Prompt gamma rays induced by inelastic scattering of fission neutrons on iron

Prompt gamma rays induced by (n,n′γ) reactions on iron were measured with the instrument FanGaS (Fast Neutron induced Gamma-Ray Spectrometry) operated at the Heinz Maier-Leibnitz Zentrum (MLZ) in Garching. The measurement was performed at an angle of 90° between neutron beam and detector. The fast neutron flux at the sample position was determined to be 1.40 × 108 cm−2 s−1 by using the foil activation method. Energies, relative intensities and fast neutron spectrum averaged isotopic cross section for production of 81 prompt gamma lines are presented. The results obtained are found in good agreement with literature data. The new set of gamma lines is recommended to replace the old dataset with several new lines also recognizing a few false identifications. This work is an important step towards the future chemical analysis of large samples at FanGaS employing highly penetrating fission neutrons.


Introduction
Accurate non-destructive chemical analysis of materials is of fundamental importance in many fields of science and for industrial applications. Prompt Gamma Neutron Activation Analysis (PGNAA) based on cold/thermal neutron capture is well established as a powerful non-destructive analytical technique to determine the elemental composition of small and thin samples [1]. Large objects may be investigated to some extent by PGNAA using cold or thermal neutron beams [2][3][4]. Nevertheless, depending on the neutron absorption properties of the sample, the penetration depth of cold/thermal neutrons is limited and the beam attenuation must be corrected for [4,5]. Therefore, neutrons of higher energies are a better choice for the analysis of large and thick objects. Unlike cold/thermal neutrons inducing (n, γ) reactions, high-energy neutrons induce other reactions, particularly (n,n′) or (n,p), (n,α) or even (n,2n) in some cases. Cross sections for these reactions are generally lower compared to thermal neutron capture reactions. However, as capture cross sections outside nuclear resonances follow a 1/v trend (v being the neutron velocity), at higher energies e.g. at 2 MeV mean energy of fission neutrons, inelastic scattering with the emission of isotope-specific prompt gamma rays prevail.
The possibility to determine the elemental composition of large samples by measuring prompt gamma rays with a NaI(Tl) detector following the inelastic scattering of 14-MeV pulsed neutrons for remote analysis of surfaces was reported first in 1961 by Schrader and Stinner [6]. In 1976, Jiggins and Habbani [7] used 3.29 MeV neutrons, produced by the 2 H(d,n) 3 He reaction, for the determination of iron in iron ores measuring prompt gamma rays with a NaI(Tl) detector and presented analytical sensitivities for 23 elements. Two years later, Yates et al. [8] proposed a time-of-flight method based on neutron/gamma coincidence to improve sensitivity of prompt gamma-ray detection with a Ge(Li) detector rejecting background signals induced by scattered neutrons. The method was applied to the analysis of metal alloys using 2.5 MeV neutrons and limits of detection for 38 elements were determined. In 1979, Sowerby [9] investigated the use of isotopic neutron sources for elemental analysis of kilogram samples by neutron inelastic scattering associated gamma rays. These preliminary works have resulted in the following years till now to the development of various laboratories, in situ or online techniques using either isotopic neutron sources or neutron generators and mainly scintillation detectors (NaI(Tl), BGO or LaBr 3 ) for bulk analysis (well and bore-hole logging, process and quality control of materials such as coal, cement and ores) or for detection of explosive and illicit materials. However, due to the low fast neutron flux delivered by these sources and the poor resolution of the employed detectors, the analytical sensitivity of the developed techniques is limited to few % per sample weight. Therefore, it was decided to use the intense fission neutron beam delivered by the SR10 (Strahlrohr 10) channel of the research reactor FRM II (Forschungs-Neutronenquelle Heinz-Maier-Leibnitz) for accurate analysis of large samples measuring prompt gamma rays induced by inelastic scattering of fission neutrons.
Compared to the well documented thermal neutron prompt gamma spectra and associated energies [1], a tabulation of prompt gamma energies and associated relative intensities induced by fission neutrons of all elements has been published only once in 1978 by Demidov et al. [10]. The measurements were performed at the Baghdad Nuclear Research Institute, while the evaluation has been carried out at the Kurchatov Institute, Moscow. A fission neutron beam (filtered with 9 cm of lead, 1 cm boron carbide and 1 mm of cadmium) with the diameter of 3 cm was used for the irradiation. The gamma rays emitted by the sample under 90 degrees were filtered using 8 cm of LiH and acquired by a 30-cm 3 (equivalent to 10% relative efficiency) Ge(Li) detector. The detector was shielded with 5 cm iron, 8 cm boron carbide-loaded paraffin, 10 cm of lead, and 3 mm of 6 Li. This pioneering work covering a reasonable range of gamma-ray energies is valuable. However, the energy resolution of the Ge(Li) detector was degrading after an extended neutron exposure. Thus, to perform precise chemical analysis of samples with fission neutrons a comprehensive data catalogue on (n,n′γ) reactions, prompt gamma-ray energies and absolute intensities is urgently needed. Furthermore, these data may help in the development of nuclear data libraries that serve a multitude of applications.
To achieve this, the FaNGaS (Fast Neutron induced Gamma Spectrometry) instrument [11,12] has been designed and installed at the MEDAPP (Medical Application) [13] facility of FRM II (Fig. 1). The first characterization of FaNGaS and the neutron spectrum at sample position is given in [11]. In this work, the fast neutron spectrum and flux at sample position is determined again due to a modification of the fast neutron collimation. The results obtained from the measurement of prompt gamma rays induced by inelastic scattering of fission neutrons on iron at an angle of 90° between the neutron beam and the detector are presented and compared to literature data.

FaNGaS instrument
In the first version of the FaNGaS instrument the collimation of fast neutrons was achieved using a set of two collimators made of polyethylene, boron carbide and lead. The inner collimator was placed inside the filter bench room while the outer collimator was positioned in the opening of the multileaf-collimator of the irradiation facility MEDAPP inside the biological shield. Technical details and dimensions of the collimators are given in [11]. Due to the upgrade of the fast neutron imaging facility NECTAR (Neutron Computerized Tomography and Radiography) to perform radiography or tomography also with thermal neutrons [14], the filter setups inside the filter bench room have been modified and the FaNGaS outer collimator was removed from the MEDAPP multi-leaf-collimator. In order to filter thermal neutrons from the fast neutron beam and to attenuate gamma radiation coming from the reactor, a boron carbide plate with a thickness of 1 cm and two lead plates with a total thickness of 5 cm were placed at the upstream beam side of the inner collimator (see Fig. 2). Due to these changes, a new determination of the fast neutron flux at sample position was necessary.
In addition, the shielding of the HPGe-detector was also partially modified. In order to increase thermal neutron absorption, the 30 cm thick polyethylene layers at the front side of the shielding have been replaced by borated polyethylene of same thickness. For gamma-ray collimation, a removable cylindrical lead collimator with 6 cm inner diameter, 2 cm wall thickness and 16 cm length was inserted into the cylindrical aperture (10 cm diameter) of the front shielding. The detector set up at experimental position is shown in Fig. 2.

Neutron flux determination
The fast neutron spectrum in the energy range 0.075-20 MeV at the sample position was determined by means of the foil activation technique. High-purity foils of various elements (Al, Ti, Fe, Ni, Zr and In) were sealed in Teflon bags and irradiated separately for 8-18 h. The dimension of the foils is about 25 × 25 × 0.25 mm 3 . After irradiation, the gamma-ray spectra of the activated foils were measured at a distance of 17 cm from the HPGe-detector. The counting times ranged from 2 to 21 h. The gamma-ray spectra were analyzed with the HYPERMET-PC software [15]. The reaction rates, R, for neutron spectrum unfolding were calculated using the following relation: where P E is the net count for the gamma-ray of energy Eγ, E is the full-energy-peak efficiency at measuring position determined in [11], I E the gamma emission probability, T is the half-life of the activation product, t i is the irradiation time, t c is the counting time and t d the decay time, i.e. the time between end of irradiation and beginning of the counting. Corrections for neutron and gamma absorption were neglected since the foils are very thin. The masses of the foils, the investigated reactions and the calculated reactions rates per atom are given in Table 1.
The software suit STASYL PNNL was used for neutron spectrum unfolding [16]. This code provides a solution for the neutron spectrum using the generalized least-square method. Detailed information about the method can be found in [17]. The code takes as input the reaction rates and a predefined neutron spectrum divided into a certain number of energy groups. For the purpose of this work, the neutron spectrum previously determined with the initial setup of neutron collimators was used as an input and the number of energy groups was set to 100. The obtained neutron spectrum is compared with the previous one determined with the former set of neutron collimators in Fig. 3. A relatively higher average neutron energy of 2.30 MeV and a fast neutron flux (1.40 ± 0.05) × 10 8 cm −2 s −1 were obtained due to the removal of the outer collimator from the MEDAPP  Table 1. The results compare well with the values evaluated for a fission spectrum (kT = 1.35 MeV) given in JANIS (Java-based Nuclear Data Information System) Book of neutron induced cross section [18] (see Table 1). The differences may be related to the deviation of the fast neutron spectrum from a Watt spectrum. The neutron flux in the energy range 10 −8 -0.075 MeV was not determined in this work since these neutron energies are not expected to contribute significantly to the inelastic channel. As shown in Fig. 3 (orange histogram, (a)), the neutron flux integrated over this region (mainly resonance neutrons) represents only 2% of the total neutron flux. Here, we may suppose that the resonance neutron flux is almost the same since the rate measured for the reaction 115 In(n,γ) 116m In, (5.63 ± 0.08) × 10 −17 atom −1 s −1 is close to the value measured in [11], (5.03 ± 0.08) × 10 −17 atom −1 s −1 . (Color figure online)

Prompt gamma rays of iron
The gamma-ray spectrum of the iron foil (m = 1.282 g) was recorded during irradiation. The measurement was performed at an angle of 90° with respect to the neutron beam Table 1 List of irradiated foils with their respective masses, investigated reactions with their corresponding threshold energies, E thr [11], considered gamma-rays energy, Eγ, and determined reaction rates, R is the neutron spectrum averaged cross section of the reaction. fission is the cross section evaluated for a fission spectrum (kT = 1.35 MeV) in JANIS (mean value from various nuclear data libraries) [18] a Value taken in Ref. [25] Element  direction. The gamma lead-collimator was used. The distance between foil and detector was 67 cm. The iron foil of natural composition was irradiated and counted for 10 h (live time was 7.6 h). To support the identification of the prompt gamma lines, a beam background (i.e. irradiation without sample) was also recorded for 12.9 h. The spectra were analyzed with the software HYPERMET-PC [15]. The gamma-ray spectra are shown together for various energy ranges in Figs. 4, 5, and 6. The identified isotopes with the associated gamma-ray energies are given in the spectra; those with asterisks belong to the beam background. The latter contains prompt and delayed gamma rays induced by fast neutron interaction or neutron capture with the HPGe detector (Ge, Al, Cu, In), the shielding (B, H, Pb), the supporting frame (Fe), the sample holder made of Teflon (F) and the air (N, O). It was also seen that when the lead collimator was close to the detector, the boron peak at 478 keV is fully suppressed (Fig. 4) and the count rate of the 2223 keV hydrogen gamma line is reduced by a factor of about 3, both gamma rays being mainly produced in the front shielding. Besides background lines, the spectrum of the iron contains the most intense prompt gamma rays induced by the inelastic scattering of fast neutrons on the iron isotopes 54 Fe, 56 Fe, 57 Fe and 58 Fe. Gamma lines of 19 F also appear due to the sample packing made of Teflon. In comparison to the beam background, the count rates of lines attributed to the background are higher in the iron spectrum by a mean factor of 1.32 ± 0.05 due to neutrons scattered by the sample towards the detector. This factor was used to correct for the background interferences. The iron gamma rays were assigned to specific nuclear transitions of an iron isotope based on the database NuDat 2.8 [19]. Contributions from (n,p) and (n,α) reactions were neglected due to their low cross sections compared to the (n,n′) reaction. A total of 81 prompt gamma lines of iron were identified, 59 associated to 56 Fe, 12 to 57 Fe, 9 to 54 Fe and 1 to 58 Fe (see Tables 2, 3 , 4). Compared to the work of Demidov et al. [10], additional gamma lines were also detected (23 for 56 Fe, 7 for 57 Fe and 3   cases. The intensities of the gamma rays were calculated relative to the 847-keV line of 56 Fe (100%), and they are given with the values determined in [10] in Tables 2, 3

cm thick iron plate in front
Eγ is the gamma-ray energy, P E 90 • ∕ E the net count in the gamma ray peak divided by the full-energy-peak efficiency, I R the relative intensity of the gamma ray and ⟨ E � 90 • � ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at angle of 90° between neutron beam and detector determined with Eq.   Table 3 Prompt gamma rays of 57 Fe Eγ is the gamma-ray energy, P E 90 • ∕ E the net count in the gamma ray peak divided by the full-energy-peak efficiency, I R the relative intensity of the gamma ray and ⟨ E � 90 • � ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at angle of 90° between neutron beam and detector determined with Eq.

3
of the shielding of the Demidov´s spectrometer as prompt gamma rays of iron are also visible in many spectra of the Demidov Atlas. The net peak area of a prompt gamma ray of energy Eγ measured at the angle of 90° between neutron beam and detector, P E 90 • , may be expressed by the following equation: where m (g) is the amount of element, M (g mol −1 ) the molar mass of the element, N A the Avogadro number, h the abundance of the isotope considered, Φ (cm −2 s −1 ) the integral fast neutron flux at sample position, t c (s) the counting (live) time, E the full energy peak efficiency previously determined in [11] with the same gamma-ray collimation (6 cm diameter opening). E 90 • is the fast neutron spectrum averaged isotopic cross section for gamma ray production which may be given also by: where (E) is the differential neutron flux density and E 90 • , E the isotopic cross section for gamma ray production at the corresponding neutron energy E. The values of E 90 • deduced by means of Eq. (2) are given in Tables 2,  3 and 4. Corrections for neutron absorption and multiple scattering and for gamma absorption were neglected since the iron foil is very thin.
The neutron spectrum averaged isotopic cross section for gamma-ray production was calculated with Eq. (8) which is an approximation for relation (3).
where E i is the neutron flux in the neutron energy bin i calculated from the neutron spectrum measured in this work (column 2 of Table 5) and Φ the fast neutron flux. The values of E 90 • obtained with Eq. (8), are: 576 ± 75 mb, 59 ± 6 mb and 35 ± 5 mb for the gamma-rays at 847, 1238 and 1810, keV respectively. These values agree well with the experimental values calculated with Eq. (2), 586 ± 41 mb, 58 ± 5 mb and 37 ± 3 mb. Thus, we can assume that the neutron spectrum averaged isotopic cross sections for the production of the others iron prompt gamma rays detected in this work are reliable.

Conclusions
Prompt gamma-ray emission induced by inelastic scattering of fission neutrons on iron was measured with the FaNGaS instrument operated at MLZ. The measurements were performed at an angle of 90° between the neutron beam and the detector with a fast neutron flux of 1.40 × 10 8 cm −2 s −1 at sample position. A total of 81 prompt gamma rays were detected and their relative intensities (using the 847 keV gamma-ray of 56 Fe as reference) and fast neutron spectrum averaged production cross sections were determined. Compared to the work of Demidov et al. [10], 33 gamma lines were detected additionally. We also found out that 11 gamma lines were wrongly assigned  to iron in the Demidov Atlas. For only the half of the gamma rays observed in both works, the intensities agree well with each other considering their uncertainties. For the remaining gamma rays the intensities listed in Demidov Atlas are largely higher probably due the presence of iron in the shielding of the Demidov´s spectrometer. Additionally, the reliability of the gamma-ray production cross sections measured at 90° was demonstrated from the gamma rays at 847, 1238 and 1810 keV by convoluting their discrete-energy gamma-ray production cross sections obtained at 125° [20] with the fast neutron spectrum delivered at the sample position and taking into account angular correlation factors. Thus, the FaNGaS instrument proved to be a suitable tool to investigate fast neutron induced prompt gamma-ray emission to create a comprehensive data catalogue on (n,n′γ) reactions and to perform chemical analysis of large samples or small samples complementary to PGNAA with cold neutrons as well.