [67] in Table 14. The values are generally different from, but compatible with, both Mughabghab and JEF(F) 2.2–3.2.

The thermal cross sections are combined with resonance parameters from experiment [192,193,194] and other data from TALYS-1.8 [43] using the parameter distribution of TENDL 2015 [5]. Both these sets of data are also sampled. For each realisation of data, the resonance parameters are matched with the thermal cross sections by sampling bound resonances (\(E < 0\)) based on average level spacings and widths from the corresponding TALYS run, and the resonance widths of these bound resonances are adjusted such that the thermal cross sections are reproduced. If the adjustment fails, the combination of sampled thermal cross sections and sampled resonance parameters is considered unphysical, and both sets of data are redrawn, as can be motivated by Bayes’ theorem. For further details see Ref. [190].

The procedure results in 300 sets of complete nuclear data, which implicitly includes uncertainties of almost all the data. Also, all subsets of the data are correlated, since the sampling of bound resonances is based on TALYS results, and because of the matching between resonance parameters and thermal cross sections. For illustration, Figure 28 shows the (n,\(\alpha \)) cross sections for the \(^{59}\hbox {Ni}\) JEFF-3.3 evaluation compared to JEFF-3.2 and JENDL-4.0. JEFF-3.2 is copied from previous JEF(F) versions since JEF-2.2. ENDF/B-VIII.0 is also based on this evaluation. More illustrations of the new JEFF-3.3 evaluation are found in Ref. [190].

The 300 sets of nuclear data are condensed into one single ENDF file with covariances. Because of format limitations, correlations between some subsets of data are lost, e.g., between URR parameters and the cross sections. Higher moments than covariances are also lost. The impact of cross correlations can however be studied by the direct use of the 300 ENDF formatted files (the so-called random-files) which also were produced.

2.2.7 Copper

For the \(^{63}\hbox {Cu}\) and \(^{65}\hbox {Cu}\) isotopes the resonance region was set from \(10^{-5}\, \hbox {eV}\) to 300 keV. Resolved resonance parameters for neutron interactions with \(^{63}\hbox {Cu}\) and \(^{65}\hbox {Cu}\) in the energy region below 6 keV were taken from the work of Tsuchiya et al. [195]. They result from a combination of the radiation widths reported by Weigmann and Winter [196] and a resonance shape analysis of transmission data obtained at GELINA using REFIT [59]. To account for external contributions the bound state parameters of JEFF-3.2 were adopted. This contribution is not consistent with the one used in Ref. [195]. This explains the inconsistencies observed in Ref. [197] between experimental transmission data and the calculated ones using the parameters in JEFF-3.3. The results in Ref. [197] reveal also problems with the parameters recommended by Mughabghab [67], Sobes et al. [198] and ENDF/B-VIII.0 [180].

The nuclear model simulations of the \(\hbox {n} + {}^{63,65}\hbox {Cu}\) reactions were performed using the TALYS-1.8 code [43] for neutron energies between 1 keV and 200 MeV [199]. In spite of the general predictive power of TALYS, certain improvements can be gained by inclusion of an extra model for pre-equilibrium reactions, known as the Geometry Dependent Hybrid model (GDH) [162]. With the GDH model added to TALYS-1.8, the system provides more accurate results for n+Cu reactions compared to the existing models within the code. The nuclear level density was described with a back-shifted Fermi-gas model [200].

Fig. 29
figure 29

Left: evaluated \(^{63}\hbox {Cu}(\hbox {n,2n}) {}^{62}\hbox {Cu}\) cross section. Right: evaluated \(^{65}\hbox {Cu}(\hbox {n,2n}) {}^{64}\hbox {Cu}\) cross section

Fig. 30
figure 30

Left: evaluated \(^{63}\hbox {Cu}(\hbox {n,p}) {}^{63}\hbox {Ni}\) cross section. Right: evaluated \(^{65}\hbox {Cu}(\hbox {n,p}) {}^{65}\hbox {Ni}\) cross section

Fig. 31
figure 31

Left: evaluated \(^{63}\hbox {Cu}\)(n,n’) cross section for the first excited level. Right: evaluated neutron emission spectra for \(\hbox {n} + {}^{\text {nat}}\hbox {Cu}\) at 26 MeV

All optical model calculations for neutrons and protons were performed using TALYS built-in Optical Model Potentials (OMPs). In the case of other charged particles, external global OMPs were used for deuterons [201] and alphas [202]. For tritons and helions, new OMPs were elaborated using a large experimental database and available OMPs for some target nuclides. The parameters of the global OMPs for charged particles (except incident protons) were separately prepared and used in TALYS calculations invoking the cycling through the available options. For all OMPs, the same incident energy range from keVs up to 200 MeV was used to keep continuity and consistency of the evaluated data. All changes arising in the evaluations due to the adjustment procedure of the reaction cross sections are accounted for in the elastic scattering cross section, keeping the total cross section unchanged.

The procedure applied to these nuclear data evaluations is based on an optimised fit to the experimental data [203]. The nuclear model parameters were adjusted stepwise, resulting in an optimal set that results in evaluated data that best fits the experimental results. Shown in Fig. 29 are the newly evaluated (n,2n) cross sections for \(^{63,65}\hbox {Cu}\). The results for \(^{63,65}\hbox {Cu}\)(n,p) cross sections compared to the measured and other evaluated data are presented in Fig. 30. Great attention was paid to the evaluation of the inelastic scattering cross sections for all excitated states of the \(^{63,65}\hbox {Cu}\). The latest measured data of Takamiya et al. [204] cannot be reproduced by any nuclear model simulations considered and they were not used for the adjustment of the nuclear model parameters. The results of the evaluation for \(^{63}\hbox {Cu}\)(n,n’) inelastic scattering cross sections are given in the Fig. 31. The inclusion of the new GDH option enabled significant improvements in the calculated pre-equilibrium particle emission spectra compared to the original TALYS-1.80 results (Fig. 31). The JEFF-3.3 and JEFF-3.2 results are compared with ENDF/B-VIII.0 [180], TENDL-2017 [5] and IRDFF-2 [205].

Fig. 32
figure 32

Top left: evaluated total cross section for the \(\hbox {n} + {}^{90}\hbox {Zr}\). Top right: the evaluated (n,n’) cross section for the 2\(^{nd}\) excited level of the \(^{91}\hbox {Zr}\). Row 2 left: evaluated \(^{90}\hbox {Zr}\)(n,2n) cross section. Row 2 right: evaluated \(^{96}\hbox {Zr}\)(n,2n) cross section. Row 3 left: evaluated \(^{92}\hbox {Zr}\)(n,p) cross section. Row 3 right: evaluated \(^{94}\hbox {Zr}\)(n,p) cross section. Row 4 left: neutron emission spectrum for \(^{nat.}\hbox {Zr}\) at 14 MeV. Row 4 right: neutron emission spectrum for \(^{nat.}\hbox {Zr}\) at 18 MeV. Comparisons are with experimental data, JEFF-3.2, ENDF/B-VIII.0 and TENDL-2017 [5, 180]

2.2.8 Zirconium

The evaluation n+Zr data was performed in the same way as in the n+Cu case [199]. However, for zirconium the \(\hbox {n} + {}^{90, 91, 92, 94, 96}\hbox {Zr}\) resonance data for the resolved and unresolved ranges were taken from the ENDF/B-VII.1 [121]. For the fast range, the available experimental database was used to apply a consistent procedure for the evaluation of the exclusive reaction cross sections. Examples of evaluated cross sections compared with experimental data and other evaluations are given in Fig. 32 for the evaluated total cross section of \(\hbox {n} + {}^{90}\hbox {Zr}\), where the resonance data are quite different in various libraries, for the evaluated neutron inelastic scattering cross section (n,n’) for the 2nd excited state of \(^{91}\hbox {Zr}\) and for evaluated exclusive (n,2n) and (n,p) cross sections are given. The new evaluations account for the latest measured data and show a good agreement with the available experimental data below 20 MeV, as well as a significant improvement compared with other evaluations. The neutron emission spectra presented in Fig. 32 also demonstrate an improvement in the pre-equilibrium components due to the inclusion of the GDH model. In the figure, the JEFF-3.3 and JEFF-3.2 results are compared with ENDF/B-VIII.0 [180], TENDL-2017 [5] and IRDFF-2 [205]. The JEFF-3.3 evaluation generally compares well to its predecessor and these other evaluations.

For the ENDF-6 representation of the data, the following structure of the data files was adopted: below 20 MeV the full detailed information for all open reaction channels is given and above 20 MeV total and elastic scattering cross sections are provided alongside total particle emission spectra and total cross sections for the production of the residual nuclides with their recoil spectra.

2.2.9 Cadmium

An ENDF-6 compatible evaluation for neutron induced reactions in the resonance region has been completed for \(^{106,108,110,111,112,113,114,116}\hbox {Cd}\). The resonance parameters were derived from an analysis of experimental data available in the literature together with a parameter adjustment to transmission and capture data obtained at the time-of-flight facility GELINA. The REFIT code [59] was used for the resonance shape analysis. A detailed description of the experimental data and the analysis in the resolved resonance region was reported by Volev et al. [206]. For neutron induced reactions in the unresolved resonance region the JENDL-4.0 evaluation for \(^{111}\hbox {Cd}\) and \(^{113}\hbox {Cd}\) was adopted. The evaluated files have been processed with the latest updates of NJOY.99 to test their format and application consistency as well as to produce a continuous-energy data library in ACE format for use in Monte Carlo codes. The ACE files have been utilised to study the effect of the evaluated resonance parameters on results of integral experiments. The production of the file together with its validation is described by Sirakov et al. [207].

2.2.10 Hafnium

Hafnium is a ductile metal which does not exist as a free element in nature. The stable hafnium isotopes for A = 174,176,177,178,179 and 180 are found combined in zirconium compounds with a respective natural abundance of \(0.16\%\), \(5.26\%\), \(18.60\%\), \(27.28\%\), \(13.62\%\) and \(35.08\%\). Hafnium is very corrosion resistant, has impressive mechanical properties and shows good absorption for thermal and epi-thermal neutrons. Due to these properties, it is commonly selected in reactor engineering as a neutron absorbing material in steel clad control rods to regulate the fission process.

Fig. 33
figure 33

The solid line represents the natural hafnium capture cross section calulated with the Reich–Moore formalism using the resonance parameters compiled in the JEFF library. The dashed lines show the contributions of the six hafnium isotopes

In JEFF-3.3, hafnium evaluations are based on the TENDL files produced in 2015 [5]. They were used as templates for the six stable hafnium isotopes. The resolved resonance parameters were replaced by those of Ref. [208]. The unresolved resonance parameters and the neutron cross sections above the upper energy limit of the resolved resonance range are from Ref. [209]. The covariance files for the neutron cross sections are derived from the work reported in Ref. [210].

In contrast, the ENDF/B-VII.1 resonance region data is taken from JEFF-3.1 for \(^{174,176,178,180}\hbox {Hf}\) and JENDL-3.3 for \(^{177,179}\hbox {Hf}\), with some adjustments to bound levels, RRR upper limits and URR average parameters. ENDF/B-VIII.0 [180] uses the ENDF/B-VII.1 resonance region data with cross sections and energy spectra above the resonance region produced by Kawano (LANL) using the CoH3 code in 2016.

The resolved resonance parameters established by Trbovich from RPI data [211] were introduced in the JEFF-3.1 evaluations. They were replaced by the new parameters determined with time-of-flight data measured at the GELINA facility of JRC-Geel [208]. The natural hafnium capture cross section reconstructed with the parameters compiled in the JEFF-3.3 (and JEFF-3.2) library is shown in Fig. 33. The complex resonance structure is dominated by the \(^{177}\hbox {Hf}\) isotope. The peak cross section values of the resonances at 1.1 eV and 2.4 eV reach respectively 5200 barns and 8800 barns (\(T=300\) K). For reactor applications, these two first \(^{177}\hbox {Hf}\) resonances represent the most important contribution to the Hf reactivity worth. Near 7.8 eV, one can distinguish the non-negligible contribution of the \(^{178}\hbox {Hf}\) isotope. Between 15 and 45 eV, the behavior of the natural Hf capture cross section is characterized by several multiplets of \(^{177}\hbox {Hf}\) resonances overlapping resonant structures of the \(^{179}\hbox {Hf}(\hbox {n}, \gamma )\) reaction.

Table 15 Upper energy limit of the resolved resonance range and number of resonances

In order to determine accurate resonance parameters, a wide experimental program was carried out at the JRC-Geel facility. Detailed explanations can be found in the PhD thesis of Tim Ware [212]. Sixteen sets of capture data were collected at different repetition rates (50 Hz, 800 Hz) and different flight paths (12.89 m, 28.82 m, 58.586 m) with 4 natural Hf samples (0.024 mm, 0.079 mm, 0.26 mm, 1 mm) and additional samples enriched in \(^{176}\hbox {Hf}\) (\(65\%\)), \(^{177}\hbox {Hf}\) (\(85.4\%\)), \(^{178}\hbox {Hf}\) (\(92.4\%\)) and \(^{179}\hbox {Hf}\) (\(72.1\%\)). The transmission of a thick natural Hf sample (16 mm) was also measured at the 49.34 m station. Resonance parameter were determined with the REFIT code [59]. Previous capture and transmission data were also included in the analysis such as those reported in Refs. [211, 213, 214]. As shown in the Table 15, the upper energy limits of the resolved resonance range and the number of resonances were significantly increased.

The variances and covariances of the Hf resonance parameters were obtained with the CONRAD code [153]. A retroactive analysis [215] was used in order to determine the resonance parameter covariance matrix without changing the resonance parameters reported in Refs. [208, 212]. Systematic uncertainties related to experimental parameters (normalisation, background, temperature ...) were propagated by using a marginalisation procedure [97]. Uncertainties on the thermal capture cross section and on the capture resonance integral were used as constraints. For the thermal capture cross sections and resonance integrals, we obtain:

$$\begin{aligned} \begin{array}{ccrclc} \sigma _{th}(174)&{}=&{}651 &{}\pm &{} 110 &{} (17\%), \\ \sigma _{th}(174)&{}=&{}651 &{}\pm &{} 110 &{} (17\%), \\ \sigma _{th}(176)&{}=&{}16.8 &{}\pm &{} 2.0 &{} (12\%), \\ \sigma _{th}(177)&{}=&{}371 &{}\pm &{} 13 &{} (3.5\%),\\ \sigma _{th}(178)&{}=&{}85 &{}\pm &{} 5 &{} (6\%), \\ \sigma _{th}(179)&{}=&{}40 &{}\pm &{} 3 &{} (7.5\%),\\ \sigma _{th}(180)&{}=&{}13.1 &{}\pm &{} 1.1 &{} (8.4\%),\\ \\ I_{\gamma }(174)&{}=&{}453 &{}\pm &{} 21 &{} (4.7\%), \\ I_{\gamma }(176)&{}=&{}634 &{}\pm &{} 21 &{} (3.2\%), \\ I_{\gamma }(177)&{}=&{}7165 &{}\pm &{} 218 &{} (3.0\%), \\ I_{\gamma }(178)&{}=&{}1798 &{}\pm &{} 64 &{} (3.5\%), \\ I_{\gamma }(179)&{}=&{}530 &{}\pm &{} 16 &{} (3.0\%), \\ I_{\gamma }(180)&{}=&{}37.4 &{}\pm &{} 1.8 &{} (4.8\%). \\ \end{array} \end{aligned}$$

Above the upper energy limit of the resolved resonance range up to 20 MeV was carried out as follows (for further details see Ref. [209]). The strength and originality of this work lie in the Reich–Moore interpretation of the resolved resonance range in association with optical model calculations based on parameters established by Morillon et al. [216, 217] with deformation parameters initially proposed by Avrigeanu et al. [218]. Links between the collision matrix elements calculated by the optical model code ECIS [155] and the average R-Matrix parameters (neutron strength function \(S_l\) and distant level parameters \(R_l^\infty \)) were established by using the ESTIMA [52] and SPRT methods [219]. Inherent difficulties in assessing unambiguous average resonance parameters from neutron spectroscopy measurements are not only the correct determination of the s-wave parameters but also the generalisation of the obtained results to higher order partial waves (\(l=1,2,3 \cdots \)). These difficulties can be partially solved with a sequential (and iterative) analysis of the low and high neutron energy ranges. The accuracy of the final results depends mainly of the quality of the experimental data available in the unresolved resonance range, and of the choice of the optical model parameters established for the nuclei involved in the nuclear reactions of interest. The consistency of the resulting neutron strength functions, mean level spacing and average radiation width was tested by comparing experimental total and capture cross sections with theoretical curves calculated with the nuclear data code CONRAD [153]. Results are reported in Fig. 34 up to 1 MeV.

Fig. 34
figure 34

Top: CONRAD results (open circle) and uncertainties (gray zones) compared with ECIS calculations based on the optical model parameters of Morillon et al. [216, 217] and Young (see Ref. [218]) using deformation parameters from Ref. [209]. Experimental data were measured at the VdG facility of Karlsruhe with the time-of-flight technique. Bottom: CONRAD results (solid line) and uncertainties (gray zones) obtained by using the average parameters and the uncertainties reported in Ref. [209]. They are compared with calculations (dashed line) based on the local approach and parameters given in Ref. [218] with the average radiation widths of Ref. [209]. The experimental data were retrieved from the EXFOR data base [179]

Fig. 35
figure 35

Relative uncertainties in % (top) and correlation matrix for the \(^{177}\hbox {Hf}(\hbox {n}, \gamma )\) reaction up to 20 MeV. The ordinate scales are neutron energy in eV

For JEFF-3.3, the neutron cross section files up to 20 MeV were produced with the TALYS code [5]. The option for unresolved resonance calculation implemented in TALYS allows users to simultaneously create a consistent set of unresolved resonance parameters. Covariances between the neutron cross sections were generated with a two-step CONRAD calculation, involving a standard least-square fit followed by the marginalisation of the nuisance parameter uncertainties. Results for the \(^{177}\hbox {Hf}(\hbox {n}, \gamma )\) reaction is shown in Fig. 35.

Trends for the natural hafnium capture cross section have been deduced from critical experiments performed in zero-power reactors located at Cadarache [220,221,222]. Interpretations of these experiments with the APOLLO2 deterministic lattice code [82] and with the Monte-Carlo code TRIPOLI-4® [53] have demonstrated the good description of the low energy natural hafnium capture cross section compiled in the JEFF-3.1.1 and JEFF-3.2 libraries. Integral trends obtained for the CAMELEON and AMMON programs are summarized in Table 16. Discrepancies between the calculated and experimental reactivity worth remain less than \(3\%\) on average. The slight increase of the reactivity worth (\(+0.5\%\)) indicates that the capture resonance integral in JEFF-3.1.1 [211] and JEFF-3.2 [208] are consistent. Similar trends are expected with the hafnium evaluations of the JEFF-3.3 library, as JEFF-3.3 and JEFF-3.2 evaluations share the same resolved resonance parameters.

Impact of the Hf nuclear data accuracy on integral calculations were investigated with the experimental data measured in the frame of the CAMELEON program [210]. Final uncertainties are reported in Table 17 for two CAMELEON configurations (17 Hf pins, 25 Hf pins). Results obtained for each configuration differ from a factor 1.5 which is consistent with the ratio between the Hf reactivity worth of \(\sim 10,000~ \hbox {pcm}\) (25 Hf pins) and \(\sim 7000 \, \hbox {pcm}\) (17 Hf pins). The global uncertainty of \(\sim \)300 pcm (\(3\%\)) is consistent with the integral trends reported in Table 16.

2.2.11 Tantalum

Nuclear data for \(\hbox {n} + {}^{181}\hbox {Ta}\) were evaluated for JEFF-3.2 and this evaluation was adopted for JEFF-3.3. The GNASH Hauser–Feshbach code described in Ref. [236] was used, which includes statistical, pre-equilibrium and direct-reaction models. The global optical model potentials of Koning and Delaroche [237] were used in coupled-channels calculations for incident neutrons and protons in the energy region from 0 to 150 MeV. The Bojowald potential [238] was used for deuterons. For tritons and \(^3\hbox {He}\) the simplified folding approach of Watanabe [239] was used with the neutron and proton potentials of Ref. [237]. This approach leads to underestimation of cross sections for all energies. Below 20 MeV (n,t) and (n,\(^3\hbox {He}\)) cross sections were calculated by folding with the Becchetti-Greenlees potential [240]. For alphas the Avrigeanu global potential was used [202]. The ECIS code [155] was used for the couple-channels and Distorted Wave Born Approximation (DWBA) calculations. The gamma transmission coefficients were calculated using the Kopecky-Uhl model [241]. The parameters of Gurevich [242] were used for the description of the giant dipole resonances. The model of collective excitations [243] included for continuum inelastic scattering and the GNASH multiple particle emission option improved the neutron emission spectra.

The resonance range evaluation was taken from JENDL-3.3 [122]. Elastic scattering cross sections and angular distribution in the range from 0.5-3 MeV are from JENDL-3.3, as well. For the (n,2n) reaction JEFF-3.0 activation data are taken below 12 MeV neutron energy. This gives an excellent description of the data by Fréhaut et al. when renormalized by a factor 1.1 [225]. Above 12 MeV the GNASH results are taken. Below 4 MeV the neutron capture cross section is from JENDL-3.3 and above the GNASH results normalized to the JENDL data are used. The capture gamma-rays are from JENDL-3.3. For the (n,p) channel the GNASH calculation is normalized to the data of Refs. [234, 235]. GNASH (n,t) channel estimates are normalized to the systematics of Ref. [244].

Table 16 Integral trends on the Hf reactivity worth calculated with the Monte-Carlo code TRIPOLI-4®[53] for the CAMELEON (17 and 25 Hf pins) and AMMON program carried out in the EOLE facility of CEA Cadarache
Table 17 Reactivity worth uncertainty (in pcm) due to the accuracy on the Hf capture cross sections. The Hf reactivity worths calculated with APOLLO2 are close to 7000 pcm and 10,000 pcm for the 17 Hf and 25 Hf pins configurations, respectively
Fig. 36
figure 36

Experimental data for \(\hbox {n} + {}^{181}\hbox {Ta}\) cross sections and spectra compared with the JEFF-3.3 evaluation, TENDL-2017 and ENDF/B-VIII.0. The JEFF-3.2 evaluation was adopted in JEFF-3.3. The data are from Refs. [223,224,225,226,227,228,229,230,231,232,233,234,235]

Results for the \(^{181}\hbox {Ta}(\hbox {n}, \hbox {2n}) {}^{180}\hbox {Ta}\), \(^{181}\hbox {Ta} (\hbox {n}, \hbox {p}) {}^{181}\hbox {Hf}\), \(^{181}\hbox {Ta} (\hbox {n}, \hbox {3n}) {}^{178}\hbox {Ta}\) and \(^{181}\hbox {Ta} (\hbox {n}, \alpha )^{178}\hbox {Lu}\) cross sections and the \(^{181}\hbox {Ta}\)(n, xn) spectra for 6.7 MeV and 14 MeV incident neutrons are shown in Fig. 36. The evaluation agrees well with the experimental data and clearly compares well with the recent TENDL-2017 and ENDF/B-VIII.0 evaluations. Differences between evaluations are noteworthy for the (n,p) and (n,3n) cross sections and for the neutron emission spectra in the energy region just below the incident neutron energy.

Fig. 37
figure 37

Comparisons of the JEFF-3.3 evaluation for \(\hbox {n} + {}^{182,184,186,nat}\hbox {W}\) to experimental data and the TENDL-2017, JENDL-4 and ENDF/B-VIII.0 evaluations. Some cross sections, angular distributions and spectral are shown

2.2.12 Tungsten

New evaluations of neutron induced cross-sections up to 150 MeV were performed for the stable \(^{182,183,184,186}\hbox {W}\) isotopes [245]. A good description of the available total cross section and neutron elastic and inelastic (differential) cross section data was obtained by adapting the optical potentials of Koning and Delaroche [237] and Young. The reaction data were calculated with ECIS95 and GNASH using both global and local potentials for neutrons, protons, deuterons, tritons and alphas and taking into account collective excitations.

In Fig. 37 the JEFF-3.3 evaluation is compared with experimental data, the TENDL-2017, JENDL-4 and ENDF/B-VIII evaluations. The evaluated JEFF-3.3 total cross sections for \(\hbox {n} + {}^{182,184,186}\hbox {W}\) follow the data well above 10 MeV and are in reasonable agreement with the data below that energy, although the evaluation is clearly on the low-side of the data for \(\hbox {n} + {}^{182,184}\hbox {W}\). The other evaluations are higher for these nuclides but none is uniformly best. The \(^{184,186}\hbox {W}\)(n,2n) cross section data are well described by the JEFF-3.3 evaluation and the latter compares well with ENDF/BVIII.0 and TENDL-2017. The data for inelastic scattering to the second level (\(4^+\)) of \(^{182}\hbox {W}\) and the first level (\(2+\)) in \(^{186}\hbox {W}\) compare best with ENDF/B-VIII.0, while JEFF-3.3 is somewhat low near the maximum and TENDL-2017 is respectively in the middle and high. Angular distribution data for one particular energy above the maximum are shown for each of these cases. The distributions are similarly described by the three libraries and the normalization differences reflect the difference in cross section.

Good agreement is observed for JEFF-3.3 with the (n,xn) neutron spectra at 14 and 26 MeV. Also the elastic scattering angular distribution of JEFF-3.3 at 14 MeV for natural tungsten describes the available data reasonably well up to a scattering angle of 100 degrees after which only JENDL-4 remains in reasonable agreement with the data.

The evaluations were further optimized to obtain good agreement for the available data for the (n,p), (n,\(\alpha \)) reaction cross sections on \(^{182,183,184,186}\hbox {W}\) and the remaining experimental data not shown in the figure.

Neutron resonance parameters for the \(^{182,183,184,186}\hbox {W}\) isotopes were obtained in the energy region below 2 keV from a resonance shape analysis with REFIT of transmission and capture data that were measured at GELINA [63]. Details about the measurements and the analysis are given in Reference [246]. Starting parameters for the least squares adjustment were obtained by combining the results of transmission and capture measurements reported by Camarda et al. [247] and Macklin et al. [248], respectively. The parameters of negative resonances have been adjusted to match the coherent scattering lenghs of Ref. [249] and the capture cross sections at thermal energy of Ref. [250]. General purpose data files for transport calculations were prepared in ENDF-6 data format, processed with NJOY [41] and tested with MCNP calculations of the output ACE files.

2.2.13 Gold

An evaluation for neutron induced interactions with \(^{197}\hbox {Au}\) in the resolved and unresolved resonance region was produced starting from the ENDF/B-VII.1 library file [121]. Despite the importance of neutron capture reactions on gold in the energy region between 5 keV and 150 keV for astrophysical applications, no unresolved resonance region (URR) has previously been considered in the major general purpose nuclear data libraries, in particular in ENDF/B-VII.1 [121]. This was a reason for the former unjustified extension of the resolved resonance region (RRR) up to 5 keV. The only other evaluation for \(^{197}\hbox {Au}\) in terms of average resonance parameters can be found in the TENDL nuclear data library [5]. Unfortunately, this evaluation was performed with incorrect values of the elastic degrees of freedom for five of the spin sequences. In addition, the upper limit of the URR is restricted up to the inelastic scattering threshold of 77.75 keV.

To evaluate the cross section data for \(^{197}\hbox {Au}\) in the RRR the resolved resonance parameters in ENDF/B-VII.1 [121] were inspected and partly revised based on a resonance shape analysis of transmission, capture and self-indication data using the REFIT code [59]. The experimental data were obtained at the time-of-flight facility GELINA [63] by Massimi et al. [251]. The upper limit of 5 keV of the RRR, as adopted in ENDF/B-VII.1, was reduced to 2 keV due to the lack of reliable capture data above 2 keV which are needed for the analysis of weak resonances. This solution seems to be a more justified alternative than generating unobserved ‘resolved’ resonances as in the IRDFF file of Ref. [252]. In addition, it resulted in a better agreement between calculated and experimental results of lead slowing-down experiments (Ref. [253]). The sum of the p- and d-wave contribution to the capture cross section at the 2-keV boundary of the RRR was estimated to be 86 mb or about 2%. This estimation was based on the average parameters resulting from the URR evaluation. To match the capture cross section at the boundary between the RRR and URR, a smoothly increasing background cross section was introduced from thermal energy to 2 keV as compensation for the missing p- and d-waves. This procedure is similar to the one used in the IRDFF file [252]. Parameters of the negative resonance with \(J = 2\) were adjusted to reproduce both the thermal capture cross ection \(\sigma _{\gamma }=98.67(10)~\hbox {b}\) by Holden and Holden [254] and the bound coherent scattering length \(b_{c}~=~7.9~(7)~\mathrm{fm}\) by Koester et al. [65]. The value of Holden and Holden [254] is also adopted in the 2009 standards file of Carlson et al. [27]. The corresponding calculated cross sections at thermal energy together with some resonance integrals are summarised in the file description.

Fig. 38
figure 38

Left: Average total cross section for neutron induced reactions in \(^{197}\hbox {Au}\) as a function of neutron energy in the URR. The cross section in JEFF-3.3 is compared with the experimental data of Seth et al. [255], Purtov et al. [256] and Sirakov et al. [253] and with the one recommended in ENDF/B-VII.1 [121]. Right: Average neutron induced capture cross section for \(^{197}\hbox {Au}\) as a function of neutron energy in the URR. The cross section in JEFF-3.3 is compared with the one recommended by Carlson et al. [27] and the experimental data of Massimi et al. [257]

The evaluation of the URR between 2 keV and 100 keV is based on a generalised single-level representation compatible with the energy-dependent option of the ENDF-6 format as described in Ref. [258]. The average partial cross sections are expressed in terms of transmission coefficients by applying the Hauser–Feshbach statistical reaction theory including width fluctuations. The transmission coefficients and the scattering radius were deduced from a combined analysis of the capture cross section resulting from the standards evaluation project [27] and theoretical non-fluctuating cross sections derived from a dispersive coupled channel optical model [70]. The parameters at zero energy used to describe the average total and partial cross sections were: a hard-sphere scattering radius independent from the orbital angular momentum \(\ell \); neutron strength functions for s-, p- and d-wave (\(\ell =0,1\) and 2) and capture transmission coefficients for positive and negative parity. The neutron strength functions and scattering radius were adjusted to reproduce both the compound formation cross sections and the shape elastic cross section of the dispersive coupled channel optical model (DCCOM) potential RIPL1483 derived by Capote et al. [70]. The DCCOM smooth and weak energy dependence at energies below 100 keV were approximated by second order polynomials. The coupled-channel OPTMAN code [95, 259] incorporated into the EMPIRE system [102] was used for the optical model calculations. The capture transmission coefficients at zero energy were adjusted by fitting to the capture cross section recommended by Carlson et al. [27]. This cross section, which resulted from international cooperative efforts of the IAEA, NEA, and CSEWG to improve cross section standards for neutron induced reactions, was based on a simultaneous analysis of data from 62 experiments that are specified in Refs. [27, 260]. The evaluated average parameters together with their relative uncertainty and correlation matrix are reported in the description of the library file. The covariance matrix was calculated for the present ENDF-6 convention supposing a zero uncertainty for the scattering radius. A small background capture cross section was introduced between 3.75 keV and 11.75 keV to make the capture cross section in this energy region identical to the one of Carslon et al. [27].

The total cross section from 5 to 20 keV in ENDF/B-VII.1 is substantially (up to 15%) lower than the results of the DCCOM and the present evaluation. This is mainly due to the fact that the cross section in ENDF/B-VII.1 is largely based on the data by Seth et al. [255] and disregard the data by Purtov et al. [256]. Measures were taken in the URR to reduce the non-Hauser–Feshbach processing for the \(J^{\pi }\)-sequences (\(1^{+}, 2^{+}\)) of double-orbital contribution. The flexibility of the ENDF-6 format was used to achieve this goal. As known, the above short-coming is due to the ENDF-6 simplifying (but anti-Hauser–Feshbach) assumption for orbital momentum conservation. The latter removes the competition e.g. of the s-wave elastic channel for the above d-wave reactions. The effect for gold at 100 keV reaches an increase of 10% in the capture cross section. To solve the problem, a reduction and adjustment of the corresponding d-wave contribution was used. The total cross section remains intact in such a procedure, so that the elastic cross sections is also corrected. The results were compared making use of a URR code that can process with and without the assumption for \(\ell \)-conservation.

The results of the present evaluation were validated by a comparison with results of transmission [253] and capture [257] experiments carried out at the time-of-flight facility GELINA. The results of these experiments were not included in the present evaluation. The good agreement between the experimental and evaluated data in the URR is shown in Fig. 38, for the total and capture cross section. The capture cross section resulting from the latest neutron standards evaluation reported by Carlson et al. [40], which included the data of Massimi et alo. [257], is also shown in Fig. 38. In addition, ACE files were produced to compare results of Monte Carlo simulations using the MCNP-5 code [72] and results of measurements with a lead slowing-down spectrometer carried out by Perrot et al. [261]. Also this comparison shows a good agreement between the cross section data in JEFF-3.3 and the experimental results. A more detailed discussion on this validation exercise can be found in Reference [253].

2.2.14 Lead

The neutron transport sublibraries for \(^{204,206,207,208}\hbox {Pb}\) of JENDL-4 were adopted in JEFF-3.3. Above the resonance region modifications were made to the inelastic cross sections due to experimental data reported in Refs. [178, 262]. The choice of JENDL-4 is based on a study of nuclear data relevant for MYRRHA as part of the CHANDA project. The quality of the data recommended in independent versions of the main data libraries, i.e. CENDL, ENDF, JENDL, JEFF and TENDL, was verified using energy dependent microscopic cross section data and results of integral measurements including lead slowing down and integral benchmark experiments.

The inelastic scattering cross sections in JENDL-4 were modified for \(^{206,207,208}\hbox {Pb}\) on the basis of time-of-flight data taken at the GELINA facility of the JRC Geel, i.e. data for \(^{207,208}\hbox {Pb}\) reported by Mihailescu et al. [262] and those for \(^{206}\hbox {Pb}\) reported by Negret et al. [178]. The data of Mihailescu et al. [262] were renormalized according to the procedure described in Ref. [178] and as detailed in the respective EXFOR entries [179]. For \(^{206}\hbox {Pb}\) the cross sections of Reference [178] were adopted up to 3.1 MeV for levels 1,3-10. For \(^{207}\hbox {Pb}\) the cross sections from Mihailescu et al. [263] were taken for levels 1-2,4-6 and 8 up to 3.2 MeV and for \(^{208}\hbox {Pb}\) the levels 1-3 up to 4.1 MeV. From these maximum energies to 20 MeV a linear factor was used to multiply the JENDL-4.0 evaluation for each affected level to ensure continuity at the transition energy and no correction above 20 MeV. The total cross section of JENDL-4.0 was left unchanged by modifying the elastic cross section to respect the sum rule.

2.2.15 Bismuth

A study of cross section data for neutron interactions with Bi was part of the CHANDA project. Similar to the evaluations for the Pb isotopes, the JEFF-3.3 file for \(^{209}\hbox {Bi}\) was created using JENDL-4.0 as a basis and by including modifications based on results of inelastic scattering cross section measurements by Mihailescu et al. [264] at GELINA. The time-of-flight data for level inelastic cross sections of [264] were used to replace the cross sections for the levels 1-11 up to 4 MeV. The data were renormalised following the same procedure as the one applied for the Pb isotopes.

Fig. 39
figure 39

Comparison of the branching ratio BR=\(\sigma _{\gamma }/\sigma _{\text {m}}\) of the capture cross section to the ground state \(^{209}\hbox {Bi}(\hbox {n}, \gamma )^{210g}\hbox {Bi}\) and to the isomeric state \(^{209}\hbox {Bi}(\hbox {n}, \gamma )^{210m}\hbox {Bi}\) as a function of incident neutron energy. The ratios resulting from measurements of Refs. [265, 266] are compared with the ratios derived from the evaluated cross sections in the JENDL-4.0, JEFF-3.2, BROND-3.1, JENDL/A-96 and ROSFOND-2010 libraries

Neutron capture on \(^{\text {209}}\hbox {Bi}\) leads to the formation of \(^{\text {210}}\hbox {Po}\) through the decay of \(^{\text {209}}\hbox {Bi}\) in its ground state. Since \(^{\text {210}}\hbox {Po}\) is a highly radiotoxic nuclide, it is an important contribution of the radioactive source term of a LBE coolant. To predict the production of \(^{\text {210}}\hbox {Po}\) the branching ratio \(\hbox {BR} = \sigma _{\gamma }/\sigma _{\text {m}})\), i.e. the ratio of the cross section \(\sigma _{\gamma }\) for production of the ground state \(^{\text {210g}}\hbox {Bi}\) to the cross section \(\sigma _{\text {m}}\) for production of the isomeric state \(^{\text {210m}}\hbox {Bi}\), is required. Unfortunately, the energy dependence of this BR is difficult to measure. Experimental data that can be used to evaluate this ratio above thermal energy are limited to the results of activation measurements at 30 keV and 534 keV by Saito et al. [265], and measurements by Borella et al. [267] at GELINA. The BR derived from these experimental data together with the one derived from measurements at the cold neutron beam of the research reactor in Budapest [266] are plotted as a function of energy in fig. 39. The BR obtained from \(^{209}\hbox {Bi}(\hbox {n}, \gamma )\) cross sections in the JENDL-4.0, JEFF-3.2, BROND-3.1, JENDL/A-96 and ROSFOND-2010 files are also shown.

At low energies, the BR in JENDL-4.0, JEFF-3.2 and BROND-3.1 are consistent with the experimental value determined in Ref. [266]. The BR from the JENDL/A-96 and ROSFOND-2010 files are larger by a factor 6.7 and 1.8, respectively. In general the best agreement between experimental and evaluated BR is obtained with the BROND-3.1 data. Therefore, this BR that has not been included in JEFF-3.3 file for \(^{\text {209}}\hbox {Bi}\) is recommended for future JEFF-4.0 evaluation. Nevertheless, to reduce the uncertainty on the estimated production of \(^{\text {210}}\hbox {Po}\) additional experimental data of the energy dependent BR are required. In addition, results obtained within the CHANDA project reveal that both the total and capture cross sections of \(^{\text {209}}\hbox {Bi}\) can be improved by new TOF cross section measurements.

2.3 Use of TALYS and TENDL

In its latest release, the JEFF library uses 312 TENDL-2015 evaluations for the neutron sub-library. This is not a unique step in the recent JEFF history, as the JEFF-3.2 library already used about 150 evaluations from TENDL-2012. Additionally, the complete charged-particle and photon sub-libraries from TENDL-2017 are also adopted in JEFF-3.3 and the JEFF-3.3 neutron activation sub-library corresponds to TENDL-2017 neutron sub-library produced in the European Activation File (EAF) format. Details about these evaluations are given below.

2.3.1 The TENDL environment

A short description of the TENDL methodology will be presented here. For further details, see the different references proposed in this section.

TENDL stands for the “Talys Evaluated Nuclear Data Library” and it has been produced since 2008. In its early versions, it was largely based on the TALYS nuclear reaction code [43] and the TEFAL data parsing program. Over the years, the TENDL production relied on additional codes, such as TASMAN (for the production of random model parameters), TARES (for the resonance range), TAFIS (for the number of fission neutrons \({\overline{\nu }}\) and fission yields) and TANES (for the prompt fission spectra). These six programs (all starting with a “T”) are simply named T6 and are driven by the wrapping script “autotalys”, allowing to produce the full TENDL library.

Additional databases are used within T6 by the different programs. One such database contains all the necessary model parameters to produce the adequate nuclear data quantities. The adjustment of such model parameters, as for any other evaluation work, represents the traditional evaluation effort. All the other aspects, including the formatting, checking and processing, are taken care of by the T6 system. In some regards, TENDL can be seen as an output database of the T6 system.

A special feature of the T6 system of particular help in the evaluation process is referred to as “autonorming”. In the TENDL evaluation process, the evaluator first adjusts the different model parameters (as for TALYS), in order to reproduce the desired experimental data. In some cases, the different models do not have the required flexibility, possibly due to theoretical shortcomings. A solution is then to calculate the ratio between the desired cross section and the calculated cross sections, and to multiply all related quantities by this ratio. In this way, the desired cross sections are obtained, together will the other quantities such as angular or energy distributions.

The TASMAN code can generate sampled model parameters to provide varied inputs that simulate the space of possible evaluations based on our understanding of the input parameters and their uncertainties. This code is used for the generation of the covariance matrices using a Monte Carlo approach. Before 2015, all model parameters were sampled using un-correlated multi-variate Gaussian distributions. The widths of such distributions were chosen so that selected experimental data from the EXFOR database were covered by the random cross sections obtained from the use of random parameters (see Ref. [268] for details). From 2015 a different method is used, known as the Bayesian Monte Carlo (BMC) approach (see Refs. [269,270,271] for details). This is a two-step approach where the model parameters are first sampled in an independent and uniform manner, with a relatively large standard deviation – typically 5 times larger than the normally adopted value. A comparison with selected experimental differential cross sections is performed and each random realisation is weighted according to its agreement with the experimental values. A weighted distribution is then obtained for each model parameter, reflecting the experimental data information. An example is presented in Fig. 40 for the optical model parameter \({\hbox {a}}_v\) of \(^{30}\hbox {Si}\).

Fig. 40
figure 40

Example of the posterior parameter distribution obtained with the TENDL Bayesian Monte Carlo method (BMC) for the optical model parameter \(a_{\text {v}}\) of \(^{30}\hbox {Si}\). The prior distribution, not shown here, is uniform

In a second step, a sampling based on the posterior parameter distributions is done to generate the TENDL random cross sections. In this way covariance matrices can be obtained from calculating the moments associated with these samples. They are formatted with TEFAL in the MF33 format and added to the nominal TENDL file.Footnote 4

In the resonance range, a different approach is followed. The cross sections are not represented in a pointwise format, but rather with resonance parameters, following the MF2 format. The following steps are followed:

  • resonance parameters are obtained from compilations or experimental databases;

  • uncertainties for the bound levels and the low energy resonance are estimated to reproduce the thermal cross section uncertainties;

  • such parameters and their uncertainties are used by SAMMY and the retroactive method to generate a complete parameter covariance matrix, as well as a cross section covariance matrix; and

  • these matrices, in the MF32 or MF33 format are included in the TENDL nominal file.

Up to (and including) the TENDL-2015 version, the MF32 data is calculated and stored in the resonance range. Starting from the 2017 TENDL version, the MF33 format is used in the resonance range, merged with the MF33 file coming from the fast energy range, allowing to use cross section covariances over the entire energy range. In general, TENDL evaluations contain MF31-35 and MF40 for various types of covariance data.

In the following, specific details for each sub-library adopted in JEFF-3.3 are presented.

2.3.2 Neutron files

As mentioned, a total of 312 TENDL-2015 evaluations were adopted in JEFF-3.3. The complete list is too long to be given here, but some representative examples are presented in the following.

Stable isotopes

Table 18 The 111 stable nuclide evaluations from TENDL adopted in the JEFF-3.3 neutron sub-library

The majority of the adopted TENDL files are not for stable isotopes, although for 111 stables isotopes listed in Table 18 TENDL-2015 was adopted. These isotopes were either not present in the previous JEFF releases, or were present in the form of very incomplete evaluations (e.g. only cross sections were given, without the so-called MF6, or gamma production data). These TENDL evaluations allow JEFF-3.3 to globally bring a uniform and complete format. An example of improvements from JEFF-3.2 to JEFF-3.3 are presented in Fig. 41 for a specific stable isotope.

Fig. 41
figure 41

Example of the new evaluated capture cross section for the \(^{102}\hbox {Pd}\) stable isotope from TENDL

Filling the gaps

Many TENDL-2015 isotopes adopted in JEFF-3.3 are long-lived isotopes, allowing to provide a full isotopic chain for specific elements, complemented with original JEFF evaluations or evaluations adopted from other libraries. This is of importance for activation calculations, as demonstrated in Ref. [273]. Due to the TENDL data, more complete chains can be found for C, O, Si, P, S, Cl, Ar, Ca or Sc, amongst others. Isotopes from TENDL have been adopted so that at least all isotopes with a half life longer than 1 year are now in JEFF. For many of these isotopes, experimental data are relatively scarce, and the evaluations heavily rely on default TALYS calculations in the fast neutron range and on systematics in the resonance range. In the resonance range, the so-called High Fidelity Resonance (HFR) method is applied, producing statistically-generated resonances where no measurement exists [274]. The HFR approach utilises average resonance parameters from TALYS calculations extended to the low energy region. Such parameters can either be formatted using the unresolved formalism, or used to generate one set of resonances calculated from statistical sampling of these parameters. Such resonances are then adjusted to reproduce thermal cross sections from a systematics developed for the EAF library [275]. It also allows TENDL to reach consistency between the low and high energy range, as the TALYS parameters are used from 0 to 200 MeV. The prediction of thermal cross sections is almost impossible, due to the fact that only a very limited number of resonances determines these values and thus no statistical assumption can be applied. However, in spite of the expected very large uncertainty in these predictions, they account at least for the global trends. Starting from the expression for the average capture cross section in the statistical region, after several simplifications, the parameterised formula

$$\begin{aligned} \sigma _{\mathrm{th}}(n,\gamma )=C \times (a \times U)^x \end{aligned}$$

can be used to fit the constants C and x to the measured data. U is the effective excitation energy defined as the neutron separation energy minus the pairing energy, and a is the level density parameter. The application of this approach at 30 keV is generally justified, however, at thermal energy the influence of the resonance region on the cross section value is dominant and any dependence on \(a\times U\) is masked by large Porter-Thomas fluctuations. Nevertheless, a least square fit was applied to the thermal cross section data. In the case of the fission cross section, we use \(\sigma _{\mathrm{th}}(n,f)=\sigma _{\mathrm{th}}(n,\gamma )/(A^2/15930)\) for non-fissile nuclei, and \(\sigma _{\mathrm{th}}(n,f)=\sigma _{\mathrm{th}}(n,\gamma )\times (A^2/1593)\) for the other ones. An example for the capture cross section of \(^{58}\hbox {Co}\) is presented in Fig. 42, showing the improvement in the resonance range compared to the JEFF-3.2 library.

Fig. 42
figure 42

Example of the new evaluated capture cross section for the short-lived \(^{58}\hbox {Co}\) isotope (\({\hbox {t}}_{1/2}=70\) days) from TENDL

Meta-stable states

The final category for the isotopes coming from the TENDL-2015 library concerns the evaluations for reactions on the relatively long-lived isomeric states as targets. These were relatively few in number in the JEFF-3.2 library (12, from which 4 came from TENDL-2012), and are still limited in JEFF-3.3 with 16 evaluations. Among these 16, 12 evaluations come from TENDL-2015: \(^{58m}\hbox {Co}\), \(^{62m}\hbox {Co}\), \(^{84m}\hbox {Nb}\), \(^{106m}\hbox {Ag}\), \(^{127m,129m,131m}\hbox {Te}\), \(^{135m}\hbox {Xe}\), \(^{148m}\hbox {Pm}\), \(^{152m}\hbox {Eu}\), \(^{166m}\hbox {Ho}\) and \(^{180m}\hbox {Ta}\). For these isotopes, a limited amount of measurements are usually available, and the same approach as for the previous category is applied. If the thermal capture cross section is not known, a similar systematics as in Eq. (2) is used, multiplied by the ratio of the average radiation width of the isomer over the one for the ground state.

2.3.3 Photon and charged particle sub-libraries

Following the same approach as for the neutron sub-library, charged particle induced evaluations are produced with TALYS. JEFF-3.3 takes advantage of the TENDL-2017 data (not 2015) by adopting the entire sub-libraries for incident protons, deuterons, helions, tritons, alphas and gammas. In total, there are 2804 proton evaluations, 2811 deuteron evaluations, 2805 triton evaluations, 2806 He3 evaluations, 2809 alpha evaluations and 2809 gamma evaluations. To compensate for the weakness of the TALYS models for the light elements, a number of isotopic evaluations are imported from the ENDF/B-VIII library and are replacing the original TALYS files. These include all the isotopes below \(^{19}\hbox {F}\) which are included in ENDF/B-VIII [180].

Covariance matrices based on a simple Monte Carlo approach are included for proton and gamma induced reactions. The applied procedure is not the BMC method, but a simple variation of all input parameters using default input parameter distributions.

2.4 Gamma emission

2.4.1 Fission products

In 2011, a study was undertaken to provide gamma production data for 89 major fission products. The optimal solution would be to automatically adopt all available data from EGAF [276], but this feature has not yet been added to the TENDL library. Instead, for all 89 nuclides capture gamma data from the TENDL-2011 evaluated library replaced the existing capture gamma data, with cross-section data taken from either JEFF-3.1.1 or ENDF/B-VII.0. This implies that the capture gamma-rays are obtained from a TALYS calculation combining continuum and discrete level decay as described in Ref. [43]. These fission product files were released in JEFF-3.1.2 and retained for JEFF-3.2.

For JEFF-3.3, new or updated evaluations have been adopted for many of the 89 fission products and a significant number of these did not include gamma production data. It was necessary to reinstate the gamma production data for these nuclides. This was done by following the methodology of the earlier study by adopting gamma production data from the TENDL library. For JEFF-3.3, the required data were taken TENDL-2015.

There were two classes of nuclides for which the gamma production data needed to be reinstated. The first included those nuclides for which there were no capture gamma data in the evaluations adopted for JEFF-3.3. The nuclides in this class were Ru-102, Ru-103, Ru-104, Pd-107, I-131, I-135, Xe-130, Xe-132, Xe-134, Xe-136, Ba-134, La-139, Ce-141, Pr-143, Pm-148m, Eu-154 and Eu-155.

The second set were nuclides for which the evaluated files contained capture gamma data but as continuum spectra only, with no discrete gamma lines. For the majority of these, the files were taken from ENDF/B-VII.1 and the gamma data were unchanged from the ENDF/B-VII.0 data that were considered in the original study. Thus, the original decision, to replace the gamma data for these files, was still valid. For these nuclides, the existing MF6/MT102 data were replaced by discrete data taken from TENDL-2015. The nuclides in this class were; Y-89, Zr-93, Mo-95, Pd-104, Pd-105, Pd-106, Pd-108, Cs-133, Cs-135, Pr-141, Nd-144, Nd-146, Nd-147, Pm-149, Pm-151, Sm-144, Sm-148, Sm-149, Sm-153, Sm-154, Eu-157, Dy-161, Dy-162 and Dy-163.

For the remainder of the 89 fission product nuclides, gamma production data were already present in the evaluated files adopted for JEFF-3.3 and no update was necessary. These again fell into two sets. The first, covered nuclides that were either unchanged from JEFF-3.2, adopted from TENDL-2015 or were new evaluations that included discrete capture gamma data. The nuclides in this set were; Zr-91, Zr-95, Zr-96, Tc-99, Ru-105, Rh-103, Ag-109, I-127, I-129, Xe-135, Pm-147, Pm-148, Gd-155, Gd-156, Gd-157, Gd-158, Cd-110, Cd-111, Cd-113, Kr-83, Ru-100, Ru-101, Rh-105, Xe-131, Cs-134, Cs-137, Nd-143, Nd-145, Nd-148, Nd-150, Sm-147, Sm-150, Sm-151, Sm-152, Eu-153, Eu-156 and Tb-159.

The final set were files that were adopted from JENDL-4.0 evaluations that contained gamma data only for the total non-elastic reaction and not for individual reactions. As the capture component could not be isolated in these data, the choice was either to retain the existing JENDL-4.0 gamma data or replace all the gamma data with MF6 MT102 data taken from TENDL-2015. The decision was taken to retain the JENDL-4.0 gamma data as the alternative involved the loss of some data. The nuclides in this set were; Nb-95, Mo-96, Mo-97, Mo-98, Mo-100, In-113, In-115, Xe-128, Xe-129, Xe-133, Ce-142 and Ce-144.

2.4.2 TALYS and EGAF

Gamma emission evaluations for neutron radiative capture by \(^{54, 56, 56, 58}\hbox {Fe}\), \(^{107, 109}\hbox {Ag}\), \(^{113, 115}\hbox {In}\), \(^{113}\hbox {Cd}\), \(^{155, 157}\hbox {Gd}\), \(^{174, 177, 178, 179, 180}\hbox {Hf}\) were made combining TALYS calculations with the discrete gamma-rays from the EGAF database. These were included in JEFF-3.2. They were taken over in JEFF-3.3 except for \(^{107}\hbox {Ag}\) and \(^{113, 115}\hbox {In}\) for which other evaluations were adopted (TENDL-2015 and JENDL-4). The evaluations correct major deficiencies in total gamma-energy release for predecessors of JEFF-3.2. Above 1 keV incident neutron energy the evaluated file sections were entirely made with the TALYS code. The default composite Gilbert-Cameron model was used for the level density model and the default Kopecky-Uhl model for the gamma-ray strength function [5, 43]. Below a neutron energy of 1 keV use was made of the Evaluated Gamma-ray Activation File (EGAF [276]) to include an evaluated set of experimentally determined discrete gamma-rays. These were judiciously combined with estimates for the continuum contribution made with TALYS. For the iron nuclides the discrete data were so complete that a continuum contribution was not needed (it would be redundant). Even when the continuum contribution was dominant, such as for silver and hafnium, important corrections result from including the discrete gamma-rays from EGAF. The gamma emission data were stored in the MF6/MT102 section.

2.4.3 Prompt fission gammas

Motivation for new evaluations

For several years and following the request from the High Priority Request List (HPRL) [277], significant efforts have been made by the community of experimenters to improve our knowledge of the prompt fission gamma characteristics (spectra, multiplicities and energies). These characteristics are very important for the modeling of current and innovative reactors. According to Rimpault et al. and Luthi et al. [278, 279], the \(\gamma \)-heating in the center of a typical fast reactor core comes from several components:

  • 20% from the \(\gamma \) produced in radiative capture;

  • 10% from the inelastic scattering reactions;

  • 30% from the delayed \(\gamma \) produced by fission products; and

  • 40% from the prompt \(\gamma \) emitted by fission fragments.

The first three components are rather well known, while the fourth is poorly known. In the previous JEFF evaluated nuclear data files (JEF-2.2, JEFF-3.1.1, JEFF-3.1 and JEFF-3.2), evaluations of both Prompt Fission Gamma Spectra (PFGS) and Prompt Fission Gamma Multiplicities (PFGM) were based on measurements from the 1970s. In addition, PFGS was not given for the \(^{241}\hbox {Pu(n,f)}\) reaction. These may explain the strong observed discrepancies (from 10 to 28%) for C/E ratios in various benchmarks [278, 279].

Recent measurements

Table 19 Survey of the experimental data for the four n-induced fission reactions investigated for JEFF-3.3: the average \(\gamma \)-ray multiplicity (\(\langle M_{\gamma }\rangle \)), the mean photon energy (\(\langle \epsilon _{\gamma }\rangle \)) and the average total \(\gamma \)-energy released (\(\langle E_{\gamma } \rangle \)). N is the target nucleus and \(E_n\) the incident neutron energy (T for thermal and F for 2.4 MeV). \(T_w\) corresponds to the coincidence time used during the experiment

After about 40 years since the first prompt fission gamma observable measurements related to the reactions \(^{235}\hbox {U} ({\hbox {n}}_{th}, \hbox {f})\) [285,286,287], \(^{252}\hbox {Cf}\)(sf) [285], \(^{233}\hbox {U}({\hbox {n}}_{th},\hbox {f})\) [288] and \(^{239}\hbox {Pu}({\hbox {n}}_{th},\hbox {f})\) [285, 288], new experimental results are now available thanks to the development of experimental techniques for the gamma detection (as explained in Ref. [289]). In particular, reliable data (see Table 19) obtained for 4 neutron induced fission reactions \(^{235}\hbox {U} ({\hbox {n}}_{th},\hbox {f})\) [280], \(^{239}\hbox {Pu} ({\hbox {n}}_{th}, \hbox {f})\) [283], \(^{238}\hbox {U} ({\hbox {n}}_{2.4MeV},\hbox {f})\) [281, 282] and \(^{241}\hbox {Pu} ({\hbox {n}}_{th}, \hbox {f})\) [284]) were used for a re-evaluation of the PFGS and PFGM in JEFF-3.3.

Each measurement is characterised among others by a low and high gamma detection thresholds ([\(E_l\)-\(E_h\)]) and by a time window (\(T_{w}\)) corresponding to the coincidence time between the fission fragment detection and the prompt gamma detection. In Table 19, \(E_l=0.1 \, \hbox {MeV}\) and \({\hbox {E}}_h=6 \, \hbox {MeV}\) (7 MeV for \(^{239}\hbox {Pu}\)). As discussed later on, these experimental conditions are important for the simulation with the de-excitation Monte Carlo codes.

\(\underline{\hbox {Advanced modeling of prompt fission}~\gamma \hbox {-ray emission}}\)

Parallel to improvement of experimental technique, new computer codes were developed aiming at predicting characteristics of both prompt neutrons and prompt gamma [290,291,292,293]. In the context of a new evaluation of the PFGS and PFGM for the JEFF-3.3 library, we have decided to use the code FIFRELIN. In this code, the de-excitations of the fission fragments are simulated from statistical Hauser–Feshbach model [294], following Becvar’s procedure [295]. It accounts for the competition between neutron and gamma emission as well as for the conservation of energy, spin and parity of the initial and final states. Note that conversion electrons emission is also taken into account. All the details related to the code can be found in Refs. [293, 296, 297]. The reference case of \(^{252}\hbox {Cf}\)(sf) has been chosen to validate our calculation scheme. The PFGS calculated with FIFRELIN is then compared to the experimental data obtained by Bilnert et al. [298] in Fig. 43.

Fig. 43
figure 43

PFGS measured by Bilnert [298] for \(^{252}\hbox {Cf}\)(sf) (black line) compared to FIFRELIN calculation (red line). The calculation is normalised to the experimental \(\gamma \)-multiplicity in [140 keV–10 MeV] \(\gamma \)-energy range. In order to see the whole spectra, a log-log scale is used (top), while to enlighten structures below 1 MeV, a lin-lin scale is chosen (bottom)

Fig. 44
figure 44

Evaluations of the PFGS adopted in JEFF-3.3. In order to see the whole spectra, a log-log scale is used (top), while to enlighten structures below 1MeV, a lin-lin scale is chosen (bottom)

The calculation is normalised to the average measured \(\gamma \)-multiplicity (\(\langle \hbox {M} \gamma \rangle =8.14\)) in the [140 keV–10 MeV] \(\gamma \)-energy range. It can be observed that the shape of the PFGS is nicely reproduced as well as the structures of the spectrum which are visible below 1 MeV. This nice result is partly obtained thanks to the coupling between FIFRELIN and RIPL3 reference input parameter library [70] which provides the nuclear level scheme at low energy (the scheme being completed at higher energy by FIFRELIN).

Prompt fission gamma spectra/multiplicities

The strategy for the PFGS evaluations in JEFF-3.3 is to adopt the experimental results and to complete them (below \(E_l\) and above \(E_h\)) by a FIFRELIN calculation normalised to the experimental average \(\gamma \)-multiplicity (Table 19). Results obtained in this way for the 4 neutron-induced fission reactions are shown in Fig. 44.

All spectra are defined on the same energy grid and are re-normalised to 1 as requested in evaluated nuclear data libraries. Lastly, due to the lack of data, PFGS in JEFF-3.3 are assumed to be independent of the incident neutron energy. The average \(\gamma \)-multiplicity over the whole \(\gamma \)-energy range can be deduced and are given in Table 20. A comparison between the PFGS evaluations in JEFF-3.1.1 and JEFF-3.3 libraries for \(^{235}\hbox {U}\) and \(^{238}\hbox {U}\) can be seen in Fig. 45.

Table 20 Survey of the average prompt fission gamma multiplicities (PFGM) at thermal incident neutron energy (\(\langle M_{\gamma }(E_{th}) \rangle \)) adopted in JEFF-3.3 for the four investigated (n,f) reactions. Values from previous JEFF evaluated nuclear data files are also given
Fig. 45
figure 45

Comparison between JEFF-3.1.1 (black line) and JEFF-3.3 (red line) PFGS evaluations for \(^{235}\hbox {U(n,f)}\) (top) and \(^{238}\hbox {U(n,f)}\) (bottom) reactions

The dependence of the average PFGM (\(\langle M_{\gamma } \rangle \)) with the incident neutron energy \(E_n\) is calculated from an empirical law proposed by Oberstedt [299]:

$$\begin{aligned} \begin{aligned} \langle M_{\gamma }(E_n)\rangle&= \langle M_{\gamma }(E_{th})\rangle \\&\quad +(C_0+C_1Z^{5/3}A^{-1/2})(\langle \nu ^{corr}_P(E_n)\rangle \\&\quad -\langle \nu ^{corr}_P(E_{th})\rangle ) \end{aligned} \end{aligned}$$

where \(\langle \nu ^{corr}_P(E_n) \rangle \) is the average prompt fission neutron multiplicity, Z and A are the nuclear charge and mass of the compound nucleus. The \({C}_0\) and \({C}_1\) constants were obtained from a fit of experimental data: \({C}_0=16.6 \pm 0.5\); \({C}_1=-(11.0 \pm 0.4) \times 10^{-2}\). The average PFGM at thermal energy (\(\langle M_{\gamma }(E_{th}) \rangle \)) is taken from Table 20. The corrected average prompt fission neutron multiplicity \(\langle \nu ^{corr}_P(E_n) \rangle \) is calculated by removing from the total prompt neutron multiplicity \(\langle \nu _P(E_n)\rangle \) the contribution of neutrons emitted prior to fission:

$$\begin{aligned} \langle \nu ^{corr}_P \rangle = \frac{\langle \nu _{P}\rangle \sigma _{n,f}+(\langle \nu _{P}\rangle -1)\sigma _{n,n'f}+(\langle \nu _{P}\rangle -2)\sigma _{n,2n'f}}{\sigma _{n,f}+\sigma _{n,n'f}+\sigma _{n,2n'f}} \end{aligned}$$

where \(\sigma _{n,f}\), \(\sigma _{n,n'f}\) and \(\sigma _{n,2n'f}\) correspond to the first, second and third fission chance cross-sections respectively. All the quantities needed for the \(\langle \nu ^{corr}_P(E_n) \rangle \) calculation are taken from JEFF-3.1.1. Evaluations of the PFGM for the four neutron-induced fission reactions are shown in Fig. 46.

Fig. 46
figure 46

Evaluations of the PFGM as a function of the incident neutron energy (adopted in JEFF-3.3)

Up to now, \(\gamma \)-heating calculations have not yet been performed with the new PFGS and PFGM adopted in JEFF-3.3. In view of their average \(\gamma \)-energies and multiplicities, it seems that JEFF-3.3 will not be able to correct for the significant underestimation of the total \(\gamma \)-heating observed in various benchmarks. Nevertheless, since \(\gamma \)-spectrum shapes are also very important, these calculations have to be done.

Fig. 47
figure 47

Monte-Carlo simulations of gamma spectra from Al-27 inelastic scattering with 4.5 MeV neutrons, with excited level energies of Al-27 shown in blue

2.4.4 Inelastic scattering photon correlations

Discrete inelastic scattering produces a nucleus in an excited state that typically returns to its ground state by emitting one or more photons. The ENDF-6 format offers two main options for storing these data. The first option is to use the MF12 format for photon production multiplicities, allowing us to define all the intermediate states of the decay. In this case, it is easy to reconstruct the decay cascade. The second is the use of the double differential format of MF6 for which data on photon production are given in the form of total photon multiplicity and probabilities for each photon in the decay. In this case, the average statistical behavior is respected but it is no longer possible to define the photon decay chain of the excited state.

This offers the ability to generate more accurate gamma spectra from inelastic scattering. This is demonstrated in Fig. 47, where the total energy of the photons emitted event by event for the interaction of 4.5 MeV neutrons in an Al-27 sphere is shown. The results presented are obtained with the libraries JENDL-4.0 (green), JEFF-3.2 (black) and JEFF-3.3 (red). The JEFF-3.3 Al-27 evaluation corresponds to the JEFF-3.2 evaluation corrected for the gamma production of inelastic scatterings. The blue dashed lines indicate the energies of the excited levels of Al-27. We observe the good agreement between JENDL-4.0 and JEFF-3.3. The peaks observed correspond to the energies of the excited states of Al-27. These results are obtained with the Monte-Carlo code TRIPOLI-4®.

We have modified 31 evaluation files to restore these correlations between decay photons, which are very important in the case of analog Monte Carlo simulation.

The general methodology for this work was to:

  1. 1.

    use the SIXPAK module [300] to generate neutron angular distributions (MF4 files) from MF6 Files;

  2. 2.

    use the ENSDF database [301] to define gamma cascade for each excited state in agreement with data used in the evaluated file, including all the excited states describe in MF12; and

  3. 3.

    add new MF4, MF12 and MF14 (photon angular distributions) for discrete inelastic scatterings in a modified evaluation file.

The list of modified evaluation files includes: Al-27, Eu-153, Eu-156, I-127, I-129, In-113, In-115, Mo-92, Mo-94, Mo-96, Mo-97, Mo-98, Nd-148, Pb-206, Pb-207, Pb-208, Pd-104, Pd-106, Pd-108, Rh-103, Sn-112, Sn-114, Sn-115, Sn-116, Sn-117, Sn-118, Sn-119, Sn-120, Xe-128, Xe-129 and Xe-133.

2.5 Covariances

Nuclear data evaluated files are of major interest for fission and fusion applications. Until recently, the performance of existing nuclear data libraries is demonstrated by calculating an exhaustive list of public integral experiment benchmarks (ICSBEP/IRPHE) with complementary validation coming from internal sets of experiments from different participating institutions. This benchmarking allows an estimation of residual biases of nuclear data files. An extensive international work is underway not only to properly quantify these biases but also to evaluate the uncertainties associated with these nuclear data files. These uncertainties express a certain degree of confidence in the use of the nuclear data files for various energy domains and various nuclear data types. A modern general purpose nuclear data library is meant to provide these data for end-users with well estimated and realistic uncertainties.

A covariance working group was proposed in 2013 in the JEFF community with the objectives of defining a work plan for next JEFF Mandates. The strategy is to increase the number of covariance estimations for next JEFF releases, identifying missing data and performing evaluations.

2.5.1 Major isotope list

About 25-30 high priority nuclides were identified as being the major tasks for JEFF releases. Of those, the nuclides in Table 21 were addressed by dedicated efforts for either the JEFF-3.2 or JEFF-3.3 release.

Table 21 List of isotopes with new covariance data in JEFF-3.3, which were not taken from TENDL files

To allow the evaluation of proposed covariances, various tools were provided: testing tools for simple verification (such as for example positive definiteness of matrices), treatment (from parameters or cross sections uncertainty to multigroup cross sections), more elaborate tools quantifying final uncertainty contributions to a limited set of applications (fission, fusion, integral experiments) and, finally, visualisation tools (figure/plots) to allow a simple representation of this type of data.

2.5.2 JEFF-3.3 covariance data description

In principle, for each evaluated file we should have covariances for all quantities possible. It is not always the case for various reasons, including formatting issues, file size, evaluator choices and technical capability. In JEFF-3.3, 50 files contain MF31 values, 442 files contain at least MF32 or MF33 and 34 files contains MF35 information. For cross section covariances (MF33), various energy group structures were proposed and all processed matrices are block diagonal (blocks for the resonance range and the high energy range) except for \(^{23}\hbox {Na}\) and \(^{59}\hbox {Ni}\). No cross correlations between different types of data are given, except for cross sections where cross correlation of reactions for one isotope are available. Some formatting issues exist with the ENDF format that do not permit cross correlations between, for example prompt fission neutron spectra, neutron multiplicities and fission cross sections. A general international work is underway to propose a new generic format that may solved this kind of issue within WPEC Subgroup 44 [302].

For neutron induced cross sections covariances are available for the full energy range for \(^{23}\hbox {Na}\), \(^{235,238}\hbox {U}\), \(^{239,240}\hbox {Pu}\), Hf, Co and \(^{58,59}\hbox {Ni}\). In addition, covariance data for the prompt fission neutron spectrum PFNS and the mean prompt neutron multiplicity from fission \({\bar{\nu }}\) are now available for \(^{235,238}\hbox {U}\) and \(^{239}\hbox {Pu}\). The main missing covariance information concerns \(^{241}\hbox {Am}\) neutron induced cross sections and missing official releases of covariances for fission yields, thermal scattering data, delayed neutrons and prompt gamma fission spectra and multiplicities.

To obtain the evaluated covariances, various methods were used by different evaluators, including Bayesian inference based on Monte-Carlo or Generalised Least Square (GLS) algorithms (for example for \(^{239}\hbox {Pu}\) and \(^{23}\hbox {Na}\)). These consist of a comparison of nuclear reaction models to experiments with a posteriori parameters and vectors of uncertainties. Other Monte-Carlo propagation methods use sampling of initial model parameter distributions with parameter distribution moments adjusted to reproduce experimental uncertainties (example of TENDL covariances and \(^{235}\hbox {U}\) high energy range for cross sections, PFNS and \({\bar{\nu }}\)). The experimental information could have been treated differently, taking into account only microscopic data, or data from integral experiments, or both.

Even if this first set of covariances may seem a patchwork that might have benefitted from a stronger coherence, a large effort was made that is a major step forward and that makes JEFF-3.3 a competitive library with respect to the availability of covariance data. Section 4.2 contains several examples where JEFF-3.3 covariances have been used to propagate uncertainties into integral benchmark or reactor concepts.

Fig. 48
figure 48

\(^{239}\hbox {Pu}\) fission multigroup cross section correlations. Energies are in eV, uncertainties in % and cross-sections in barns

2.5.3 JEFF-3.3 covariance highlights

\(\underline{{}^{235,238}\hbox {U}~\hbox {and}~{}^{239,240}\hbox {Pu}}\)

In JEFF-3.3 a complete set of covariances for \(^{235,238}\hbox {U}\) and \(^{239,240}\hbox {Pu}\) in the resonance range and the high energy range were provided. Not only are cross section covariances given but also PFNS and nu-bar.

Figure 48 clearly shows that the \(^{239}\hbox {Pu}\) fission cross section in the unresolved resonance range is much less known than the thermal and high energy ranges. This is mainly due to the lack of precise experimental data from both microscopic and integral experiments. Table 22 presents classical integral values for resonance analysis and the related uncertainties.

Table 22 Integral values for \(^{239}\hbox {Pu}\)

Covariances for the \(^{235}\hbox {U}\) resolved resonance parameters were determined with the CONRAD code [153]. A retroactive analysis [215] was used with the marginalisation procedure of CONRAD [97] to determine the resonance parameter covariance matrix without changing the resonance parameters that was established before. Constraints were applied to the thermal cross sections and to the fission integral between 7.8 eV and 11 eV by using the latest values and uncertainties recommended by the “neutron cross section standards” group of IAEA [40]. According to an independent analysis with the CONRAD code of the thermal constants reported by Axton [303] and of the experimental review reported in Ref. [179], relative uncertainties on the thermal fission and capture cross sections were set to \(\pm 0.6\%\) and \(\pm 2.2\%\), respectively. Analysis of several time-of-flight data have provided a 7.8–11 eV integral uncertainty close to \(2\%\). Results obtained for JRC-Geel fission data are shown in Fig. 49. Final uncertainties of the \(^{235}\hbox {U}\) resonance parameters were propagated on the calculated multiplication factor \(k_{eff}\) of the critical Benchmark UH1.2 carried out in the EOLE reactor of CEA Cadarache. A realistic uncertainty of 316 pcm was obtained. This result provides an order of magnitude which is valid for UOX configurations in a PWR-type neutron spectrum. Figure 50 shows the correlations and uncertainties evaluated for the \(^{238}\hbox {U}\) neutron induced capture cross sections.

Fig. 49
figure 49

Fission cross sections and correlation matrix obtained with the CONRAD code between 7.8 and 11 eV. The theoretical curve is compared with data retrieved from the EXFOR data base [179]. The ordinates of the correlation matrix are neutron energy in eV

Fig. 50
figure 50

\(^{238}\hbox {U}\) capture multigroup cross section correlations. Energies are in eV, uncertainties in \(\%\) and cross-sections in barns

\(\underline{{}^{23}\hbox {Na}}\)

A new evaluation of sodium is proposed in JEFF-3.3 ([153], Sect. 2.2.2). This work has been motivated mainly because the earlier JEFF-3.1.1 sodium evaluation showed large differences with microscopic measurements and did not provide covariance data. A new experiment performed at the JRC Geel [158] was analyzed in conjunction with high-resolution measurements from Larson [157] with the data assimilation code CONRAD [153]. In addition, a proper covariance estimation was done for the whole energy range. A previous paper [304] pointed out effects of consistent uncertainties treatment over a “large” energy range requiring two nuclear reaction models for the analysis. It showed that, if only experimental statistical uncertainties are considered, no cross correlation appears for the cross section between the energy ranges analyzed by the two models. On the contrary, when systematic uncertainties (such as normalisation, background, detector efficiency, ...) are considered, it is possible to propagate cross correlations all the way, from experiment to evaluated cross section. The result for the sodium neutron-induced inelastic cross section is given in Fig. 51. Experimental systematic uncertainties have been propagated to nuclear reaction model parameters in order to produce a consistent set of covariance data over a large energy range of 0 eV–20 MeV.

Fig. 51
figure 51

Covariances of neutron-induced inelastic cross section of sodium (left). The results take full account of systematic uncertainty over the wide energy range. The corrected JEFF-3.3 covariance matrix for \(^{16}\hbox {O}\) inelastic scattering (right)

\(\underline{{}^{16}\hbox {O}}\)

During a sensitivity and uncertainty analysis an error was detected in the JEFF-3.3 covariance matrix for \(^{16}\hbox {O}\) inelastic scattering (standard deviations up to and above 10,000 %, probably an error of a factor of 100). This can lead to severe overestimation of uncertainty. Prior to use the covariance matrix should be corrected, e.g. by reducing the standard deviations to a maximum of 100% as was done in the latest version of the XSUN-2017/SUSD3D package [305] (Fig. 51).

2.5.4 JEFF-4 covariance data

Covariance add-ons to JEFF-3.3

A significant effort was devoted to propose uncertainties for thermal scattering data (\({\hbox {S}}_{\alpha \beta }\)). Figure 52 gives the impact of this work on the effective hydrogen elastic cross section covariance matrix. A difficulty arises with the ENDF format that cannot represent \({\hbox {S}}_{\alpha \beta }\) uncertainties and covariance matrix in a suitable format.

Fig. 52
figure 52

Propagation of thermal scattering uncertainties to the total cross section of hydrogen in water

Furthermore, proposals for fission yields covariance data were made for the JEFF-3.1.1 set of fission yields. These data are availiable for the JEFF community and explanations of these can be found in the literature [271, 306, 307]. These contributions are not part of the official JEFF-3.3 release but they will form the basis of ongoing and future activities in the field.

Covariances data for JEFF-4

For the future JEFF-4 library the aim is to provide full covariance data from evaluations considering the full energy range and accounting for all microscopic data constraints in a consistent way. Integral experiments should be included in a second step through a systematic approach leading to a separate file. JEFF-4 must keep the momentum gained with developing covariance data for JEFF-3.2 and JEFF-3.3 taking advantage of international collaborations under the auspices of OECD-NEA and IAEA. In particular, the JEFF working group will try to assess the main difficulties related to the evaluation of uncertainties

2.6 Displacement damage data

Atomic displacement cross sections were calculated using the standard NRT [308] model and the recently proposed a-thermal recombination-corrected dpa (arc-dpa) model [309, 310]. The arc-dpa model makes possible a more accurate estimate of the damage production in irradiated materials.

According to the arc-dpa concept the number of stable defects produced under irradiation is parameterized in the following form

$$\begin{aligned} \begin{matrix} N_d &{}= &{} \left\{ \begin{matrix} 0 &{} \,\,\text{ when } T_{dam}< E_d \\ 1 &{} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{ when } E_d< T_{dam}< \gamma \\ (1/\gamma ) \,\, \xi _{arc}\,\,\,T_{dam} &{} \text{ when } \gamma <T_{dam} \end{matrix} \right. \end{matrix} \end{aligned}$$

where \(\gamma =2E_d/0.8\), \(E_d\) is the average displacement threshold energy [311], and \(T_{dam}\) is the ‘damage energy’ or energy available for atom displacements in elastic collisions calculated using the Robinson formula [312].

The defect generation efficiency \(\xi _{arc}\) in Eq. (5), equal to the ratio of the calculated number of defects to one predicted by the NRT model, is calculated as follows [309, 310]

$$\begin{aligned} \xi _{arc} \,\,\, = \,\,\, \frac{1-c_{arc}}{\gamma ^{b_{arc}} }\,\,\,\,T_{dam}^{b_{arc}}+c_{arc} \end{aligned}$$

where \(b_{arc}\) and \(c_{arc}\) are parameters obtained based on results of molecular dynamics simulations or experimental data [311, 313].

For Fe, Ni, Cu, Pd, Ag, W, Pt, and Au the parameters included in the arc-dpa formalism were taken from Refs. [309, 310, 314] and for other materials were estimated using a semi-empirical systematic approach [315]. The approach uses the correlations between minimum, averaged, and effective threshold displacement energies and a number of quantities such as melting temperature, material density, cohesive energy, and others.

As an illustration Fig. 53 shows the \(c_{arc}\) parameters evaluated using experimental data and systematics [315]. Obtained \(E_d\), \(b_{arc}\), and \(c_{arc}\) values [315] and data from References [309, 310, 314] were employed for the calculation of atomic displacement cross sections for elements from lithium to uranium. The NJOY code with Eqs. (5) and (6) implemented was used for calculations.

Fig. 53
figure 53

The \(c_{arc}\) values evaluated for different materials with red points for experimental data and yellow for systematics

Figure 54 shows a typical example of atomic displacement cross sections calculated using Eqs. (5), (6) and the NRT model for Al. The plotted data represent the energy group averaged values.

Fig. 54
figure 54

Displacement cross section for aluminum calculated using the arc-dpa and NRT models (top). Displacement cross sections for nickel obtained using JEFF-3.3 and TENDL-2015 data using the arc-dpa model (bottom)

The data obtained on the basis of JEFF-3.3 were extended, if necessary, up to 200 MeV incident neutron energy using TENDL-2015. Figure 54 shows an example of such an extension for Ni. The displacement cross sections were recorded in ENDF-6 and ACE formats.

Because results of arc-dpa calculations are absolute numbers of stable displacements, the final values were recorded as cross sections in barns. This data representation is different from the common recording of “damage energy production cross sections” with MT = 444 by the NJOY processing. In the latter case, the displacement cross section varies according to the \(E_d\) value, which is not reasonable for the current results. The resulting arc-dpa cross sections were recorded in the file MF = 3 and the section MT = 900. Absolute values of displacement cross sections obtained using the NRT model [308] were written in MF = 3, MT = 901 for better comparison with arc-dpa cross sections.

2.7 Fission yields

A new fission yield library, UKFY-3.7 [316], has been created as part of the JEFF collaboration and is included in the JEFF-3.3 release. This includes 19 neutron-induced fission yield files, with thermal, fast and/or high-energy evaluations, as well as three spontaneous fission yield evaluations, for 252Cf, 242Cm and 244Cm. The neutron-induced isotopes have been selected, as indicated in Table 23, based on their contribution to the overall number of fissions in thorium, uranium and MOX-fuelled thermal and fast reactors. This is complemented by a small set of ‘high’-energy, 14 MeV fission yield data sets and 236U.

Table 23 Fission yield evaluations in the JEFF-3.3 sub-library, classified by the maximum fraction of fission rates in UOX- and MOX-fuelled thermal or fast reactors. T, F, and H refer to thermal, fast and high energy incident neutron spectra, respectively
Table 24 Number of experimental measurements used in the evaluation of all fissioning systems with new data in the JEFF-3.3 fission yield sub-library

2.7.1 Evaluation methodology

The JEFF-3.3 fission yield library was built using the same general evaluation methodology that was employed for all UKFY evaluations made in the past 20 years [317]. This employs the following eleven sequential steps:

  1. 1.

    perform statistical analysis of a database of experimental measurements to estimate a set of recommended chain, independent and cumulative fission yields and their corresponding uncertainties;

  2. 2.

    for all required fissioning systems, use a suitable model to predict the independent yields and their uncertainties for all fission product nuclides- the uncertainities being based upon the model parameters uncertainities;

  3. 3.

    calculate the chain yield distributions from a model and adjust these to fit the recommended chain yields;

  4. 4.

    use the modelled independent yields to derive fractional independent yields and then combine these with the chain yield distributions to produce a modified set of independent yields;

  5. 5.

    adjust the modified independent yields to fit the physical constraints, such as mass or charge conservation, as well as detailed complementary element balances;

  6. 6.

    calculate isomeric branching ratios based on the Madland-England model;

  7. 7.

    split the independent yields using the isomeric branching ratios;

  8. 8.

    calculate cumulative fission yields using the isomeric split adjusted independent yields and the most recent decay data evaluation decay branching ratios;

  9. 9.

    increase the uncertainities on the recommended cumulative yields by the difference between the recommended and calculated cumulative yields;

  10. 10.

    from the cumulative yields with uncertainities (i.e. those with measurements) use the independent yield uncertainities to estimate the cumulative yield uncertainities on their parent nuclides higher in the decay chain; and

  11. 11.

    parse all data into an ENDF-6 formatted data file.

2.7.2 New data considered in the evaluation

The previous JEFF-3.1.1 fission yield files [4] were based on experimental data found in literature reviews performed up to the year 2000. A new review was carried out between 2013-2016, identifying 1234 new data measurements that have been used in the JEFF-3.3 evaluation. These are summarised in Table 24 for all systems that had an updated experimental database. Notably, this updated data set includes new fast neutron spectrum measurements for 148Nd, which are summarised in Table 25.

The integration of these new data into the database provides two kinds of improvements. In some cases, the addition of more precise data improves the accuracy of the fission yield evaluation or reduces their uncertainties. In other cases, the measurements are first-of-a-kind and allow the evaluation to rely directly upon experimental data, rather than model calculations and/or the application of constraint equations in the evaluation process. Examples of the latter include the thermal fission of 238Np, where measurements are available for masses between 74 and 85; thermal fission of 239Pu, where masses 80, 82 and 130 have now been measured; and thermal fission of 249Cf, where masses 69–82 have now been measured.

Table 25 Fast neutron spectrum 148Nd cumulative yields determined from statistical analysis of experimental measurements

2.7.3 New modelling methods

In the previous JEFF-3.1.1 evaluation, the 5-Gaussian and Wahl Zp models were used to supplement experimentally-measured yields with semi-empirical data [4]. The parameterisation of these models were fitted separately for each fissioning system, where possible, or the parameters were extrapolated where there was insufficient data to perform a reliable fit.

The development of the ‘GEneral description of Fission observables’ (GEF) code [290] since the previous JEFF fission yield evaluation has offered another model for the calculation of fission yields. This uses a single set of physically-inspired semi-empirical parameters for all fissioning systems and offers impressive predictive capability for fissioning systems ranging from thorium to californium, and beyond. It has been used for incident neutron energies ranging from thermal to tens of MeV, and includes multi-chance fission.

Following several preliminary comparison studies, it was decided to use the GEF code as the model to estimate independent and chain yields required as an input to the evaluation. Although GEF also possesses an isomeric branching simulation feature, the Madland-England model was retained in JEFF-3.3. The isomeric splitting has a significant effect on short-term decay heat from fission products, and thus it was decided to keep the existing Madland and England model until any improvements from using the GEF code could be quantified.

2.8 Decay data

The JEF-2.2 library included the reference decay data in Europe since being released in the early 1990s. However, various shortcomings, both in content and evaluation methodology, led to the establishment of a new decay data evaluation system developed through the JEFF project. The initial construction of the JEFF-3.0 decay data sub-library [4] used the most recent versions of the NUBASE [318] and Evaluated Nuclear Structure Data File (ENSDF) [301] databases, complemented with specialised decay data evaluations from the United Kingdom Activation Product Decay Data (UKPADD) and Heavy Element and Actinide Decay Data (UKHEDD) libraries [319], the Decay Data Evaluation Project (DDEP) [320], the IAEA Actinide Decay Data Library [321] and the International Reactor Dosimetry and Fusion File (IRDFF) [252]. The different data sources are sequentially processed with various quality checks, e.g. intensity and energy balance verification, performed in each step. The result is a library that recognises and incorporates the most rigorous available evaluation for each of the 3852 radionuclides, whether that represents a bespoke evaluation or a translation of an ENSDF file into the ENDF-6 format. For the JEFF-3.3 release the source libraries are listed in Table 26, including updates to the UKPADD and UKHEDD versions and several newly evaluated files from the DDEP, including \(^{18}\hbox {F}\), \(^{59}\hbox {Fe}\), \(^{82}\hbox {Rb}\), \(^{82}\hbox {Sr}\), \(^{88}\hbox {Y}\), \(^{89}\hbox {Zr}\), \(^{94m}\hbox {Tc}\), \(^{109}\hbox {Cd}\), \(^{133}\hbox {Ba}\), \(^{140}\hbox {Ba}\), \(^{140}\hbox {La}\), \(^{151}\hbox {Sm}\) and \(^{169}\hbox {Er}\).

Table 26 Source libraries and the number of evaluations adopted in the JEFF-3.3 decay data sub-library

2.8.1 Inclusion of TAGS measurements

The well-known Pandemonium effect [322] results in mis-allocation of beta and gamma decay intensities, and has resulted in several experimental campaigns to provide new non-spectroscopic data to improve the decay data evaluations. The initial benchmarking of the JEFF-3.1 decay sub-library [4], alongside work of the OECD-NEA Working Party on International Evaluation Co-operation subgroup 25 [323] highlighted inconsistent simulation results for decay heat calculations. These were a direct result of the mean gamma and beta decay energies calculated from the discrete decay scheme data suffering from the Pandemonium effect, and it was assumed these mean energies could be better determined using Total Absorption Gamma-ray Spectroscopy (TAGS) experiments. A set of 29 nuclei, shown in Table 27 had their mean energies updated from the work of Greenwood et al. [324] for JEFF-3.1.1 [4]. For the release of JEFF-3.3, nine new nuclei were updated using data from the groups at Valencia, Spain and SUBATECH, the University of Nantes, France, working at the University of Jyväskylä, Finland, as shown in Table 28. The differences are often substantial.

Table 27 Nuclei updated in JEFF-3.1.1 using Greenwood et al.’s [324] TAGS mean energy values (in MeV, [4]). (An uncertainty of 10% was applied to the adopted mean energies.)
Table 28 Nuclei updated in JEFF-3.3 using recently measured TAGS mean energy values (in MeV) at the University of Jyväskylä by the Valencia [325, 326] and Nantes [327] groups (Uncertainties not shown)

The JEFF-3.3 radioactive decay data library does not contain beta or neutrino spectra. Estimates of these spectra are of interest to various problems and require additional models besides the data provided in the present and previous JEFF radioactive decay data library. Examples of such estimates may be found in Refs. [328, 329] for the estimation of reactor anti-neutrino spectra and in Ref. [330] for beta (\(\beta ^-\) and \(\beta ^+\)) and (anti-)neutrino spectra.

2.9 Neutron activation

The JEFF-3.3 files are complemented by an activation library that includes 2797 neutron-induced reaction files in the so-called European Activation File (EAF) format. All previous JEFF-3 libraries utilised the most recent version of the European Activation File, with the EAF-2010 library [331, 332] being the last release of that project. Since 2010, the development of the TALYS-based TENDL [5] files has replaced this activity within Europe and several verification and validation exercises that had been performed for the EAF libraries (c.f. [333]), have been redone using the TENDL files with superior results [273]. In order to maintain compatibility with the activation simulation codes that have traditionally relied upon EAF formatted data files, a special processed version of TENDL-2017 was prepared and has been the subject of validation activities under the EUROfusion nuclear data programme [334]. As a result, the JEFF-3.3 library has adopted this EAF formatted TENDL-2017 neutron library. Work is in progress on the generation of a EAF-type 211 group cross-section data library (up to 60 MeV) which can be used by any activation code.

2.10 Thermal scattering

The thermal neutron scattering sublibrary contains 20 evaluations for 16 materials. The evaluation for heavy water was updated and now has components for deuterium and oxygen bound in heavy water. Nine new materials (sapphire-\({\hbox {Al}}_2 {\hbox {O}}_3\), silicon, mesitylene, toluene, ortho- and para- hydrogen, ortho- and para-deuterium, and light water ice) were included, and the remaining evaluations were carried forward from JEFF-3.2. The current status of the evaluations is summarized in Table 29. Details of the evaluation and validation methodologies are given below for each of the new and updated materials.

Table 29 Thermal scattering libraries included in JEFF 3.3. Notation: \({\hbox {Al}}_2 {\hbox {O}}_3\) for sapphire, L for liquid, o- for ortho-, p- for para-, Mes. for phase II Mesitylene, \(({\hbox {CH}}_2)_n\) for polyethylene
Fig. 55
figure 55

Inelastic scattering cross section of sapphire (top) and silicon (bottom) at room temperature. The calculations are compared with experimental data by Cantargi [338], and Brugger [339]. The evaluation for silicon is normalized to the free gas scattering cross section of Si-28, whereas the measurements by Brugger correspond to natural silicon

2.10.1 Silicon and sapphire

Silicon and sapphire (\({\hbox {Al}}_2 {\hbox {O}}_3\)) are two materials used in single crystal form as neutron filters at neutron beam facilities. For this application, single crystals are aligned to the neutron beam in a way that the incident neutrons do not satisfy any Bragg condition. A precise representation of this system requires the calculation of the interaction of neutron waves with the single crystal and consider the extinction of reflections caused by destructive interference [335]. This cannot be computed using neutron transport codes which assume non-oriented, isotropic materials. Therefore, in order to introduce filters into these codes a simplification was applied: we only consider inelastic interactions. This approximation works for simulating neutron filters [336], but also was found to be satisfactory for the calculation of the neutron irradiation of silicon single crystals for transmutation doping [337].

The models use a simple Debye spectrum with Debye temperature \({\hbox {T}}_D = 485 \, \hbox {K}\) for silicon and \({\hbox {T}}_D = 1032 \, \hbox {K}\) for sapphire. The models show a good agreement with measurements of the total neutron cross section, as shown in Fig. 55. Details of the evaluation can be found in Reference [338]. The libraries are evaluated at T  =  293 K for sapphire and T  =  296 K for silicon. When the libraries are reconstructed using NJOY to produce ACE libraries, the parameter mte should be set to 0 to create a library without the elastic component.

2.10.2 Liquid hydrogen and deuterium

Liquid hydrogen and liquid deuterium are among the most used materials for the production of cold neutrons in pulsed neutron sources and nuclear research reactors. Hydrogen and deuterium form diatomic molecules with two spin states: symmetric (ortho) and antisymmetric (para). At low temperatures, for which few rotational levels are excited, the selection rules caused by the correlation between the total nuclear spin \({\mathbf {I}}\) and total angular momentum \({\mathbf {J}}\) affect the neutron interaction probability changing the cross section [340].

Compared with previous models by Keinert and Sax [341] included in ENDF/B-VII.1, this evaluation improves the calculation of interference effects by including a Sköld correction computed using molecular structure factors derived from measurements performed by Zoppi [342]. The structural correction, as in a previous evaluation by Granada and Gillette [343], is separated into an analytical component that is applied to the internal dynamics of the molecule, and a numerical component that is applied to the rigid-body dynamics of the molecule.

Calculations for para-hydrogen show a better agreement with experimental measurements of the total cross section by Celli [344] and Grammer [345] (Fig. 56a), and calculations for ortho-deuterium show an improvement over previous models when compared with measurements performed at Paul Scherrer Institut by Kasprzak [346] and Atchison [347] (Fig. 56b).

The libraries are evaluated at \(T = 14\), 15, 16, 17, 18, 19 and 20 K for ortho- and para-hydrogen, and \(T=19\), 20, 21, 22 and 23 K for ortho- and para-deuterium.

Fig. 56
figure 56

Total scattering cross section of liquid para-hydrogen (top) and liquid ortho-deuterium (bottom) at 19 K. The calculations are compared with experimental data by Celli [344], Grammer [345], Kasprzak [346], Atchison [347], and Seiffert [348]