Improving fission-product decay data for reactor applications: part I—decay heat

Abstract

Effort has been expended to assess the relative merits of undertaking further decay-data measurements of the main fission-product contributors to the decay heat of neutron-irradiated fissionable fuel and related actinides by means of Total Absorption Gamma-ray Spectroscopy (TAGS - sometimes abbreviated to TAS) and Discrete Gamma-ray Spectroscopy (DGS). This review has been carried out following similar work performed under the auspices of OECD/WPEC-Subgroup 25 (2005–2007) and the International Atomic Energy Agency (2009, 2014), and various highly relevant TAGS measurements completed as a consequence of such assessments. We present our recommendations for new decay-data evaluations, along with possible requirements for total absorption and discrete high-resolution gamma-ray spectroscopy studies that cover approximately 120 fission products and various isomeric states.

1 Introduction

Decay heat is generally defined as the energy released from the direct and indirect fission reaction products, neglecting the contribution of antineutrinos that do not deposit any energy in the reactor core. The main contributors to reactor decay heat are the fission products that accumulate during reactor operation, followed by the actinides generated via neutron capture along with their heavy-element decay products and various activation products [1, 2]. Such decay heat is extremely significant at short (up to $\sim$ 1 day) and intermediate (from $\sim$ 1 day to 3 years (10$^{8}$ seconds)) cooling times after an accidental or planned shutdown of a nuclear reactor, and is most immediately dependent on the resulting inventory of fission products, actinides and their natural decay-chain products as a function of the time after shutdown. Accurate estimates of the resulting decay heat are required in safety assessments of all types of reactor and fuel-handling plant, the storage of spent fuel, the transport of fuel-storage flasks, and the intermediate-term management of any resulting radioactive waste. Most of the above phenomena are also associated with the related emission of antineutrinos that provide an important means of monitoring reactor operations in a benign manner, as well as defining the constraining fundamental physics quantities that determine their oscillation properties.

Both the actinide and fission-product inventories of neutron-irradiated fuel are calculated for known operational conditions and all subsequent cooling periods. These inventory data are used in conjunction with radionuclide half-lives, and all relevant heavy-particle, light-particle and electromagnetic radiation characteristics to determine the total energy release rates for heavy particles, light particles and electromagnetic radiations. Heavy particles are primarily identified with alpha particles, light particles are defined as $\beta$ $^{-}$, $\beta$ $^{+}$, and internal-conversion and Auger electrons, and electromagnetic radiation consists of $\gamma$, X-rays, annihilation radiation and internal bremsstrahlung. Along with neutron-induced cross sections and fission yields, the radioactive decay data constitute key input to the summation calculations used to determine the release of decay heat during reactor operation and as a function of time after the termination of fuel irradiation within the reactor core [1,2,3]. These calculations require the inclusion of mean $\alpha$, $\beta$ and $\gamma$ energies derived normally from the decay schemes of a significant number of radionuclides dominated by fission products at early and intermediate cooling times, and the results need to be compared with experimental decay-heat benchmarks. However, the determination of $\beta$ $^{-}$ emission probabilities has long been problematic in decay-scheme studies. Although $\gamma$-ray emission probabilities and internal conversion coefficients can be used to derive $\beta$ $^{-}$ feeding to daughter nuclear levels, experiments based on Ge detectors suffer from low efficiency for the detection and quantification of high-energy $\gamma$ rays above $\sim$ 1.5 MeV that undermines such an approach. The determination of direct $\beta$ $^{-}$ decay to the ground state of the daughter nucleus can also pose serious problems. Hardy et al. proposed that $\sim$ 20$\%$ of the true $\gamma$-ray intensity above 1.7 MeV for a fictional radionuclide (Pandemonium) may remain undetected [4], impacting significantly on the use of $\gamma$-ray singles data (as opposed to $\gamma$-$\gamma$ coincident data) to calculate $\beta$ $^{-}$ transitions by means of gamma population-depopulation balances of the proposed nuclear levels. This problem also exists in experiments based on coincident data even in the case of relatively high-efficiency Ge detector arrays [5, 6]. Furthermore, defining the nature of each individual $\beta$ $^{-}$ transition can result in differing energy distributions to create distinct total $\beta$ $^{-}$ energy spectra. Such unknown beta shape factors may impact on the average $\beta$ $^{-}$ energy of many of the radionuclides under consideration. Total Absorption Gamma-ray Spectroscopy (TAGS) measurements can overcome these difficulties in order to provide the necessary mean beta and gamma decay energies for more comprehensive and satisfactory decay-heat calculations [7,8,9].

While fission-product and actinide decay are the most significant contributors to decay heat, caution is required with respect to the first $\sim$ 200 s after reactor shutdown as other effects play immediate initial roles, such as a brief plant-driven period of continued thermal impact along with declining fission multiplication driven by delayed-neutron precursors [10]. Beyond 200 s after reactor shutdown, $\beta$- and $\gamma$-decay processes of the fission products play a dominant role leading up to approximately 10$^6$ s (12 days). While both $^{239}$U and $^{239}$Np make noteworthy contributions up to one hour and < 10$^6$ s cooling times, respectively, other actinides such as $^{238}$Pu, $^{241}$Am and $^{242,244}$Cm take their place in this respect at much longer times. Following on from assessment studies discussed and undertaken in 2005–2007, 2009/2010 and late 2014 [11,12,13,14] and various highly relevant TAGS measurements completed as a consequence of such assessments, further efforts have now been made to re-assess the requirements for additional measurements that effectively embrace singles $\gamma$-ray spectroscopy, $\gamma$-$\gamma$ coincidence and TAGS. One extended aim would be for TAGS to quantify the degree of Pandemonium in particular fission products through the existence of previously unknown and ill-defined nuclear levels populated in the $\beta$ $^{-}$ decay process. Such studies would also underline the requirements for more extensive singles $\gamma$-ray spectroscopy and $\gamma$-$\gamma$ coincidence techniques with appropriate types of detector by which to recognise and quantify the higher-energy gamma emissions in order to improve decay-heat assessments, as well as dosimetry and shielding calculations.

Several exploratory studies have been carried out recently in order to improve specific $\beta$ $^-$ decay data as an aid in undertaking more accurate and precise antineutrino spectral calculations [15,16,17,18,19,20]. Recommendations have been made to perform TAGS measurements that differ in priority to current decay-heat requirements due to the fact that such antineutrino calculations are more relevant and sensitive to the nature of the shorter-lived fission products. While work is underway to extend this effort towards the determination of the antineutrino spectral requirements for $\gamma$-ray spectroscopy, $\gamma$-$\gamma$ coincidence and TAGS measurements, these particular assessments are beyond the scope of the current publication and will be the subject of a future article.

2 Total absorption gamma-ray spectroscopy (TAGS/TAS)

Nuclear structure and decay data are important facets and spectral aspects of nuclear physics. These properties and associated parameters aid extensively in the characterisation of the nucleus, and provide definitive descriptive features of all nuclei for direct adoption in a wide range of nuclear applications that include the safe control and normal operation of power reactor systems and the detection of any clandestine procedures, as well as extending our basic understanding of the more exotic features of nuclear physics. The emission probabilities of beta-decay are important in this respect from the point of view of quantifying the mean beta (most frequently the main contributor to the light-particle component of the decay process) and mean gamma decay heat (most frequently the main contributor to the electromagnetic component), along with the antineutrino spectral signatures that can potentially assist greatly in the detection of illegal procedures undertaken to produce weapons-grade materials.

A major problem in both decay-heat and antineutrino studies is determining both the $\beta$ $^{-}$ and $\gamma$ feeding with good accuracy and confidence, which has in the recent past relied most frequently on direct experimental studies by means of various forms and arrays of Ge detector. While these detector systems are entirely suitable for multiple coincidence studies to define and resolve nuclear levels and decay schemes, they have long been known to possess limited $\gamma$-ray detection efficiency that falls dramatically with increase in $\gamma$ energy particularly above 1.5 MeV, as noted in Sect. 1. Under these circumstances, an entirely different method of spectral study and analysis has been considered and developed, based on the attempted total absorption of all $\gamma$-ray emissions to determine full $\beta$ $^{-}$ feeding to all individual nuclear levels [21,22,23,24,25]. Although complete 100$\%$ efficiency is not fully feasible, scintillator $\gamma$ detector systems with geometries as close to 4$\pi$ as possible possess the capabilities to determine $\beta$ $^{-}$ feeding up to an excitation energy of the daughter nucleus that could match the parent Q-value. While under development in the early 1970 s, TAGS/TAS involved the adoption of two large cylindrical NaI detectors, before moving in the 1990 s to one large NaI-well counter to host the radioactive source of interest along with Si detectors [23, 24, 26]. Other larger NaI(Tl) crystals have subsequently been used with a high degree of success in conjunction with various other smaller NaI, Ge-planar and thin Si $\Delta$E positron detectors to determine specific forms of coincidence, for example, GSI TAS (GSI) [27] and Lucrecia TAS (ISOLDE) [23]. These studies have been extended to significant arrays of Ge detectors in a compact geometry, such as Clustercube and Gammasphere to study a number of more complex beta spectra, providing opportunities to compare the results obtained by means of different techniques [5, 6].

Recent measurements related to power reactor operations and antineutrino physics have been performed at the IGISOL facility in Jyvÿskylä, Finland. These studies have involved the use of the ion-guide technique in which many of the refractory fission products of interest have been successfully generated, and high isotopic purity has been achieved by means of the JYFL Penning trap operated as a high-resolution mass separator [25]. Accurate and valid analyses of the spectral data have also been an important feature of this work, based on a sound starting knowledge of the level scheme up to a reasonable excitation energy. As outlined in Refs. [24, 28, 29], these spectral analyses take into account non-linearity of the light output in the NaI(Tl) scintillator and pile-up in the electronic signals.

Exploiting the experience gained, various spectrometers have been commissioned to better absorb and quantify all gamma emissions. These studies have extended our understanding of the nucleus with respect to $\beta$ decay and the weak interaction, and so aided in the development of related modelling calculations over the full chart of the nuclides. Improvements have also been made in the handling of the radioactive species to obtain clean beams for spectral studies by means of various forms of ancillary detector located close to the main counting area of the multi-array of segmented 4$\pi$ NaI(Tl) scintillators. A key aspect of this work is “segmentation” whereby additional information on the multiplicity of the gamma cascades can be used to test assumptions made during the analyses. Rocinante [30] is an example of such a detector system, which is composed of twelve optically-isolated BaF$_{2}$ crystals assembled in a cylindrical geometry and operated in conjunction with an approximately 30$\%$ efficient Si detector or plastic detectors, together with the ion-guide source of the IGISOL mass separator and JYFLTRAP Penning trap at the University of Jyvÿskylä [30,31,32]. A similar segmented arrangement of sixteen modular NaI(Tl) scintillators in a combined cuboid form has been developed as the DTAS (Decay Total Absorption Spectrometer) for DESPEC (DEcay SPECtroscopy) at FAIR (Facility of Antiproton and Ion Research, near Darmstadt, Germany) [33,34,35]. These detector systems have been used to study various beta-decaying radionuclides of relevance to decay-heat assessments and the prediction of antineutrino spectra that arise from reactor operations, along with more basic nuclear structure research in facilities such as RIKEN and GSI(FAIR).

A segmented detector array has been designed, developed, and assembled as the Modular Total Absorption Spectrometer (MTAS) at the Holifield Radioactive Ion Facility of the Oak Ridge National Laboratory. MTAS consists of nineteen NaI(Tl) hexagonal modules arranged as a honeycomb-like structure. Radioactive sources are delivered by means of a moving-tape system to the central module which also contains two Si-strip detectors for $\beta$ $^{-}$ coincidence studies. Initial measurements of seventy fission products from $^{238}$U fast fission have focused on TAGS studies of $^{86,89}$Br, $^{89,90}$Kr, $^{88,89,90,90m,92}$Rb, $^{96}$Y, $^{98}$Nb, $^{137}$I, $^{137,139}$Xe, $^{142}$Cs, $^{142}$Ba and $^{142}$La [36,37,38,39,40,41,42]. Measurements have also been performed at Argonne National Laboratory with isotopically pure beams, see for example [43]. The SuN spectrometer is another example of a segmented TAS detector that was originally designed for reaction studies [44], and has also been used for decay studies in fragmentation facilities [45,46,47,48]. A new segmented central module for MTAS has been provided by the University of Warsaw [49], and the array assembled at the Facility for Rare Isotope Beams (FRIB), Michigan State University, East Lansing, USA. This improved detector system has been located at the FRIB Decay Station initiator (FDSi), and is operational [50].

3 Analytical procedures and assessments

Extensive inventory and decay-heat calculations have been performed with the UKAEA FISPACT-II code by Fleming and Sublet [51,52,53]. All relevant nuclear data addressed in these studies have involved the main fission-product contributors from thermal and fast fission identified with all the fissionable radionuclides to be found in various types of irradiated fuel (Table 1).

Table 1 Irradiated fuel inventories and decay-heat calculations [51,52,53]

Selection criteria for the current assessment of Pandemonium include the following: identification and detailed inspection of the nuclear structure of fission products with $\ge 2\%$ contribution to the total decay heat, along with both their light-particle and electromagnetic components; comparison of the Q-values recommended in AME2020 [54] with the highest known energies of daughter nuclear levels that possess either unknown or commensurate spin-parity with the ground state of the parent fission-product; and assessment of possible Pandemonium within the decay schemes as currently defined. Under such circumstances, such judgements are inevitably subjective in nature and are best described as indicative, with emphasis placed on the possible existence of previously undetected high-energy $\gamma$-ray emissions. The primary aim has been to identify radionuclides that may possess the potential for Pandemonium so as to formulate recommendations concerning the need for further quantification of individual fission-product decay schemes by means of Total Absorption Gamma-ray Spectroscopy (TAGS/TAS) and/or Discrete Gamma-ray Spectroscopy (DGS). Furthermore, improved quantification of the related nuclear structure and antineutrino emissions will also be inevitable consequences of such dedicated studies. These assessments may either support TAGS measurements for the first time, or reveal the need for further additional TAGS along with improved $\gamma$-ray spectroscopy and $\gamma$-$\gamma$ coincidence studies that will be more fundamentally necessary if TAGS reveals the existence of significant Pandemonium. Such judgements have been made on the basis of what we know about the nuclear structure of each of almost 120 fission products chosen for consideration from the FISPACT-II decay-heat calculations for the thermal fission of $^{235}$U, $^{238,239,240,241,242}$Pu, $^{241}$Am, $^{243,245}$Cm, and fast fission of $^{232}$Th, $^{233,238}$U and $^{237}$Np.

A notable feature of the various sets of fission products is that they exhibit a fair degree of commonality. What we observe is that the more dominant decay-heat fission products for $^{232}$Th, $^{233,238}$U and $^{237}$Np fast fission and $^{241,242}$Pu and $^{245}$Cm thermal fission are those that do not appear in such a manner in the equivalent exercise for $^{235}$U, $^{238,239,240}$Pu, $^{241}$Am and $^{243}$Cm thermal fission as a consequence of differences in the individual fission yields and the subsequent impact of their decay chains. The potential for Pandemonium within the known $\beta$ $^{-}$ decay of a particular fission product is based on the documented nuclear properties, Q-value of the $\beta$ $^{-}$ decay, and the possible existence of higher-energy nuclear levels that could be populated by $\beta$ $^{-}$ emissions and depopulated by as yet unknown high-energy $\gamma$ rays, both of which would impact on their contribution to their decay-heat components. A further issue in such assessments is the perceived correctness and accuracy of the absolute intensity of $\beta$ $^{-}$ decay feeding directly to the ground state of the daughter, which could possibly impact the complete decay scheme greatly through the normalization of the beta intensities (i.e., all $\beta$ $^{-}$ emissions, $\gamma$ rays, antineutrino spectra, and additional features of the decay process).

TAGS/TAS measurements can improve our understanding of incomplete and therefore erroneous decay schemes as formulated mainly by $\gamma$-ray spectroscopy identified with Ge-based detectors. Comments concerning TAGS/TAS and other $\gamma$-decay studies are given in Tables 6 and 7 of Appendix A:. A total of almost 120 fission products have been assessed as significant contributors to the decay heat of various fissionable materials used to determine and benchmark the residual post-irradiation decay heat for the fast fission of $^{232}$Th, $^{233,238}$U and $^{237}$Np, and the thermal fission of $^{235}$U, $^{238,239,240,241,242}$Pu, $^{241}$Am and $^{243,245}$Cm. A similar statement can also be made when considering predictive spectral calculations of the resulting antineutrinos emitted by operational reactor systems. References assigned Nuclear Science References (NSR) keynumbers that appear in Tables 6 and 7 are fully listed in Table 8 of Appendix A:. Highly-specific recommendations have been made as to whether additional discrete $\gamma$-ray spectroscopy and/or TAGS/TAS measurements are merited, as comprehensively summarized in Table 2.

Table 2 Summary assessments/re-assessments of fission-product decay data for decay-heat calculations: requests for specific measurements by means of Discrete Gamma-ray Spectroscopy (DGS) or Total Absorption Gamma-ray Spectroscopy (TAGS) denoted by ‘y’ $\rightarrow$ ’yes’ (‘?’ $\rightarrow$ may need to be assessed further at a later date), with priorities judged in terms of 1 high, 2 intermediate, 3 low, and – satisfactory status and therefore not assigned a priority

4 Relevant TAGS/TAS measurements

Various nuclear decay data derived from TAGS/TAS have been compared with the equivalent data to be found in recommended decay data libraries, and more specifically the Evaluated Nuclear Structure Data File (ENSDF) [55], the Evaluated Nuclear Data File/B-VII and VIII [56,57,58], the Joint Evaluated Fission and Fusion Files 3.x [59,60,61], and the Japanese Evaluated Nuclear Data Files JENDL-Decay Data File-2011, 2015 and JENDL-5 [62,63,64]. ENSDF is primarily defined as an evaluation of experimental nuclear structure and decay data which constitutes a comprehensive database maintained on a mass-chain basis over an approximate eight- to ten-year re-evaluation cycle. The decay-data files within ENDF/B-VIII are incremental updates of the re-evaluated contents of ENSDF with various additions and a series of modest modifications as defined at the time of their assembly and issue for public access. An improved and updated re-release occurred in early 2018 as ENDF/B-VIII.0 [58]. Similarly, the JEFF-3.3 decay data sub-library is the latest version of an assembly of decay data [61] from ENSDF, the Decay Data Evaluation Project (DDEP) [65] and evaluations performed for the United Kingdom UKPADD-6.7 and UKHEDD-2.5 libraries [59, 66]. The recently released JENDL-5 decay data sub-library includes evaluated data from ENSDF combined with theoretical calculations using the Skyrme-Hartree-Fock theory combined with the Quasi-particle Random-Phase Approximation (Skyrme HF+QRPA) approach of Minato [67].

An impressive systematic study of TAGS spectra for almost 50 important fission products was undertaken in the 1990 s by Greenwood and co-workers at the Idaho National Engineering Laboratory, USA [7, 8, 26]. A tape system was used to collect and transport selected fission-isotope mass fractions from the spontaneous fission of a $^{252}$Cf-based ISOL system (Isotope Separation On-Line) for spectral analysis by means of a large single-ingot NaI(Tl) scintillation detector with an axial well that contained a Si detector to provide the means of obtaining $\beta$-$\gamma$ coincidence data along with $\beta$ $^{-}$ and $\gamma$ singles spectra (non-coincident). Their pioneering work involved TAGS measurements ranging from rubidium (starting with $^{89}$Rb) to yttrium (ending with $^{95}$Y) and from caesium (starting with $^{138}$Cs) to samarium/europium (ending with $^{158}$Eu) that has been substantially reconfirmed in more recent years, as outlined below. A major gap in their work arose as a consequence of the inability at that time to volatilise effectively the fission products of the refractory elements zirconium, niobium, molybdenum, technetium, ruthenium and rhodium in order to achieve optimum/suitable source preparation. Some of the radionuclides identified with these particular elements are expected to be important contributors to resulting reactor inventories, decay heat and antineutrino emissions of commercial irradiated nuclear fuel.

During the course of earlier assessments of the nuclear data needs for decay-heat and antineutrino spectral calculations as encouraged by the OECD-NEA and IAEA from 2005 to 2014 [11, 12, 14] and beyond, portions of the research programmes of a number of TAGS facilities were re-aligned towards the study of potential Pandemonium within the ill-defined decay schemes of specific chosen fission products (see for example, Refs. [9, 68, 69]). These more recent and on-going experimental studies are described below, along with earlier notable work that remains highly relevant to our existing objectives within both nuclear applications and basic nuclear physics research. First motivated by Yoshida et al. [70] and evaluation work undertaken as part of an OECD-NEA/IAEA initiative [11], a series of dedicated experimental TAGS/TAS studies were undertaken at the University of Jyväskylä, Finland, by the TAGS team from the Instituto de Física Corpuscular, CSIC, Universidad de Valencia, Spain, and co-workers. Work began to assess and confirm known decay-heat benchmarks, and was rapidly extended to consider observed difficulties in reproducing and defining the antineutrino spectra emitted from commercial reactor systems. Experiments were performed at the IGISOL (Ion-Guide Isotope Separator On-Line) facility, University of Jyväskylä, in which fission products produced by proton bombardment of $^{238}$U recoiled out of the target and were transported by helium gas flow to the early stages of a separator and Penning trap with a mass-resolving power of 10$^{5}$ (JYFLTRAP) located adjacent to a Total Absorption Gamma-ray Spectrometer. Adoption of the Penning trap as an isotope separator resulted in high-purity sources that are of great benefit for this type of study. The first measurements were performed with a TAGS spectrometer that consisted of two cylindrical NaI(Tl) crystals, of which the larger possessed a longitudinal hole along the axis in which a silicon detector could be placed for coincidence studies at the defined measuring point and source location. A large amount of $\gamma$ strength was observed for $^{105}$Mo and $^{104,105,106,107}$Tc that had not previously been detected in earlier high-resolution $\gamma$-ray measurements [9]. Results are listed in Table 3 for a number of related studies that focused strongly on $^{102,104,105}$Tc [9, 68, 71,72,73,74]. An important conclusion from this work was that five of the seven radionuclides studied were found to exhibit the Pandemonium effect, with the need to confirm, explore and improve quantification of their inadequate decay parameters in greater detail by means of Discrete Gamma-ray Spectroscopy (DGS).

Table 3 Ground-state to ground-state $\beta$ $^{-}$ feedings, half-lives and average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ energies for $^{86,87,88}$Br, $^{91,94,95}$Rb, $^{100,100m,101,102,102m}$Nb, $^{105}$Mo, $^{102,104,105,106,107}$Tc, and $^{137}$I, determined from IGISOL-TAGS measurements published in the last decade [9, 30, 34, 68, 75,76,77], and compared with equivalent data determined from ENSDF database of 2022 [55], ENDF/B-VIII.0 data library of 2018 (ENDF/B8) [58], JEFF-3.3 data library of 2020 [61], and JENDL-5 data library of 2021 [64]. Where no values are provided for the TAGS ground-state to ground-state $\beta$ $^-$ feedings, the ENSDF values available at the time were used in the analysis leading to a fair reproduction of the measured data

As shown in Refs. [9, 68], the inclusion of TAGS average-energy values for $^{105}$Mo and $^{104,105,106,107}$Tc (particularly for $^{104,105}$Tc) in decay-heat summation calculations for a thermal-fission pulse in $^{239}$Pu results in significant improvement and better agreement with compiled experimental decay-heat benchmark data over cooling times from 300 to 3000 s, supporting the importance of identifying potential Pandemonium as highlighted by Yoshida et al. [70]. Equivalent comparisons with a thermal-fission pulse in $^{235}$U exhibit much less impact on the summation calculations, that can be attributed to the reasonably large differences in their cumulative fission yields (these particular cumulative fission yields in $^{239}$Pu are a factor of 2.5 higher than for $^{235}$U). Another point of note is that the $\beta$ $^{-}$ decay of $^{102}$Tc involves a significant fraction of direct feeding to the daughter ground state, which is deemed to be difficult to describe by means of gross $\beta$ $^{-}$ theory. Efforts were also made to describe the Gamow-Teller $\beta$ $^{-}$ decay properties of both $^{102,104}$Tc [68] employing the complex excited VAMPIR code and the gross theory of $\beta$ $^{-}$ decay.

TAGS/TAS measurements by the Valencia-led team at the University of Jyväskylä have also included the possibility of identifying Pandemonium within the decay schemes of beta-decaying isomers such as $^{100}$Nb, $^{100}$Nb$^{m}$ and $^{102}$Nb, $^{102}$Nb$^{m}$ [76, 80]. A natural uranium target was irradiated at the IGISOL facility with 25-MeV protons to induce fission prior to high-resolution mass separation within the JYFLTRAP double-Penning trap in order to isolate zirconium parents and niobium daughter nuclides for delivery to and study by means of the DTAS detector array (operated as eighteen modular NaI(Tl) scintillators in cuboid form). Several techniques were used to separate the different contributions of the metastable and ground-state decays, and their results were consistently compared. Both $^{100}$Nb and $^{102}$Nb exhibited evidence for metastable states of similar half-lives to those of their ground states, whereby $^{100}$Zr (0$^{+}$) and $^{102}$Zr (0$^{+}$) populated the low-spin niobium levels of $^{100}$Nb$^{g}$ and $^{102}$Nb$^{m}$, respectively. Absolute $\gamma$-ray emission probabilities were determined on the basis of their depopulation of $^{100}$Mo and $^{102}$Mo nuclear levels that had been populated by the $\beta$ $^{-}$ decays of $^{100,100m}$Nb and $^{102,102m}$Nb, respectively, and these values were in good agreement with known equivalent data when the branching-ratio matrix employed in the analysis was modified. Significant $\beta$ $^{-}$ intensity was found at high excitation energies for which there were no previously known data, and the resulting average $\beta$ and $\gamma$ energies obtained in this work impacted significantly on calculations of both decay heat and antineutrino spectra (listed in Table 3). Thus, the $\gamma$ component of decay heat for $^{235}$U and $^{239}$Pu exhibited an increase of $\sim 3\%$ at 10 s cooling time and a decrease of between 1$\%$ and 3$\%$ at shorter cooling times; reactor antineutrino spectral calculations revealed evidence of the significant impact of these measurements in the energy region of 5 to 7 MeV by up to 2$\%$ for $^{235}$U and 6$\%$ for $^{239}$Pu over what has previously been known as an area of excessive shape distortion [80].

The Valencia-Nantes-Surrey-Jyväskylä team has explored $\beta$ $^{-}$ intensities to daughter states above the neutron separation energy, which has involved extensive determination of the $\gamma$-ray emissions from the $\beta$ $^{-}$ decay of $^{87,88}$Br and $^{94}$Rb by means of TAGS [30, 32, 81,82,83]. Rocinante is a twelve-fold segmented BaF$_{2}$ detector system that has been operated in conjunction with the IGISOL mass separator and JYFLTRAP Penning trap to achieve a total $\gamma$ detection efficiency of greater than 80$\%$ for $\gamma$ cascades, while also possessing the advantage of reduced neutron sensitivity when compared with equivalent NaI(Tl) scintillator systems. Detailed contamination analyses of descendant $\beta$ $^{-}$ and $\beta$ $^{-}$n decay have been conducted, along with the derivation of overall uncertainty estimates. As shown in Table 3, all three radionuclides exhibit a significant Pandemonium effect, and none more so than $^{94}$Rb with an overall average $\gamma$ energy that is a factor of 2.14 larger than the calculated value from the ENDF/B-VIII.0 database. However, the thermal fission yield of $^{94}$Rb is relatively small in $^{235}$U/$^{239}$Pu nuclear fuel, which mitigates against such a radionuclide playing a significant role in the generation of substantial decay heat. A further comparison shows that the integrated intensity of $\gamma$ decay above the neutron separation energy ($S_n$) in the case of $^{87}$Br is larger than $P_n$, and is eight times more intense than known previously from high-resolution $\gamma$ spectroscopy [30]. TAGS data from all three of these fission products impact in various modest degrees on decay-heat summation calculations at short cooling times, particularly the photon component of $^{94}$Rb and $^{88}$Br to a lesser degree, while the calculated antineutrino spectrum exhibits a reduction of intensity by a maximum of 6$\%$ at 7.2 MeV for the thermal fission of $^{235}$U and $^{239}$Pu [30, 81]. As an important follow-up to the above, the new DTAS detector assembly of eighteen modular NaI(Tl) crystals has been used to study $^{93,95}$Rb, $^{103}$Mo, $^{103}$Tc and $^{137,138}$I, with the provision to install large ancillary detectors for improved energy resolution and enhanced detection efficiency [34, 83, 84]. As mentioned earlier, TAGS has been successfully used to study $\gamma$-ray emissions above $S_n$ in $\beta$-delayed neutron emitters, and in doing so has provided accurate information to improve (n,$\gamma$) cross-section assessments far from $\beta$ $^{-}$ stability. One surprising observation from this work has been the high ratio of the integrated $\gamma$ intensity for emissions from the states above the neutron separation energy ($S_n$) to the total intensity for many of the radionuclides studied. Such behaviour points firmly towards the need to improve our understanding of photon-strength functions and neutron transmission coefficients [83, 85]. These studies are complicated by contamination from $\beta$-n decay branches, and therefore efforts were made to evaluate the systematic uncertainties with greater accuracy and confidence. As described above, the decay measurements of $^{87,88}$Br and $^{94}$Rb were part of an integral experimental effort to study these beta delayed-neutron emitters by means of a number of complementary experimental techniques.

Some of the experimental work was directed towards measurements of the $\beta$-delayed-neutron emission probabilities for particular fission products of importance to decay-heat and antineutrino studies. As developed initially in Spain, the BELEN-20 4$\pi$-neutron counter consists of twenty $^{3}$He proportional counters arranged as two rings of eight and twelve tubes within a large polyethylene neutron moderator around a central hole that contained either a 0.5-mm thick Si detector or 3-mm thick plastic scintillator to count $\beta$ $^{-}$ emissions from sources of high-purity fission products implanted into a movable tape after passage through the IGISOL mass separator and JYFLTRAP at the University of Jyväskylä. Another noteworthy feature of this detector system is the incorporation of self-triggered digital data acquisition with reduced deadtime [82]. Early studies were directed towards the delayed-neutron decay of $^{88}$Br, $^{94,95}$Rb and $^{137}$I [82], and have been further extended to $P_n$ measurements of $^{135}$Sb, $^{138,139,140}$I and $^{137,138}$Te decay following the development of the BELEN-48 array of forty-eight $^{3}$He proportional counters located in three rings of six, twelve and thirty tubes around the central hole [86]. Measured P$_n$ data from these experiments are compared in Table 4 with recommended values evaluated during the course of an IAEA-coordinated research project [87]. All compiled and evaluated P$_n$ data contained within Ref. [87] are available in the form of an IAEA Reference Database of beta-delayed-neutron data (http://www-nds.iaea.org/beta-delayed-neutron/database.html).

Table 4 Experimentally determined branching fractions of $\beta$-n decay modes [82, 86], compared with recommended values from the evaluation of Liang et al. [87]

TAGS/TAS measurements performed by the Valencia-Jyväskylä-Nantes team have expanded over the years in order to improve benchmark calculations of the resulting antineutrino spectra by undertaking individual experimental measurements of $^{86}$Br and $^{91}$Rb [75, 88], $^{92}$Rb [89,90,91], $^{100,100m,102,102m}$Nb and $^{140}$Cs [35] (see Table 3), $^{100}$Tc [92] and $^{142}$Cs [90]. The $\beta$ $^{-}$ decay of $^{91}$Rb is highly relevant in decay-heat studies because the decay of this radionuclide has been adopted as a calibration point in the average $\gamma$ energy measurements performed by Rudstam et al. [93], assuming that $^{91}$Rb does not suffer from the Pandemonium effect. The work of Rice et al. [75] shows that this is not the case, and that the average energies quoted by Rudstam et al. should be re-normalised by an adjustment factor of 1.14.

Rocinante with twelve segmented BaF$_2$ crystals and DTAS with eighteen modular NaI(Tl) scintillators in cuboid form have also been employed as $\gamma$ detector assemblies to improve our knowledge of the decay of particular fission-product nuclides in terms of the quantification of their total energies, average $\beta$  and $\gamma$ energies, and contributions to summed antineutrino spectra of operational interest. Both $^{95}$Rb and $^{137}$I are $\beta$ $^{-}$-delayed neutron emitters, and were prepared on the IGISOL facility coupled to the JYFLTRAP for isobaric separation prior to $\gamma$-ray spectral analysis by means of DTAS and HPGe, along with a plastic scintillator for the detection of $\beta$ $^{-}$ emissions for gated spectra [77]. A significant amount of $\beta$ $^{-}$ intensity was observed to populate states above the neutron separation energy, which underwent subsequent $\gamma$-ray de-excitation with comparable emission probabilities to those of the delayed neutrons. While the TAGS data in Table 3 for $^{95}$Rb show the average $\gamma$ energy to be significantly underestimated and the average $\beta$ energy to be more modestly underestimated in ENDF/B calculations, the low cumulative fission yield of this particular fission product in $^{235}$U and $^{239}$Pu thermal fission will result in relatively low impact, and therefore has not been considered in Tables 6 and 7. Average energy data in ENDF/B calculations for $^{137}$I are in reasonable agreement with the average $\beta$  and $\gamma$ energies determined by TAGS (Table 3) such that the database already contains and reflects the $\beta$ $^{-}$ population of the higher-energy nuclear levels of $^{137}$Xe and delayed-neutron decay to $^{136}$Xe. Both the extracted ground-state feeding and average $\gamma$ energy validate the previous MTAS $^{137}$I values, representing another example of two distinct sets of TAGS/TAS measurements obtaining consistently similar results. The $\beta$ $^{-}$ decay of $^{140}$Cs to $^{140}$Ba has been studied by means of the DTAS spectrometer at IGISOL IV as part of a measurement campaign undertaken in 2014. Since the half-lives of $^{140}$Cs and daughter $^{140}$Ba are 63.7 s and 12.75 days, respectively, the only contamination in the measurements was summing pile-up. Results from a preliminary analysis have been presented by Guadilla et al. [35]. The feeding distribution is in good agreement with previous results obtained by Greenwood et al. employing a different experimental set-up and analysis technique [8]. These high-resolution data exhibit evidence of the Pandemonium effect. The $\beta$ $^{-}$ decay of $^{100}$Tc was also studied [92] with the aim of assessing if the decay process suffers from Pandemonium, and as a consequence would impact on related double-beta decay studies. Furthermore, $^{100}$Tc $\beta$ $^{-}$ decay is of relevance for reactor applications as the product of a second-order process, which is based on fission followed by neutron-capture activation of the fission product before $\beta$ $^{-}$ decay occurs. This phenomenon has been explored as a possible explanation for the distortion of the antineutrino spectrum from reactors in the 4–6 MeV energy range [94]. Continued TAGS/TAS measurements and more extensive data analyses are also being jointly planned or are underway that include the mass region around $^{100}$Sn by RIKEN-Valencia [95, 96] and the mass region around $^{208}$Pb at GSI(FAIR)-Valencia [97].

TAGS/TAS experimental studies commenced in early 2012 at the On-Line Test Facility (OLTF) of the Tandem accelerator of the Holifield Radioactive Ion Beam Facility (HRIBF) at the Oak Ridge National Laboratory (ORNL). The Modular Total Absorption Spectrometer (MTAS) has been designed, constructed and assembled, and work undertaken to measure and characterise the decay products from 40-MeV energy 50 nA proton-beam irradiations of a $^{238}$UC$_x$ target. An array of nineteen hexagonal-shaped NaI(Tl) detectors weighing 1000 kg are aligned in a honey-combed geometry covering 99$\%$ of the solid angle around the activity to be measured. Each NaI(Tl) crystal is 53 cm in length and just over 20 cm maximum diameter. Surrounded by bespoke shielding, including over 5000 kg of lead and borated high-density polyethylene neutron shielding, the $\gamma$ background has been reduced by a factor of 1000. Nuclei of interest are deposited on to a tape transport system monitored by HPGe detectors for isotope identification. The tape transports these nuclei to auxiliary $\beta$ $^{-}$ detector triggers, two 1-mm thick segmented Si crystals (each divided into seven 8.5-mm wide strips) surrounding the transport tape over 95% of the solid angle, and resulting in greater than 90% $\beta$ $^{-}$-trigger efficiency for most fission nuclides. The activity triggers the silicon detectors for $\beta$-$\gamma$ coincidence studies between these detectors and the MTAS NaI(Tl) array. Simulated response functions and spectral modelling combined with a series of preliminary experimental studies have assisted greatly in the development of the spectrometer towards nuclear applications and more basic nuclear physics research [29, 36,37,38,39, 69, 98].

Seventy-seven fission products were studied at various times over the course of 2012 to 2016 by means of MTAS. Relevant spectral analyses have been reported for $^{86}$Br, $^{89,90}$Kr, $^{89,90,90m,92}$Rb, $^{137}$I, $^{139}$Xe, and $^{142}$Cs [36, 39, 69, 98, 99], and to a greater extent and emphasis for $^{89}$Br, $^{96}$Y, $^{137}$I, $^{137}$Xe, $^{142}$Ba and $^{142}$La [37, 38, 40, 100,101,102]. Table 5 lists the various ground-state to ground-state and other selected $\beta$ $^{-}$ emission probabilities, as well as the average $\beta$ and $\gamma$ energies for $^{86}$Br, $^{88,89,90}$Kr, $^{88,89,90,90m,92}$Rb, $^{96}$Y, $^{98}$Nb, $^{137}$I, $^{137,139}$Xe and $^{142}$Cs as derived from MTAS measurements [39,40,41,42, 69, 99], compared with equivalent data in the ENDF/B-VIII [58], JEFF-3.3 [61], and JENDL-5 [64] libraries.

Table 5 Ground-state to ground-state $\beta$ $^{-}$ feedings, half-lives and average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ energies for $^{86}$Br, $^{88,89,90}$Kr, $^{88,89,90,90m,92}$Rb, $^{98}$Nb, $^{139}$Xe and $^{142}$Cs, as derived from MTAS measurements [39,40,41,42, 69, 99], and compared with equivalent data determined from ENSDF database of 2022 [55], ENDF/B-VIII.0 data library of 2018 (ENDF/B8) [58], JEFF-3.3 data library of 2020 [61], and JENDL-5 data library of 2021 [64]

• Studies of $^{86}$Br include the suggested introduction of 65 pseudo-levels starting at an excitation energy of 5 MeV, along with the observation of 487 additional branches that require incorporation into the proposed decay scheme [36]. Ground-state to ground-state $\beta$ $^{-}$ feeding was determined to be just over 20$\%$, compared with a previously assigned value of 15(8)$\%$. These results are also in good agreement with the studies of Rice et al. [75].

• $^{89}$Kr studies indicate the need for substantial changes in the accepted decay scheme that would appear to be incomplete and erroneous. A shift of $\beta$ $^{-}$ feeding from lower-energy states of 1530–2400 keV to higher levels was observed, and ground-state to ground-state $\beta$ $^{-}$ feeding was determined to be 11(1)$\%$ compared with a previously accepted value of 23(4)$\%$ [69].

• $^{90}$Kr also exhibits the need for substantial changes to be made to the accepted decay scheme. Ground-state to ground-state $\beta$ $^{-}$ feeding was determined to be 7(1)$\%$ compared with a previously assigned value of 29(4)$\%$ [69].

• Reductions were observed in the $\beta$ $^{-}$ feeding by both $^{90}$Rb and $^{90}$Rb$^{m}$ to the first excited 2$^{+}$ state of $^{90}$Sr to be found at 831.68 keV (15(1)$\%$ for $^{90}$Rb, and 5(1)$\%$ for $^{90}$Rb$^{m}$, compared with previously adopted values of 26(2)$\%$ and 15(4)$\%$, respectively) [69].

• TAGS measurements of $^{92}$Rb by means of MTAS are consistent and in good agreement with the studies of Zakari-Issoufou et al. [91]. Ground-state to ground-state $\beta$ $^{-}$ feeding was determined to be 91(3)$\%$ by Rasco et al. [39], compared with a similarly determined value of 87.5(25)$\%$ [91].

• Beta-decay studies of $^{98}$Nb by Rasco et al. have quantified ground-state to ground-state feeding, along with beta feeding to the second $0{+}$ state in $^{98}$Mo that de-excites via an E0 transition by exploiting the modularity of the MTAS detector and coincidences with the beta detector [42]. An average gamma energy of 275(29) keV has also been deduced. $\beta$ $^{-}$ feedings to eight excited levels above the 2608 keV level in $^{98}$Mo are reported, along with an overall impact on antineutrino calculations.

• Direct MTAS studies of $^{137}$I $\beta$ $^{-}$ decay (T$_{1/2}$ of 24.5(2) s) show a dominant ground-state to ground-state $\beta$ $^{-}$ transition of 49(1)$\%$ [40], compared with a recommended value of 45.2(5)$\%$ in ENSDF, while the average ${\overline{E}}_{\gamma }$ increases by 19$\%$ from 1050 to 1250 keV. Measured $\beta$ $^{-}$ feeding at the neutron separation energy is also greater by a factor of two, and increases by a further factor of five or more above this separation energy when compared with the ENSDF database. Altogether, there are sufficient differences in MTAS measurements and the currently recommended decay scheme data for $^{137}$I to merit further well-defined $\gamma$ singles and $\gamma$-$\gamma$ coincidence studies. An additional noteworthy observation is that a P$_n$ branch of 0.079 $(\pm ~0.004(sys))(\pm ~0.002(fit))$ has been derived which is in good agreement with a value of 0.0776 ± 0.0014 obtained by Agramunt et al. based on the use of BELEN [82].

• $^{139}$Xe exhibits the need for substantial changes in the accepted decay scheme [69, 98]. $\beta$ $^{-}$ emission probabilities to nuclear levels above 2500 keV increased by over 15$\%$, along with the introduction of various new $\beta$ $^{-}$ feedings to proposed levels above 3600 keV. Ground-state to ground-state $\beta$ $^{-}$ feeding was determined to be 2(1)$\%$ compared with a previously accepted value of 15(10)$\%$.

• Although the $\beta$ $^{-}$ decay of $^{142}$Cs is insufficient to register as significant in decay-heat calculations, the decay chain from this radionuclide generates both $^{142}$Ba and $^{142}$La that have much greater impact. Under these circumstances, TAGS and DGS decay-scheme studies of the parent fission product are of some importance and relevance. $^{142}$Cs exhibits a need for substantial changes in the accepted decay scheme, whereby $\beta$ $^{-}$ emissions were observed to populate a number of new higher-energy nuclear levels [39, 69, 102]. Ground-state to ground-state $\beta$ $^{-}$ feeding was determined to be 43(3)$\%$ compared with a previously adopted value of 56(5)$\%$, and ground-state $\beta$ $^{-}$ feeding to the first excited 2$^{+}$, 359.60-keV nuclear level of $^{142}$Ba was reduced to < 0.5$\%$ compared with a previously agreed value of 7.2(12)$\%$. While a major contributor to the high-energy component of $\overline{\nu }_e$ spectra, the observed reduced $\beta$ feeding at energies below 1.8 MeV (inverse beta-decay threshold) implies an increase in the $\overline{\nu }_e$ flux at energies below the low-energy detection limit for antineutrinos. On the other hand, the $\overline{\nu }_e$ flux between 5 and 7 MeV decreases, thereby enhancing the discrepancy between the observed and expected $\overline{\nu }_e$ spectrum.

• As studied by Wolińska-Cichocka et al. by means of the MTAS [37], the decay scheme of $^{142}$La (T$_{1/2}$ of 5466(30) s) was found to be in good agreement with another TAGS study [8], but to differ somewhat from the recommended decay data within ENSDF. $\beta$ $^{-}$ feeding to the first excited state of daughter $^{142}$Ce (2$^{+}$, 641.282 keV) was determined to be a factor of two higher than the value of 1.4(4)$\%$ in ENSDF. Discrepancies were also observed in the $\beta$- population of levels over the energy region of 2–5 MeV, along with consideration of possible $\beta$ $^{-}$ feeding at even higher levels close to the energy limit. Further TAGS/TAS analyses of existing $^{142}$La spectra would seem to be merited as an important aid in resolving these disparities.

Definitive points of note from the above MTAS campaign are the requirements for in-depth $\gamma$ singles and both $\beta$-$\gamma$ and $\gamma$-$\gamma$ coincidence measurements of $^{86}$Br, $^{89,90}$Kr, $^{90,90m,92}$Rb, $^{139}$Xe and $^{142}$Cs $\beta$ $^{-}$ decay, along with further TAGS and DGS studies of $^{98}$Nb, in order to strive for the determination of an appropriate and comprehensive set of decay schemes.

MTAS studies of other radionuclides have included observations that are in good agreement with existing HPGe measurements of their $\gamma$-ray decay, and hence align with the recommended decay schemes to be found in the ENSDF database:

• Decay data identified with the $\beta$-delayed neutron decay of $^{89}$Br have been obtained from MTAS spectral analyses involving the operation of the central NaI(Tl) crystal in coincidence with the ancillary Si detector, along with an energy gate of 6.6 MeV to the Q($\beta$ $^{-}$)-value on the inner, middle and outer rings of the main NaI(Tl) detectors. Two $\gamma$ peaks were evident at approximately 750 and 1600 keV that correspond to $\gamma$ depopulation from the first two excited states of $^{88}$Kr with energies of 775.32 and 1577.43 keV. The response function of the MTAS detector system to mono-energetic neutrons of differing kinetic energies was also shown to agree well with various other forms of dedicated experimental study [38]. To date, no ground-state to ground-state feedings or mean energies have been provided.

• Ground-state to ground-state feedings of the $\beta$ $^{-}$ decay of $^{88}$Kr and $^{88}$Rb have been determined by Shuai et al. [41]. Data precision was improved in the case of $^{88}$Kr, and the sensitivity to the shape of the first forbidden decay in the determination of the ground-state to ground-state $\beta$ $^{-}$ emission of $^{88}$Rb was also considered. Small differences in the feeding distributions were observed in both $^{88}$Rb and $^{88}$Kr decay with respect to earlier high-resolution studies.

• TAGS data for $^{89}$Rb are in good agreement with existing $\gamma$ singles (non-coincident) spectroscopy; little to no evidence of the Pandemonium effect [69].

• $^{96}$Y (T$_{1/2}$ of 5.34(5) s) was determined by MTAS to possess a high ground-state to ground-state $\beta$ $^{-}$ emission probability of 95.5(20)$\%$, in agreement with the recommended value of 95.5(5)$\%$ in ENSDF. Difficulties in detection arose as a consequence of the E0 transition from the 0$^{+}$, 1581.34-keV first excited state to the 0$^{+}$ ground state of $^{96}$Zr, which is effectively via conversion electrons that are too energetic to achieve an efficient response in the 1-mm thick silicon detectors [39, 101]. The impact of the E0 transition in this beta decay has also been fully considered in the recent work of Guadilla et al. [103].

• $^{137}$Xe (T$_{1/2}$ of 229.1(8) s) was determined by MTAS to decay almost exclusively via $\beta$ $^{-}$ emission to both the first excited state (5/2$^{+}$, 455.491(3) keV) and ground state (7/2$^{+}$, 0.0 keV) of $^{137}$Cs with emission probabilities of 31(1)$\%$ and 67(2)$\%$, respectively, to give a total probability of 98(2)$\%$. All of these particular decay data are in agreement with the equivalent recommended values of 31(3)$\%$, 67(3)$\%$ and 98(4)$\%$ in ENSDF. Another decay parameter to be highlighted is the $\beta$ $^{-}$ feeding ratio for the population of the 2850.04(9)- and 2849.11(13)-keV nuclear levels of daughter $^{137}$Cs with values of 8.0(9) measured by MTAS and 7.2(13) in ENSDF. This constitutes reasonably good agreement in a relatively complex decay scheme of predominantly low-intensity transitions, other than two higher-energy $\beta$ $^{-}$ emissions and their associated $\gamma$ ray [40, 100].

• $^{142}$Ba (T$_{1/2}$ of 636(12) s) decay scheme as determined by MTAS was found to be in good agreement with another TAGS study [8] and existing HPGe $\gamma$-ray measurements. As would be expected under such circumstances, the MTAS data for the $\beta$ $^{-}$ decay of $^{142}$Ba are also in good agreement with the equivalent data in the ENSDF database [37, 102].

Over sixty fission products studied by means of MTAS remain to be fully analysed and evaluated, and this work continues [104]. Further MTAS measurements and data analyses are also being planned that will involve the Californium Rare Isotope Breeder Upgrade (CARIBU) of the Argonne Tandem Linac Accelerator System (ATLAS facility) at the Argonne National Laboratory (ANL), USA. Along with existing lead and neutron shielding, a concrete wall separating the $^{252}$Cf spontaneous fission source of CARIBU from MTAS has reduced the background activity substantially over an energy range of 30 keV to 8 MeV, from 2.4 kHz at ORNL to 1.9 kHz at ANL. The existing facilities at ANL include a gas cell and high resolution mass separator able to handle the isotopes of refractory elements that include $^{98,99,100,101,102}$Nb, $^{103,104,105}$Mo and $^{103,104,105,106,107}$Tc. New activities are envisaged along with some repeat measurements at lower background conditions with an MTAS of greater efficiency and modularity. As noted in Sect. 2, MTAS in an improved form has also been installed as a research tool at the Facility of Rare Ion Beams (FRIB), Michigan State University, East Lansing, USA [49, 50]. An extensive range of silicon PIN detectors, double-sided silicon-strip detector (DSSD), silicon surface barrier detector and a summing NaI(Tl) SuN detector have been used to monitor and determine the half-lives of a number of separated relevant fission fragments from the spallation reaction of a 120 MeV/u $^{124}$Sn beam on a $^{9}$Be target [105]. TAGS/TAS studies have been performed by means of the SuN array of eight segments of NaI(Tl), with each segment containing three photomultiplier tubes. Both TAGS and the sum-of-segments spectra were used to identify the radionuclides of interest and determine their half-lives. Seven such nuclides were studied in this manner, of which $^{102}$Nb$^{m}$ with a half-life of 1.33(27) s and $^{104}$Nb$^{m}$ with a half-life of 0.97(10) s are of particular note. While not considered in this wide-ranging assessment because of their questionable existence in the earlier stages of our work, there is increased merit in re-considering their present status with respect to their roles in the calculation of decay heat and antineutrino spectra.

Properties of neutron-rich nuclei in the fission-product and light rare-earth regions have been explored experimentally at Argonne National Laboratory [106,107,108,109,110]. Discrete $\beta$-$\gamma$-$\gamma$ spectroscopy measurements were conducted by means of a newly-commissioned decay station at the Gammasphere facility, along with related studies employing a Canadian Penning trap and X-array spectrometer (five Ge clover detectors). Initial studies were motivated by nuclear structure research whereby the emphasis was placed on $^{160,162}$Eu, followed by DGS measurements of $^{98}$Y, $^{102,104}$Zr, $^{98}$Nb, $^{102}$Nb$^{g,m}$, $^{104}$Nb$^{g,m}$, $^{102,104}$Mo, $^{144,146}$Ba, $^{144}$La, $^{146}$La$^{g,m}$ and $^{146}$Ce. Neutron-rich $^{98}$Nb, $^{102}$Nb$^{g,m}$, $^{104}$Nb$^{g,m}$, $^{102,104}$Mo, $^{144}$Ba, $^{144}$La and $^{146}$La$^{g,m}$ are of particular interest with respect to decay-heat and antineutrino calculations, and these measurements will be further analyzed and assessed in order to improve our knowledge of their decay schemes.

5 Impact of TAGS measurements on decay-heat calculations

Nuclear fuel decay-heat calculations require individual quantitative inventory data for all the actinides, their heavy-element decay products, and nearly a thousand fission products produced within the fuel as a function of the cooling time after shutdown. After the changing inventories of all the fission-product nuclides and actinides have been calculated on the basis of their formation cross sections and subsequent decay, these data for a particular radionuclide can be multiplied by the relevant decay constant and the various average energies released per decay. These energies are summed over all the radionuclides and all possible decays to yield the resulting total decay heat at designated cooling times. The total average energy per decay ${\overline{E}}_{T}$ released by a fission product or actinide consists of contributions from the average energy released as the kinetic energy of light-particle transitions ${\overline{E}}_{LP}$ (most frequently as $\beta {^-}$ emissions), heavy particles ${\overline{E}}_{HP}$, and as electromagnetic radiation ${\overline{E}}_{EM}$:

$$\begin{aligned} {\overline{E}}_T = {\overline{E}}_{LP} + {\overline{E}}_{EM} + {\overline{E}}_{HP}, \end{aligned}$$

where

$$\begin{aligned} {\overline{E}}_{LP}= & {} {\overline{E}}_{\beta ^-} + {\overline{E}}_{\beta ^+} + {\overline{E}}_{ce} + {\overline{E}}_{Auger}, \\ {\overline{E}}_{EM}= & {} {\overline{E}}_\gamma + {\overline{E}}_{X-ray} + {\overline{E}}_{annih} + {\overline{E}}_{bremss},\\ {\overline{E}}_{HP}= & {} {\overline{E}}_\alpha + {\overline{E}}_{n,p} + {\overline{E}}_{SF}~\ldots , \end{aligned}$$

in which:

${\overline{E}}_{\beta ^{\pm }}$ is the average kinetic energy of $\beta ^{\pm }$ particles,

${\overline{E}}_{ce}$ is the average kinetic energy of the internal-conversion electrons,

${\overline{E}}_{Auger}$ is the average kinetic energy of the Auger electrons,

${\overline{E}}_\gamma$ is the average $\gamma$-ray energy,

${\overline{E}}_{X-ray}$ is the average X-ray energy,

${\overline{E}}_{annih}$ is the positron annihilation energy associated with $\beta ^+$ decay,

${\overline{E}}_{bremss}$ is the internal bremsstrahlung energy,

${\overline{E}}_\alpha$ is the average kinetic energy of the $\alpha$ particles,

${\overline{E}}_{n,p}$ is the average kinetic energy of neutron/proton emissions,

and ${\overline{E}}_{SF}$ is the total recoverable energy associated with spontaneous fission.

These average energies are normalized per decay of the fission-product nuclides and parent actinides (including spontaneous fission), and are determined or adopted directly from decay-data libraries containing best recommended data for the radioactive properties of the emitted light particles, heavy particles and electromagnetic radiation (see Ref. [111] for details).

The first appropriate decay-data libraries were developed at the end of the 1970 s as a consequence of separate efforts in Europe, Japan and the USA. These libraries were largely based on experimental discrete spectral data available at the time. However, they all failed to reproduce the integral-type sample-irradiation measurements of decay heat performed by Dickens et al. [112] and Akiyama and An [113] that had become available as potential benchmarks to validate the above three libraries. Comparisons of the measured light-particle (LP) and electromagnetic (EM) decay heat with calculated values indicated that the LP (${\beta ^-}$) component was overestimated, while the EM (${\gamma }$) component was significantly underestimated.

Members of the Japanese Nuclear Data Committee (JNDC) implemented the gross theory of $\beta ^-$ decay [114,115,116] in calculations of the average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ energies per decay. After applying the gross theory to fission-product nuclei for which no experimental information was available, this approach was applied further to all fission products with high $Q_\beta$ values, leading to significant improvements in the ${\beta }$ and ${\gamma }$ components of the decay heat in reproducing the sample-irradiation experiments [117]. An NEANDC specialists meeting on fission yields and decay data held in 1983 reached the following conclusions regarding the status of the decay-heat calculations [118]: (1) discrepancies between the calculated components of decay heat and their experimental measurements were defined as a manifestation of the Pandemonium effect in beta decay arising from incomplete high $Q_\beta$-value decay schemes used in the benchmark calculations, (2) adoption of gross $\beta ^-$ theory was only free from the problem in an average or aggregate sense, and (3) targeted experiments such as TAGS were required to assist in solving the problem. Extensive TAGS measurements of an impressive range of fission products of interest were performed by Greenwood et al. [8] in the mid-1990 s. The introduction of these resulting data into decay-heat summation calculations revealed the usefulness of this approach compared with the averaging inadequacies of the gross $\beta ^-$ theory [119]. More focused studies designed to address the decay heat of $^{239}$Pu were completed and made available for analysis by means of further decay-heat calculations approximately thirteen years later [9].

Theoretical values obtained from gross $\beta ^-$ theory were adopted for the mean decay energies of nuclides with $Q_\beta \ge$ 5 MeV in the JNDC fission-product decay data library [120], which eventually became part of JENDL. A similar approach that involved fitting parameters in a model based on gross $\beta ^-$ theory to replace $\beta ^-$ and $\gamma$ experimental energies was tentatively applied to the ENDF/B-IV decay-data sub-library with some success, and has been used up to and including ENDF/B-VI [121]. Both JENDL and the ENDF/B decay-data libraries up to version VI are effectively “contaminated” by theoretical values, creating difficulties in disentangling and clearly demonstrating the importance of TAGS data. On the other hand, average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ decay energies in the JEFF-3 decay-data files from the first release of JEFF-3.1 are based solely on experimentally-determined decay schemes. When no reliable or complete experimental decay data are available, the empirical $Q_\beta /3$ rule has been used as an estimate of the partition of the total released energy ($Q_\beta )$ into ${\overline{E}}_{LP}$, ${\overline{E}}_{EM}$ and the unrecoverable neutrino energy. The first TAGS data included in the JEFF-3.1.1 decay-data library [59] were taken from Greenwood et al. [8]. A comparison of the decay-heat calculations obtained with different versions of the series of JEFF-3 libraries in their chronological order offers insights into the growing impact of TAGS. Partial decay-heat calculations based on different releases of the JEFF-3 library are compared in Fig. 1 with the Tobias evaluated decay-heat data for thermal pulse fission of $^{239}$Pu [1]. JEFF-3.1 [59] does not include any gross $\beta ^-$ theory or TAGS data, and overestimates the LP ($\beta$) component and underestimates the EM ($\gamma$) component. JEFF-3.1.1 [59] includes several of the Greenwood et al. TAGS data [8] to give considerably improved agreement when compared with the experimental data for both the LP and EM components of decay heat. This is mainly attributed to the TAGS data being Pandemonium-free and more correctly representative of the relative contributions of $\beta ^-$ and $\gamma$ emission energies per decay. Further improvement is obtained with JEFF-3.3 [61], especially for the EM ($\gamma$) component between 30 and 4000 s cooling times after the fission burst, which now agrees with the evaluated decay-heat data. JEFF-3.3 includes the TAGS data for Nb, Mo and Tc isotopes which were measured by Algora et al. [9] after they were identified as primary sources of the large Pandemonium problem affecting $^{239}$Pu decay heat. Figures appearing hereafter follow the same convention as Fig. 1 in which the vertical axis is decay heat (MeV/fission/s) $\times$ time after fission pulse (s) in order to achieve reasonably compact and comprehensive plots.

Fig. 1

Comparison of decay heat for $^{239}$Pu thermal fission obtained using different JEFF libraries that attempt to deal with the Pandemonium effect over the years listed. The evaluated data of Tobias [1] were taken from the IAEA CoNDERC database [122]

We have studied the impact of TAGS data on the calculated decay-heat components (LP/EM) for the different fission-based systems discussed in Sect. 3 (see Table 1), focusing on the effect of the new TAGS data mentioned in Sect. 4 (Tables 3, 5). Decay-heat calculations were performed on the basis of three available evaluated nuclear-data libraries (ENDF/B, JENDL and JEFF), with their associated decay-data and fission-yield sub-libraries. All decay-data sub-libraries by definition include the average decay energies ${\overline{E}}_{LP/EM/HP}$ followed by the individual components listed in the earlier equations above. However, in the latest versions of these sub-libraries, only the ${\overline{E}}_{LP/EM/HP}$ values are included in the data section, while the breakdown into individual components that include contributions from the atomic radiation processes (${\overline{E}}_{ce/Auger/X-rays/\ldots }$) are listed in the comments section. When TAGS data are incorporated in the ENDF/B, JENDL and JEFF libraries, the average ${\overline{E}}_{LP/EM}$ energies are replaced by the TAGS-derived average ${\overline{E}}_{\beta ,\gamma }$ decay energies, omitting any possible contributions from the atomic radiation, internal bremsstrahlung, etc. Contributions from the atomic radiation processes to the average energy emitted per decay are usually small and can normally be neglected. However, there are certain cases such as $^{101}$Nb and $^{105}$Tc, in which the sum of the conversion electron ${\overline{E}}_{ce}$ and Auger electron ${\overline{E}}_{Auger}$ mean energies as derived from the discrete $\gamma$-ray spectra in ENSDF [55] amounts to $\sim$ 100 keV, i.e., $\approx$ 5% and 13% of the average TAGS-derived ${\overline{E}}_{\beta }$ for $^{101}$Nb and $^{105}$Tc, respectively. Full consideration of the various atomic contributions requires sound knowledge of the decay scheme measured by TAGS, and re-calculation of these atomic data for inclusion in the corresponding average decay energies.

Three sets of decay-heat calculations have been performed in combination with each one of the three fission-yield sub-libraries:

• 1. decay data without measured Algora (2010) TAGS data (baseline);

• 2. decay data with measured Algora (2010) TAGS data [9] (+ TAGS 2010);

• 3. decay data with recent measured TAGS data published or communicated before the cut-off date of February 2022 (listed in Tables 3, 5 (+ TAGS 2021).

Results have been generated for the thermal fission of $^{235}$U, $^{239}$Pu, $^{241}$Pu, and fast fission of $^{232}$Th, $^{233}$U, $^{237}$Np, $^{238}$U, for which experimental decay-heat measurements on neutron pulse irradiations exist. Pulse irradiation decay-heat data for single-actinide targets were obtained from the IAEA CoNDERC database [122]. Further comparisons of the decay-heat calculations are discussed in Sect. 5.4, as obtained with the existing general purpose libraries ENDF/B-VIII.0, JEFF-3.3 and JENDL-5 for all sixteen fissioning systems mentioned in Sect. 3.

5.1 ENDF/B-VIII.0 library

ENDF/B-VIII.0 decay-data and fission-yield sub-libraries have been combined to calculate the LP and EM components of decay-heat for seven fissioning systems for which experimental pulse decay-heat data exist. Average ${\overline{E}}_\beta$ and ${\overline{E}}_\gamma$ decay energies determined mainly from the discrete decay schemes recommended in ENSDF [55] are included in the ENDF/B-VIII.0 decay-data sub-library. Conversion-electron, Auger-electron and X-ray contributions have also been derived from the decay schemes by means of dedicated codes with their input data obtained from atomic-data libraries [123]. The library also includes average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ energies from the TAGS measurements of Greenwood et al. [8] for the following fission products: $^{90,90m,91,93}$Rb, $^{93,95}$Sr, $^{95}$Y, $^{140,141}$Cs, $^{143,144,145}$Ba, $^{142,143,144,145}$La, $^{147}$Ce, $^{146,147}$Pr and $^{149}$Nd. Beta feedings taken from Tengblad et al. [124] were used to determine E$_{\beta }$ for $^{88,89}$Br and $^{138}$I. When no experimental decay scheme was available, average energies were obtained from the Finite-Range-Liquid-Drop + QRPA model of Möller et al. [125]. From the most recent TAGS measurements listed in Tables 3, 5, the data for $^{104,105,106,107}$Tc and $^{105}$Mo by Algora et al. (2010) [9] and $^{142}$Cs by Rasco et al. (2016) [39] and Fijałkowska et al. (2017) [69] have also been incorporated into the ENDF/B-VIII.0 decay-data sub-library.

The three-step process to assess the impact of the recent TAGS measurements described above was implemented as follows:

• Step 1, baseline calculations: average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ decay energies of Algora et al. (2010) [9] were replaced with average ${\overline{E}}_{LP}$ and ${\overline{E}}_{EM}$ energies derived from the discrete decay schemes in ENSDF [55]. The same was done with the average decay energies of Rasco et al. (2016) [39] and Fijałkowska et al. (2017) [69] in the case of $^{142}$Cs. Therefore, baseline calculations with the ENDF/B-VIII.0 decay-data sub-library included only the Greenwood TAGS data [8] listed above (referred to as ENDF/B-VIII.0 (Greenwood)), data from Tengblad et al. [124] and model calculations [125].

• Step 2: adopted ENDF/B-VIII.0 decay-data file as default, which includes five of the seven fission products measured by Algora et al. (2010) [9], and added TAGS average energies for $^{102}$Tc and $^{101}$Nb [9] - although not impacted by Pandemonium, with TAGS and ENSDF-derived average energies in agreement. TAGS average decay energies of $^{142}$Cs [39, 69] were replaced by ENSDF-derived values (+ TAGS 2010).

• Step 3: all of the remaining TAGS data listed in Tables 3, 5 (+ TAGS 2021) were added to the decay-data sub-library that had been modified in step 2. Hence, this sub-library included all of TAS/DTAS studies mentioned by Algora et al. (2021) [28] and MTAS measurements on $^{89,90}$Kr, $^{89,90,90m}$Rb, $^{96}$Y, $^{137,139}$Xe and $^{142}$Cs from Rasco et al. (2016) [39] and Fijałkowska et al. (2017) [69]. However, known TAGS data for $^{96m}$Y, $^{98}$Nb, and $^{140}$Cs, were not included as they were published or provided through private communication after the cut-off date (February 2022) for these wide-ranging inventory calculations.

Experimental pulse simulations and inventory calculations were performed with the FISPACT-II code [126] at incident neutron energies for which decay-heat and fission-yield data exist, and are available in the relevant ENDF/B-VIII.0 sub-libraries (i.e., at thermal (0.0235 eV) and fast (500 keV) neutron energies). The three sets of calculations are compared with experimental decay-heat data in Figs. 2, 3. A consistent trend is emerging for all of the fissioning systems and energies whereby the inclusion of average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ energies derived from measured TAGS data leads to a decrease in the LP and an increase in the EM decay heat components, respectively. These gradual modifications in this manner to the relative contributions of the LP($\beta$) and EM($\gamma$) components of decay heat is direct confirmation of the fact that the TAGS-derived data are nominally free from the Pandemonium effect.

Fig. 2

Decay heat of fissionable actinides $^{233,235,238}$U and $^{239}$Pu, as a function of cooling time as obtained using the ENDF/B-VIII.0 fission-yield and decay-data sub-libraries [58], with the addition of TAGS data from [9] (+ TAGS 2010) and Tables 3, 5 (+ TAGS 2021). Experimental data have been taken from the CoNDERC database [122]

Fig. 3

Decay heat of fissionable actinides $^{241}$Pu, $^{232}$Th and $^{237}$Np, as a function of cooling time as obtained using the ENDF/B-VIII.0 fission-yield and decay-data sub-libraries [58], with the addition of TAGS data from [9] (+ TAGS 2010) and Tables 3, 5 (+ TAGS 2021). Experimental data have been taken from the CoNDERC database [122]

While the three sets of calculations reproduce the experimental decay-heat components fairly well, a particularly marked improvement is observed when including the TAGS data of Algora et al. [9] (+ TAGS 2010) in the decay-data sub-library. This much improved agreement had already been observed in the thermal decay-heat studies of $^{239}$Pu [9], with the present results for the decay-heat components of $^{238}$U fast and $^{241}$Pu thermal also exhibiting better alignment with their equivalent experimental data. The decay-heat components of the heavier actinides are sensitive to the decay heat of five of the previously selected fission products: $^{105}$Mo, $^{104,105,106,107}$Tc [11]. These observations contrast sharply with the negligible impact of these TAGS data on decay-heat calculations for $^{232}$Th, $^{233}$U and $^{237}$Np fast-neutron fission. Consideration of $^{235}$U thermal fission is both important and noteworthy: the LP component of decay heat is not affected by the inclusion of the TAGS data and is in good agreement with the experimental data, while the EM component for all three available sets of decay-heat data exhibits discrepancies [3, 112, 127]. At cooling times ranging from 1 to 400 s, these data sets agree within the experimental uncertainties, while above 400 s there is disagreement. Without the TAGS data of Algora et al. [9], the calculated EM component agrees with the Dickens data below 400 s [112], and with the evaluated data of Tobias above 400 s [3] - these observed differences between the Dickens data and Tobias evaluation remain unresolved to date.

Inclusion of all of the recent TAGS measurements (+ TAGS 2021) displayed in Tables 3, 5 (with the exception of $^{96}$Y$^{m}$ and $^{98}$Nb) leads to a small underestimation of the LP decay heat at cooling times in the range 10–1000 s for $^{233,238}$U fast and $^{235}$U, $^{239,241}$Pu thermal fission. The EM components for $^{233,235,238}$U, $^{241}$Pu and $^{232}$Th fission exhibit improved agreement at shorter cooling times below 100 s, whereas the relatively large increase in the EM component of $^{239}$Pu approaches the upper experimental limits. These results indicate that the inclusion of the (+ TAGS 2021) data is insufficient such that additional TAGS measurements of the remaining high priority fission products are merited to arrive at a robust description of the experimental pulse decay-heat data.

A re-assessment of the known decay-scheme data for further fission products should be undertaken to justify new TAGS measurements, along with an investigation of the experimental pulse-irradiation decay-heat data to determine the need for additional such studies. Apart from discrepancies in the experimental EM decay-heat data of $^{235}$U thermal fission that remain to be resolved, there are also issues with the experimental decay-heat data of $^{238}$U and $^{237}$Np. The EM decay-heat data of Akiyama and An [113] for $^{238}$U disagree with the data from Lowell measured by Schier and Couchell [127], while the LP components are in agreement. Two sets of $^{237}$Np measurements were performed at the YAYOI reactor by Ohkawachi and Shono [128] in the form of 100 and 500 s irradiation bursts. These two separate sets of finite irradiation data were converted by the authors into instantaneous pulse data for adoption as benchmarks. The correction factor utilized in this conversion process was of the order of 2 at most, such that the experimental data possessed large uncertainties, especially at shorter cooling times (60 to 200 s) when a large scatter in the data was observed (Fig. 3). Longer cooling times between 2500 and 20000 s were also affected by significant uncertainties that arose from contamination by $\gamma$ rays emitted from $^{238}$Np produced by neutron capture on $^{237}$Np. Finally, there exists only one reliable set of data for $^{232}$Th, $^{233}$U measured at the fast-neutron reactor YAYOI by Akiyama and An [113], while for $^{241}$Pu there is only one measurement at thermal-fission energy by Dickens et al. [112]. The significant improvement in the decay-data sub-libraries that has been achieved in the past two to three decades means that we are now able to explore the impact of uncertainties of the input data on decay-heat calculations. A necessary pre-requisite is to possess accurate and precise decay-heat data, which implies a need for new measurements of the LP and EM components of the various fissioning systems discussed above.

5.2 JEFF library

JEFF-3.1.1 decay-data and neutron-induced fission-yield sub-libraries were used to calculate the LP and EM components of decay heat for the seven fissioning systems irradiated under thermal or fast neutrons for which experimental pulse decay-heat data exist. Depletion calculations for the pulse experiments have been performed with the SERPENT2 code [129], while the JEFF-3.1.1 decay-data sub-library was chosen for reference calculations because all recent TAGS measurements presented in Tables 3, 5 have not been included in this particular database. Fission-yield data were also taken from the relevant JEFF-3.1.1 sub-library for thermal (0.0235 eV) and fast (400 keV) neutron energies.

The JEFF-3.1.1 decay-data sub-library was released in November 2007 [59] after decay-heat studies of various decay-data libraries (including JEFF-3.1) by the OECD/NEA Working Party on International Evaluation Co-operation subgroup 25 (WPEC-25) [11]. Members of WPEC-25 concluded that TAGS measurements to determine the average decay energies would improve the quality of the calculated $\beta$ and $\gamma$ decay-heat components. As a result, the mean energies of twenty-nine fission-product nuclides measured by Greenwood et al. [8] were initially included in JEFF-3.1.1. Furthermore, high-quality evaluations of fifty nuclides were taken from the United Kingdom libraries UKPADD-6.7 and UKHEDD-2.5 ( [66], and Ref. [59] for selection details), while the rest of the decay data were adopted from ENSDF [55] and the Decay Data Evaluation Project (DDEP) [65].

Three sets of decay-heat calculations denoted earlier in the Sects. as 1, 2 and 3 were performed with the same JEFF-3.1.1 fission-yield sub-library each time. The first set of calculations was based on the JEFF-3.1.1 decay data described above, and formed the baseline set of data. A second set of calculations (2) was associated with the replacement of the ${\overline{E}}_{LP}$ and ${\overline{E}}_{EM}$ energies of seven fission products $^{102,104,105,106,107}$Tc,$^{101}$Nb and $^{105}$Mo by the TAGS average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ energies measured by Algora et al. (2010) [9] (referred to as + TAGS 2010 in Figs. 4, 5). The last set of calculations (3) included the addition of the remaining TAGS data listed in Table 3 of Algora et al. (2021) [28], and those for $^{89,90}$Kr, $^{89,90,90m}$Rb, $^{96}$Y, $^{137,139}$Xe and $^{142}$Cs from Rasco et al. (2016) [39] and Fijałkowska et al. (2017) [69] to the JEFF-3.1.1 decay data library (referred to as + TAGS 2021 in Figs. 4, 5). Corresponding average energies are displayed in Tables 3, 5. As mentioned in Sect. 5.1, the TAGS mean energies of $^{96m}$Y, $^{98}$Nb and $^{140}$Cs were not considered as they were available after the cutoff date.

Fig. 4

Decay heat of fissionable actinides $^{233,235,238}$U and $^{239}$Pu, as a function of cooling time as obtained using JEFF-3.1.1 fission-yield and decay-data sub-libraries [59], with the addition of TAGS data from [9] (+ TAGS 2010) and Tables 3, 5 (+ TAGS 2021). Experimental data have been taken from the CoNDERC database [122]

Fig. 5

Decay heat of fissionable actinides $^{241}$Pu, $^{232}$Th, and $^{237}$Np, as a function of cooling time as obtained using JEFF-3.1.1 fission-yield and decay-data sub-libraries [59], with the addition of TAGS data from [9] (+ TAGS 2010) and Tables 3, 5 (+ TAGS 2021). Experimental data have been taken from the CoNDERC database [122]

As shown in the Figures, results obtained for the LP and EM components of the decay heat for the seven fissioning systems exhibit the same features reported in the previous subsection devoted to the ENDF/B-VIII.0 decay-data and fission-yield sub-libraries. Inclusion of the average ${\overline{E}}_{\beta }$ and ${\overline{E}}_{\gamma }$ decay energies from the TAGS measurements (+ TAGS 2010) leads to a decrease in the LP and an increase in the EM decay-heat components, which is a direct consequence of the adoption of Pandemonium-free decay data. TAGS 2010 data improve the agreement with the pulse decay-heat measurements for $^{239,241}$Pu thermal and $^{238}$U fast fission, but has only a small impact on $^{232}$Th and $^{233}$U fast fission. While decay-heat calculations of $^{235}$U thermal fission are associated with an LP component that is not affected by the inclusion of the TAGS 2010 data, conclusions are more difficult to draw when considering the EM component because of discrepancies between the three sets of experimental pulse decay-heat data.

Insertion of all the recent TAGS measurements into the JEFF-3.1.1 decay-data sub-library (+ TAGS 2021) leads to a underestimation of the LP decay-heat component in the 10 to 1000 s cooling time for the following fissioning systems: $^{233,238}$U fast fission and $^{239,241}$Pu thermal fission. The LP component in $^{235}$U thermal fission exhibits a small improvement in the decay-heat calculations from 10 to 1000 s cooling time, along with a small yet continuous underestimation from 400 to 1000 s cooling time. EM decay-heat components for $^{232}$Th and $^{233,238}$U fast fission, and $^{235}$U and $^{241}$Pu thermal fission also improve for cooling times below 100 s. The conclusions and recommendations presented in Sect. 5.1 are also valid for the impact of TAGS data into the JEFF-3.1.1 sub-library discussed in this subsection.

5.3 JENDL library

As noted in the introduction to Sect. 5, JENDL fission-product decay-data files contain a mixture of experimental and theoretical average decay energies. JENDL/FPD-2000 includes experimental average energies from ENSDF [55] and theoretical values from gross $\beta$ $^{-}$ theory, all of which are combined to reproduce the experimental decay-heat data. An update from JENDL/FPD-2000 to JENDL/FPD-2011 includes the TAGS 2010 data of Algora et al. (2010) [9], while average ${\overline{E}}_\beta$ and ${\overline{E}}_\gamma$ energies for the other fission-product nuclides have been re-evaluated following a prescription used in all of the evaluations performed before and after FPD-2000 up to FPD-2011: adopted decay data should consistently reproduce, within the uncertainties of the experimental data and theoretical calculations, not only the available experimental decay-heat data, but also the aggregate $\gamma$-ray spectra of Ref. [112, 130] and individual $\beta$/$\gamma$ spectra of Ref. [93]. Average decay energies were also carefully compared with the measured TAGS data of Greenwood et al. [8].

The impact of the Algora et al. (2010) [9] as well as the most recent TAGS data listed in Tables 3, 5 was assessed without any “contamination” from theoretical data. Two baseline calculations were undertaken separately with the JENDL FP decay-data file 2000 (JENDL/FPD-2000) and JENDL FP decay-data file 2011 (JENDL/FPD-2011), and four sets of decay-heat calculations were also performed: one baseline calculation with JENDL/FPD-2000; second calculation in which Algora et al. (2010) TAGS data were added to the JENDL/FPD-2000 baseline (referred to as + TAGS 2010); third calculation as a baseline with JENDL/FPD-2011 (which includes Algora et al. (2010) TAGS data with minimum modification to keep consistency with the beta-ray spectrum data); and fourth calculation whereby the remaining TAGS data listed in Tables 3, 5 were added, except for $^{96m}$Y, $^{98}$Nb and $^{140}$Cs (referred to as + TAGS 2021). One notable difference between the ENDF/B-VIII.0 and JEFF-3.1.1 used in the previous subsections and the above JENDL decay-data sub-libraries is that the latter does not include any of the Greenwood et al. TAGS data [8], whereas the other two sub-libraries incorporate them either completely (ENDF/B-VIII.0) or partially (JEFF-3.1.1). Under such circumstances, theoretical average decay energies have been calculated for these specific fission products that lead to good description of the experimental decay-heat data for their subsequent introduction into the JENDL decay-data sub-libraries. The JENDL Fission-product Yield Data File 2011 [62] was used in the baseline and subsequent calculations. Both the fission-product decay and fission-product yield files originate from the JNDC Nuclear Data Library of Fission Products, as mentioned earlier in Sect. 5 [120].

All of the decay-heat calculations undertaken in conjunction with the JENDL data files were performed by means of the OYAK98 code [131], and the results have been compared with available experimental decay-heat data in Figs. 6, 7.

Fig. 6

Decay heat of fissionable actinides $^{233,235,238}$U and $^{239}$Pu, as a function of cooling time as obtained using JENDL fission-yield and decay-data sub-libraries [132] with the addition of TAGS data from [9] (+ TAGS 2010) and Tables 3, 5 (+ TAGS 2021). Experimental data have been taken from the CoNDERC database [122]

Fig. 7

Decay heat of fissionable actinides $^{241}$Pu, $^{232}$Th, and $^{237}$Np, as a function of cooling time as obtained using JENDL fission-yield and decay-data sub-libraries [132] with the addition of TAGS data from [9] (+ TAGS 2010) and Tables 3, 5 (+ TAGS 2021). Experimental data have been taken from the CoNDERC database [122]

Both of the baseline calculations for JENDL/FPD-2000 and JENDL/FPD-2011 lie predominantly within the experimental uncertainties, except for a few cases such as the EM component for $^{233}$U fast fission over cooling times of 500 to 3000 s and the LP component for $^{239}$Pu thermal fission at cooling times from 400 to 2000 s. These observations indicate that the gross $\beta$ $^{-}$ theory reproduces the average decay energies reasonably well, as applied and described in the introductory part of this section. Deviations from the baseline curves caused by the introduction of the average energies determined from TAGS measurements are relatively small. However, the introduction of TAGS data in the case of $^{239}$Pu thermal fission increases the EM component considerably beyond the experimental uncertainties at cooling times of 20 to 300 s. Possible reasons for this overestimation are discussed in Sect. 5.4. Overall, all four sets of decay-heat calculations give a reasonable description of the experimental decay-heat data as shown in Figs. 6, 7. However, this exception should not detract from the importance of including TAGS data in the decay-data sub-libraries - they are expected to represent the best recommended data for each individual nuclide, whereas gross $\beta$ $^{-}$ theory is limited to only average-energy properties.

5.4 Comparison of libraries

We have undertaken studies of the impact of recent TAGS measurements on pulse decay-heat calculations that were based upon comparisons of the available experimental decay-heat data with the results of three different modelling codes and differing input libraries of nuclear data. Assessments were made in order to judge the performance of the latest general-purpose evaluated libraries (ENDF/B-VIII.0 [58], JEFF-3.3 [61], and JENDL-5 [64]), in calculations of pulse decay heat for the sixteen fissioning systems listed in Sect. 3. The relevant sub-libraries of these databases differ in the content of their recommended cross sections, decay data and fission-yield data. Our efforts have focused mainly on actinide and fission-product decay-heat calculations that are most strongly dependent on the adopted fission yields and decay data used as input to the inventory calculations. We have described in Sect. 5.1 the inclusion of measured TAGS data within the decay-data sub-library of ENDF/B-VIII.0; JEFF-3.3 includes TAGS data from Greenwood et al. (1997) [8, 59], Algora et al. (2010) [9] (with the exception of $^{101}$Nb and $^{102}$Tc), and for $^{87}$Br, $^{88}$Br, $^{92}$Rb and $^{94}$Rb [30, 91], as defined in Sect. 5.2; JENDL-5 [64] contains all of the TAGS measurements performed as part of the TAS/DTAS collaboration listed in the review article of Algora et al. [28], and several nuclides from the MTAS collaboration published in Fijałkowska et al. [69] (see Tables 3, 5), as noted in Sect. 5.3. The JENDL-5 decay-data sub-library is judged to be the most complete database for the inclusion of available TAGS data.

Comparisons of the various calculated decay-heat studies with experimental pulse decay-heat data are shown in Figs. 8, 9, 10, 11. The resulting decay heat curves are in reasonably good agreement at cooling times above 1000 s, while they can be rather discrepant at shorter cooling times below 1000 s. The most marked discrepancies with respect to experimental decay-heat data are observed in the following cases: $^{232}$Th fast fission, where the electromagnetic component from 2 to 100 s cooling times is underestimated by both ENDF/B-VIII.0 and JEFF-3.3; $^{238}$U fast-fission cooling times of 1 to 10 s whereby JEFF-3.3 overestimates the decay heat; $^{237}$Np fast fission, for which ENDF/B-VIII.0 and JENDL-5 overestimate the decay-heat data at around 100 s cooling time; $^{239}$Pu thermal fission, where JENDL-5 overestimates the peak at cooling times from 10 to 300 s.

Fig. 8

Decay heat of fissionable actinides $^{232}$Th and $^{233,235,238}$U, as a function of cooling time as obtained using ENDF/B-V111.0, JEFF-3.3 and JENDL-5 evaluated libraries. Experimental data have been taken from the CoNDERC database [122]

Fig. 9

Decay heat of fissionable actinides $^{237}$Np and $^{238,239,240}$Pu, as a function of cooling time as obtained using ENDF/B-V111.0, JEFF-3.3 and JENDL-5 evaluated libraries. Experimental data have been taken from the CoNDERC database [122]

Fig. 10

Decay heat of fissionable actinides $^{241,242}$Pu and $^{241,242m}$Am, as a function of cooling time as obtained using ENDF/B-V111.0, JEFF-3.3 and JENDL-5 evaluated libraries. Experimental data have been taken from the CoNDERC database [122]

Fig. 11

Decay heat of fissionable actinides $^{243}$Am and $^{243,245}$Cm, as a function of cooling time as obtained using ENDF/B-V111.0, JEFF-3.3 and JENDL-5 evaluated libraries. Experimental data have been taken from the CoNDERC database [122]

Given the importance of $^{239}$Pu thermal fission for power-reactor applications, the results obtained with JENDL-5 were further investigated to identify the possible source of this overestimation. Decay-heat calculations will also be sensitive to the fission-yield libraries, and therefore the decay-heat calculations were repeated for $^{239}$Pu in terms of the same JEFF-3.3 decay-data sub-library combined with three different fission-yield sub-libraries: ENDF/B-VIII.0 fission yields, JEFF-3.3 fission yields, and JENDL-5 fission yields. The results are shown in Fig. 12.

Fig. 12

Comparison of the EM component of the decay heat of $^{239}$Pu thermal fission obtained from calculations with the JEFF-3.3 decay-data sub-library and three fission-yield sub-libraries (ENDF/B-VIII.0, JEFF-3.3 and JENDL-5)

As shown clearly in Fig. 12, adoption of the ENDF/B-VIII.0 and JEFF-3.3 fission-yield sub-libraries give similar results that agree reasonably well at and around both peaks of the experimental decay-heat data, while the JENDL-5 fission-yield sub-library leads to a significant overestimation of the first peak of decay heat at cooling times between 30 and 200 s, similar to the results obtained with the JENDL-5 decay-data sub-library in Fig. 9. This overestimation would appear to be associated with the fission yields rather than the decay data, and is now being studied in detail with respect to the planned release of improved fission-yield data in the foreseeable future [133]. A further investigation of the impact of the fission yields on decay-heat calculations was obtained with the JEFF-3.3 decay-data sub-library, and is shown in Fig. 13 for $^{238}$U and $^{237}$Np fast fission. These two cases were chosen because of the major differences observed between JEFF-3.3 and the other two libraries in Figs. 8, 9, 10, 11. One can see from Fig. 13 that the effect of the three different fission-yield sub-libraries differs for the two irradiated actinides. Adoption of JENDL-5 fission-yield sub-library leads to a significant improvement for $^{238}$U fast fission at cooling times around the first peak (i.e., 1 to 10 s cooling time); all three fission-yield sub-libraries give similar results for $^{237}$Np fast fission at cooling times greater than 80 s, while ENDF/B-VIII.0 deviates from JEFF-3.3 and JENDL-5 at shorter cooling times between 3 and 50 s.

Fig. 13

Comparison of light-particle decay heat of $^{238}$U fast fission and electromagnetic decay heat of $^{237}$Np fast fission obtained from calculations with the JEFF-3.3 decay-data sub-library and three fission-yield sub-libraries (ENDF/B-VIII.0, JEFF-3.3 and JENDL-5)

A detailed study of the fission-yield sub-libraries and their impact on decay-heat calculations is beyond the scope of this paper. Nevertheless, international effort coordinated by the IAEA is ongoing with the aim of updating and improving fission-yield data for the major actinides [133]. We expect the output and conclusions of this effort will allow clear conclusions to be drawn on the recommended fission-yield data to be used in decay-heat calculations.

Both the nature and handling of uncertainties in the decay data and fission-yield data also need to be considered. A full and respected treatment of these uncertainties, including correlation effects identified with the fission-yield data, would permit reliable and accurate assessments of the decay-data and fission-yield sub-libraries, and draw definitive conclusions on the impact of the TAGS data and the need and form of other additional measurements. Our present results indicate certain trends in such calculations, but without proper propagation of uncertainties they are not definitive. Ongoing efforts to develop suitable approaches for propagating the uncertainties in decay-heat calculations are expected to come to fruition in the near future, so that we should eventually be able to perform uncertainty quantification of such integral calculations with confidence.

6 Concluding remarks

Table 2 constitutes a brief summary of the fission-product radionuclides considered in defining the requirements for TAGS studies to detect and quantify Pandemonium, as well as elaborate on the related needs for $\gamma$ singles and $\gamma$-$\gamma$ coincidence measurements to improve the definition of each individual decay scheme. Much greater detail, various relevant information and fuller assessments are to be found within Tables 6 and 7:

• relevant nuclear properties,

• radionuclide importance from the point of view of decay heat (based on each fissionable actinide as a function of cooling time), and

• definitive recommendations as to whether to perform (or not perform) TAGS, $\gamma$ singles and/or $\gamma$-$\gamma$ coincidence studies, each defined in terms of priority from a highest of 1 decreasing to 2 and 3, or no assigned priority at all.

Further extensive assessments need to accommodate consideration of the impact of delayed neutrons on decay heat up to $\sim$ 10 s cooling time, along with an awareness of other unrelated requirements such as antineutrino spectral signatures and research studies within nuclear physics.

All of the recommendations constitute subjective judgements by individual authors that when brought together in this manner will not necessarily be fully consistent with each other. Taking these subjective judgements at face value (Table 2), the following experimental measurements would seem to be most appropriate at the present time:

• priority 1 TAGS/TAS and DGS $\gamma$ singles and $\gamma$-$\gamma$ (and $\beta$-$\gamma$) coincidence measurements of the $\beta$ $^{-}$ decay of $^{99}$Zr, $^{98,99}$Nb, $^{106}$Tc, $^{130m,132}$Sb, $^{138}$Cs and $^{142,143}$La;

• priority 1 DGS measurements only of the $\beta$ $^{-}$ decay of $^{100,100m,101,102}$Nb, $^{104,105}$Tc and $^{134}$I;

• priority 2 TAGS/TAS and DGS measurements of the $\beta$ $^{-}$ decay of $^{84}$As, $^{85}$Se, $^{84,89}$Br, $^{91}$Kr, $^{95}$Sr, $^{97}$Y, $^{105}$Nb, $^{103,104,105,107}$Mo, $^{107,108}$Tc, $^{133}$Sb, $^{136,137}$Te, $^{136,136m}$I, $^{140}$Xe, $^{139,140,141}$Cs, $^{141,143,144}$Ba and $^{144,147}$La;

• priority 2 TAGS/TAS measurements only of the $\beta$ $^{-}$ decay of $^{92,93,94}$Sr, $^{139}$Ba and $^{146}$Pr;

• priority 2 DGS measurements only of the $\beta$ $^{-}$ decay of $^{86,87,88}$Br, $^{89,90}$Kr, $^{90,90m,91,92,93}$Rb, $^{96,96m}$Y, $^{100}$Zr, $^{102}$Mo, $^{102}$Tc, $^{130,131}$Sb, $^{133,133m}$Te, $^{132,135,137}$I and $^{139}$Xe.

However, requirements and priorities can be expected to change as such work proceeds, so that consideration should also be given to some of the lesser fission products of Table 2 at later ill-defined stages of such studies. One aim of this particular work has been to provide guidance in improving our knowledge of the energy distribution between the light-particle (LP) and electromagnetic (EM) components of decay heat. Along with the need to assess properly the impact of delayed-neutron emissions on the fuel inventory at early cooling times (LP decay heat vs EM decay heat at relatively short and intermediate cooling times (up to 10 to 20 s)), we must ensure that adopted fission-yield data are also fully fit for purpose in all of the important decay-heat calculations. As was shown in the previous section, some of the pronounced features in the calculated decay heat components (LP and EM) are sensitive to fission-product yield data rather than the decay data. Although the impact of the fission-yield sub-libraries (ENDF/B-VIII.0, JEFF-3.3 and JENDL-5) on decay-heat calculations was found to vary within the uncertainties of the experimental decay-heat data, larger discrepancies were observed in the thermal decay heat of $^{239}$Pu and fast decay heat of $^{238}$U which require further investigation. The impact of the energy dependence of the fission-yield data on decay heat also merits further exploration. Envisaged improvements in some of the more important decay data and their uncertainties will inevitably necessitate better quality integral measurements of decay heat to give conclusive comparisons and more precise benchmarking.

As for repeating this exercise at a future date, changes in the total decay heat, LP and EM components will be relatively modest to small because much of the relevant data should not subsequently alter much from year to year, or even over ten years, when considering half-lives, Q-values and decay radiation characteristics (i.e., key nuclear parameters in quantifying irradiated fuel inventories to determine total decay heat). This statement contrasts with the fission yields that are expected to improve significantly in the near future, supported fully by a concerted international effort coordinated by the IAEA to update the fission-yield database through consideration of all available experimental data measured at advanced facilities with better precision and higher resolution to be coupled with developments in modelling codes and more extensive validation exercises [133]. Additional developments concerning the uncertainties in the recommended decay-data and fission-yield libraries should also include improved quantification of their correlation effects, along with propagation within inventory and summation calculations. Therefore, the current exercise should be repeated with improved fission-yield data files, as well as with codes that can accommodate full analyses and quantification of the overall uncertainties.

Assessments of the balance between performing further TAGS/TAS measurements or direct $\gamma$ singles and/or $\beta$-$\gamma$, $\gamma$-$\gamma$  coincidence spectral studies would appear best to depend upon the nature and degree of the inconsistencies and Pandemonium effects revealed by the systematic application of TAGS/TAS. Both types of measurement may be required, but there is always the possibility that only one approach is merited at a particular time in support or even contradiction of the other. Those undertaking calculations of the resulting decay heat or antineutrino emissions require reasonably comprehensive decay scheme data that are more reliably obtained directly, if possible. Under such circumstances, TAGS/TAS has proven to be highly effective at highlighting existing inadequacies within individual fission-product decay schemes, and in doing so strongly supports $\gamma$ singles and coincidence measurements by means of appropriate detector systems that may still be in the process of evolution (and are not necessarily Ge based). There are existing and will be future needs for TAGS/TAS studies that go hand-in-hand with $\beta$ $^{-}$ and $\gamma$-ray spectroscopy in order to improve various nuclear parameters in a complementary manner for their confident adoption in the evolution of nuclear physics research and a developing range of nuclear applications that includes power-reactor decay heat on shutdown.

Data uncertainties: Data and their uncertainties are presented throughout the text and tables in the form 1234(x), where x is the uncertainty expressed in terms of the last digit or digits quoted with respect to the measured or evaluated number. This uncertainty is normally expressed at the 1$\sigma$ confidence level. Examples: 41.1(11) means 41.1± 1.1, 6.783(8) means 6.783±0.008, 0.0820(17) means 0.0820±0.0017, 1.688(12)$\cdot 10^{-4}$ means (1.688±0.012)$\cdot 10^{-4}$, 26.3(+3-21) means 26.3$_{-2.1}^{+0.3}$, and 8.681(+18-25) means 8.681$_{-0.025}^{+0.018}$.

Assessment and reference tables

Table 6 Fission-product decay data: assessment of potential Pandemonium and need for further TAGS and DGS (discrete gamma-ray spectroscopy involving $\gamma$ singles and $\gamma$-$\gamma$ coincidence measurements) studies for $^{235}$U, $^{238,239,240}$Pu, $^{241}$Am and $^{243}$Cm thermal fission. Relevant references in the literature are defined in NSR keynumber format (e.g., 2017Fi06 (NSR), 2016ORNL (equivalent non-NSR)). Spin, parity (J$^{\pi }$) and half-life are from NUBASE2020 [134]. Q-value for ground state-to-ground state decay (Q($\beta ^{-}$)) and the neutron separation energy (S$_{n}$) are from AME2020 [54]. Q($\beta ^{-}$) value for an excited isomer is reported as the sum of the ground state-to-ground state decay and the excitation energy of the isomer taken from NUBASE2020 [134]. Beta-delayed neutron emission probabilities P$_n$(%) are taken from the IAEA Reference Database for beta-delayed neutron emission [87, 135, 136]. (a) Possible potential for Pandemonium effect as a consequence of large energy differential $\Delta$ (keV) = (Q($\beta ^{-}$)—excitation energy of highest known relevant nuclear level); (b) FISPACT-II calculations of fission-product inventories and their percentage decay-heat contributions as a function of the cooling time of irradiated actinides [51,52,53]: fissionable actinide, (post-irradiation cooling time, %$\gamma$, %$\beta$, %(total decay heat)), fission-product decay schemes assessed in terms of known $\beta$ $^{-}$ decay and discrete nuclear levels of the daughter [55]; (c) Request for specific measurements denoted by ‘y’ $\rightarrow$ ’yes’ (‘?’ $\rightarrow$ to be assessed further); (d) Priorities defined as 1 $\rightarrow$ high, 2 $\rightarrow$ intermediate, 3 $\rightarrow$ low,—$\rightarrow$ unassigned

Table 7 Fission-product decay data: assessment of potential Pandemonium and need for further TAGS and DGS (discrete gamma-ray spectroscopy involving $\gamma$ singles and $\gamma$-$\gamma$ coincidence measurements) studies for $^{232}$Th, $^{233,238}$U and $^{237}$Np fast fission, and $^{241,242}$Pu and $^{245}$Cm thermal fission. Relevant references in the literature are defined in NSR keynumber format (e.g., 2017Fi06 (NSR), 2016ORNL (equivalent non-NSR)). Spin, parity (J$^{\pi }$) and half-life are from NUBASE2020 [134]. Q-value for ground state-to-ground state decay (Q($\beta ^{-}$)) and the neutron separation energy (S$_{n}$) are from AME2020 [54]. Q($\beta ^{-}$) value for an excited isomer is reported as the sum of the ground state-to-ground state decay and the excitation energy of the isomer taken from NUBASE2020 [134]. Beta-delayed neutron emission probabilities P$_n$(%) are taken from the IAEA Reference Database for beta-delayed neutron emission [87, 135, 136]. (a) Possible potential for Pandemonium effect as a consequence of large energy differential $\Delta$ (keV) = (Q($\beta ^{-}$) - excitation energy of highest known relevant nuclear level); (b) FISPACT-II calculations of fission-product inventories and their decay heat as a function of the cooling time of irradiated actinides [51,52,53]: fissionable actinide, (post-irradiation cooling time, %$\gamma$, %$\beta$, %(total decay heat)), fission-product decay schemes assessed in terms of known $\beta$ $^{-}$ decay and discrete nuclear levels of the daughter [55]; (c) Request for specific measurements denoted by ‘y’ $\rightarrow$ ’yes’ (‘?’ $\rightarrow$ to be assessed further); (d) Priorities defined as 1 $\rightarrow$ high, 2 $\rightarrow$ intermediate, 3 $\rightarrow$ low, - $\rightarrow$ unassigned

Table 8 List of references cited as NSR keynumbers in Tables 6 and 7