Prompt gamma rays from fast neutron induced reactions on cerium and chlorine

Prompt gamma rays of cerium and chlorine were investigated with the FaNGaS (Fast Neutron-induced Gamma-ray Spectrometry) instrument operated at the Heinz Maier-Leibnitz Zentrum (MLZ) in Garching. The gamma radiation was emitted from (n,n’), (n,p) and (n,α) reactions induced by the irradiation of a cerium(III) chloride (CeCl3) sample with a beam of fission neutrons. Additionally, a polyvinylchloride (PVC, (C2H3Cl)n) sample was irradiated to verify possible interferences between gamma lines of cerium and chlorine. We identified 87 prompt gamma lines of cerium and chlorine. From these, we assigned 58 lines to the (n,n’) reaction in cerium (one for 136Ce, 41 for 140Ce and 16 for 142Ce), 23 to the (n,n’) reaction in chlorine (15 for 35Cl and 8 for 37Cl), 5 lines to the 35Cl(n,p)35S reaction and 1 line to the 35Cl(n,α)32P reaction. We present relative intensities and fast-neutron spectrum-averaged partial cross sections of the aforementioned gamma lines and compare them with available literature data. Identification of new lines and discussion of possible errors adds important value to the literature data found to be consistent with our results. In addition, for a counting time of 12 h we estimate the detection limits for cerium and chlorine as 1 and 2 mg, respectively.


Introduction
The advantages of using fast neutrons in non-destructive elemental analysis were demonstrated already several decades ago [1][2][3][4][5]. The FaNGaS (Fast Neutron-induced Gamma-ray Spectrometry) instrument [6][7][8][9][10][11][12], installed at Heinz Maier-Leibnitz Zentrum (MLZ) in 2014 and upgraded in 2020, advances this technique in neutron analytics and is available for a broad community of industry and research. At the FRM II (Forschungs-Neutronenquelle Heinz Maier-Leibnitz), the fast neutrons are produced using a highly-enriched uranium (93% 235 U) converter in the heavy water moderator. Passing through beamtube SR10, the beam enters the experimental room of the MEDAPP (Medical Application) instrument via a set of filters and collimators [13]. The electromechanicallycooled high-purity germanium (HPGe) detector is placed perpendicularly to the neutron beam. It is surrounded by a complex shielding against neutrons and gamma rays to reduce the spectral background. For the use of the FaN-GaS instrument in nuclear analytical chemistry we are (i) continuously improving the instrument to further improve the peak-to-background ratio and (ii) building up a comprehensive data catalogue of (n,n'γ) reactions containing relative intensities and partial gamma-ray production cross sections for all natural elements. This catalogue is intended to update and extend the "Atlas of Gamma-rays from the Inelastic Scattering of Reactor Fast Neutrons", by Demidov et al. in 1978 [14], which is the only existing database for this reaction type [15][16][17]. However, while a database [18] exists based on [14] and a reasonable agreement compared to data evaluated from work at FRM II is generally observed, we also showed the need for a meticulous validation and reevaluation of the data in our former publications [6][7][8][9][10][11][12]. Furthermore, the measurements performed at FRM II provide a valuable contribution to the nuclear data community with new gamma-ray data from an alternative fission source with an average incident neutron energy closer to that one expected from a fission spectrum and much higher than in Demidov's work.
In the present work, we provide the results from the measurement of prompt gamma rays induced by (n,n') inelastic scattering and (n,p) and (n,α) reactions on cerium and chlorine. The measurements were performed with an upgraded version of the FaNGaS instrument as described in [12]. In order to check if the cerium(III) chloride (CeCl 3 ) sample is free of water and to exclude interferences between chlorine and cerium we also report on the measurement of a polyvinylchloride (PVC, (C 2 H 3 Cl) n ) sample. Relative gammaray intensities and fast-neutron spectrum-averaged partial gamma-ray production cross sections are presented including comparisons with available literature data. In addition, we also give elemental detection limits for cerium and chlorine.

Experimental
Prompt gamma radiation induced by fast neutrons on a CeCl 3 powder sample (mass: 2.66 g, Ce: 1.51 g, Cl: 1.15 g) and on a PVC foil (mass: 0.15 g, Cl: 0.08 g, C: 0.06 g, H: 0.01 g) was investigated with the FaNGaS instrument described in [12]. The CeCl 3 powder was filled into a small PTFE (Polytetrafluorethylene) bag. The maximum thickness of the sample was estimated to be 5 mm. The thickness of the PVC foil was 0.2 mm. The samples were attached to a thin PTFE rod as the sample holder, and the samples were tilted by an angle of 45° with respect to the beam direction. They were completely irradiated by the fast neutrons with a flux at sample position of (1.13 ± 0.04) × 10 8 cm −2 s −1 and an average neutron energy of 2.30 MeV. The irradiation time was 3.4 h for CeCl 3 and 17 h for PVC, and the live times were 2.7 and 15.4 h, respectively, meaning 20% and 10% deadtimes, respectively. The measurement was performed at a sample-to-detector distance of 67 cm and at an angle of 90° to the beam direction. The acquired spectra were analyzed with the HYPERMET-PC software [19] and they are shown in Figs. 1 and 2. Prompt gamma rays emitted from the (n,n') inelastic scattering as well as (n,p) and (n,α) reactions of fast neutrons were identified using the NuDat 3.0 database [20] and associated nuclear data from various evaluations for all nuclides relevant to this work [21][22][23][24][25][26][27]. Presence of gamma rays from (n,γ) reactions and possible interferences were checked with the prompt gamma neutron activation analysis (PGNAA) database [28].
As a certain fraction of neutrons scatters towards the spectrometer, we have observed an increase of the count rate of the background lines. For the CeCl 3 sample, we found a mean factor of 1.42 ± 0.30, while for the PVC sample 1.03 ± 0.10. In the case of CeCl 3 this scattering factor was used to correct for the interfering background lines, whereas it could be neglected for PVC. Correction for interferences arising from a single or double escape peak (denoted as SE and DE, respectively) is discussed in the following section.

Method
Inelastic neutron scattering reactions have threshold energies typically above 100 keV. This is mostly true also for (n,p) and (n,α) reactions with the exception of a few light nuclides for which no thresholds are observed [29,30]. The net peak area P Eγ of a prompt gamma ray emitted from the aforementioned reactions can be described by the following relationship [9][10][11][12]: where m (g) is the mass of the considered element, M is the molar mass (g mol −1 ), N A the Avogadro constant (6.022 × 10 -23 mol −1 ), h the isotopic abundance, ε Eγ the fullenergy-peak (FEP) efficiency, < σ Eγ (90°) > the fast-neutron spectrum-averaged partial gamma-ray production cross section (cm 2 ) for an angle of 90° between neutron beam and detector, < Φ fast > the integral fast neutron flux (cm −2 s −1 ), t c the counting live time (s), f n the neutron self-shielding factor and f Eγ the gamma-ray self-absorption factor. The PVC sample is thin enough to neglect the self-attenuation factors, i.e. f n ~ 1 and f Eγ ~ 1. The neutron self-shielding of the CeCl 3 sample was investigated by numerical simulation using the Monte Carlo N-Particle (MCNP, version 6.1) [31,32] code. The Lib80x library [33] with ENDF/B-VIII.0 data was used [34]. The irradiation of a CeCl 3 slab of 5 mm thickness, tilted by an angle of 45° and having a mass equal to the one of our measurement, was simulated with a neutron-energy distribution identical to our experiment. The neutron selfshielding factor is determined as the ratio of the average fast neutron flux within the sample (F4 tally) to the incident fast neutron flux on the sample (F2 tally). The value of f n = 1.01 indicates that the neutron self-shielding can be neglected.
The gamma-ray self-absorption factor f Eγ for the CeCl 3 sample can be analytically calculated as [28,35]: where l = 0.71 cm is the effective thickness of the sample, μ/ρ (cm 2 g −1 ) denotes the mass attenuation coefficient (cm 2 g −1 ) and ρ = 3.97 g cm −3 is the density of the sample. The total value of μ/ρ including coherent scattering was taken from the NIST (National Institute of Standards and Technology) photon cross sections database XCOM [36,37]. The f Eγ values were determined with Eq. (2) for various discrete energies between 100 and 5000 keV. The dependence of the gamma-ray self-absorption factors f Eγ on the gamma-ray energy E γ is shown in Fig. 3. The data points were fitted with the following semi-empirical function: (3) f Eγ = a 0 + a 1 ⋅ 1 − e −a 2 ⋅E γ + a 3 ⋅ 1 − e −a 4 ⋅E γ Fig. 1 Gamma-ray spectra in the energy range 0-3000 keV acquired during 55,478 s counting live time for the PVC sample (green), 9743 s for the CeCl 3 sample (red) and during 51,506 s for the beam background (black). Prompt gamma rays induced by (n,p) reactions (S-35) and (n,α) reactions (P-32) on Cl-35 are written in black with an asterisk. Other lines marked in black but without an asterisk represent X-rays from cerium. Prompt gamma rays issued from (n,n') inelastic scattering of fast neutrons on cerium are written in black and bold. They are written in bold blue for the case of chlorine. Lines in light blue are capture gamma rays from Cl-35. Abbreviations SE and DE indicate single and double escape peaks, respectively. The origin of prominent lines attributed to the beam background is discussed within our former publications [7,9]. For the correction of SE and DE interferences the energy deposited by high-energy gammas in the HPGe detector was simulated using the F8 tally of the MCNP code [31,32]. Based on the technical drawing provided by the manufacturer (ORTEC®), a realistic detector model was implemented in the simulation. The gamma source was defined as a parallel photon beam of several discrete energies between 1.3 and 8.0 MeV. The ratios between net counts of SEs and FEPs and between net counts of DEs and FEPs were deduced from the simulated spectrum. The dependence of the logarithmic value of the ratios on the gamma energy is shown in Fig. 4 and was approximated with Eq. (4):

Fig. 2
Gamma-ray spectra in the energy range 3000-8000 keV acquired during 55,478 s counting live time for the PVC sample (green), 9,743 s for the CeCl 3 sample (red) and during 51,506 s for the beam background (black). Prompt gamma rays issued from (n,n') inelastic scattering of fast neutrons on cerium are written in black and bold. They are written in bold blue for the case of chlorine. Lines in light blue are capture gamma rays from Cl-35. Abbreviations SE and DE indicate single and double escape peaks, respectively. The prompt line of C-12 was observed in the PVC measurement. The origin of prominent lines attributed to the beam background is discussed within our former publications [7,9]. (Color figure online)

Prompt gamma rays of chlorine
Twenty nine gamma lines from the interaction of fast neutrons with chlorine were identified in the CeCl 3 spectrum, 15 assigned to the 35 Cl(n,n') 35 Cl, 8 to the 37 Cl(n,n') 37 Cl, 5 to the 35 Cl(n,p) 35 S and 1 to the 35 Cl(n,α) 32 P reaction, respectively (see Table 1). In the case of the PVC sample, only 14 fast-neutron-induced lines were measured, 7 related to the 35 Cl(n,n') 35 Cl, 4 to the 37 Cl(n,n') 37 Cl and 3 to the 35 Cl(n,p) 35 S reaction. The lower number of observed gamma rays in the PVC spectrum is explained with the lower sensitivity stemming from the much smaller sample mass only partly compensated by the longer measurement time.
Since PVC contains carbon we also measured the Dopplerbroadened [38,39] gamma ray of the 12 C(n,n'γ) 12 C reaction. Additionally, in both spectra, the main neutron capture lines of chlorine were identified as our neutron spectrum contains epithermal and thermal neutrons [9,10,12]. No significant interferences between the capture lines and the fast-neutroninduced lines of chlorine were observed. The PVC foil was also used to check the composition and absence of crystal water in the CeCl 3 sample, as the chlorine peak count rate ratios were found to agree with the nominal chlorine mass ratio. The interference-free (according to [20]) lines at 2645 and 3002 keV from the 35 Cl(n,n'γ) 35 Cl reaction yielded an average chlorine mass of (1.14 ± 0.05) g, which is in good agreement with the value calculated from the nominal composition of the chloride (1.15 g). Therefore, the sample is assumed to contain no water as the hexahydrate would yield a chlorine mass of 0.80 g.
Intensities of the gamma lines were calculated relative to the 1219-keV line of 35 Cl. They are compared  E thr is the threshold energy of the considered reaction taken from [29,30], E γ is the gamma-ray energy, P Eγ (90°)/(ε Eγ ·f Eγ ) the net counts in the gamma-ray peak divided by the full-energy-peak efficiency and the gamma self-absorption factor, I R the relative intensity of the gamma ray and < σ Eγ (90°) > the fission-neutron spectrum-averaged partial cross section for gamma-ray production at an angle of 90° between neutron beam and detector determined with Eq. (1). R is the residual calculated by means of Eq. (6). Cross sections written in bold are proposed a Corrected for background interferences b Unassigned by Demidov et al. c Negligible interference from the 140 Ce(n,n'γ) 140 Ce reaction [26], but interference unreported on [20] is assumed as the cross section differs much compared to that given in Table 2 d Possible interference from the 142 Ce(n,n'γ) 142 Ce reaction [27] e Maybe uncorrected interference in [14] from the SE from the 2693.8-keV line of 35 Cl f Doppler-broadened; short-lived transitions in the femtosecond range [21][22][23] g Corrected for contribution of SE from 4622 keV (32.6% of total counts) h Interference from 140 Ce(n,n'γ) 140 Ce reaction corrected with relative intensities given in the ENSDF file [26] on [20] i Might be fed from two close-lying short-lived levels; possible, but unlikely to come from 37 Cl(n,n'γ) 37 Cl reaction [22] j Data from Demidov et al. might be more accurate due to a higher chlorine mass and counting time [14] k Considerable self-absorption with f Eγ = 0.128 ± 0.013, calculated after Eq. (2) Reaction (E thr ) This work 35 Cl(n,n'γ) 35 35 Cl, the lines at 1900.0, 3625.5 and 4010.3 for the 37 Cl(n,n') 37 Cl, the line at 2714.9 keV for the 35 Cl(n,p) 35 S and the line at 78.0 keV for the 35 Cl(n,α) 32 P reaction (see also Figs. 1 and 2). Another gamma ray at 1184.6 keV, listed but unassigned in [14], was found to belong to the 35 Cl(n,n') 35 Cl reaction.
For the lines at 774.8, 1726.2, 1900.0 and 2347.6 keV in the CeCl 3 spectrum, Demidov et al. suggest interferences with lines from the 140 Ce(n,n'γ) 140 Ce reaction. They were corrected using the relative intensities in the evaluated nuclear structure data file (ENSDF) [26] for the corresponding (n,n'γ) reaction, because a large discrepancy in intensity compared to the original work of [14] for those lines was observed. The contributions from the interfering (n,n'γ) Table 2 Prompt gamma rays of 35 Cl, 37 Cl and 12 C induced by fast neutrons on PVC E thr is the threshold energy of the considered reaction taken from [29,30], E γ is the gamma-ray energy, P Eγ (90°)/ε Eγ the net counts in the gamma-ray peak divided by the full-energy-peak efficiency, I R the relative intensity of the gamma ray and < σ Eγ (90°) > the fission-neutron spectrum-averaged partial cross section for gamma-ray production at an angle of 90° between neutron beam and detector determined with Eq. (1). R is the residual calculated by means of Eq. (6). Cross sections written in bold are proposed a Unassigned by Demidov et al. b Corrected for background interferences c Doppler-broadened; short-lived transitions in the femtosecond range [21][22][23]38] d Only elemental data available from [29,30] e Unclear how this intensity is obtained, it might be a mistake or the absolute intensity determined with the integral cross section. From our work the absolute intensity is 107% by using an integral cross section for fission neutrons of roughly 12 mb [40] with an angular distribution correction factor of W(90°) = 1

Reaction (E thr )
This work 35 Cl(n,n'γ) 35  The correlation between the relative intensities in this work and in [14] is depicted in Fig. 5 for our two measurements. The values have been fitted with the following semiempirical function [10][11][12]: with a = 0.68 ± 0.10 and b = 1.07 ± 0.06 for the CeCl 3 , and a = 0.94 ± 0.14 and b = 0.99 ± 0.06 for the PVC sample.
The average intensity ratios I R /I RD of 0.83 ± 0.19 (CeCl 3 ) and I R /I RD of 0.94 ± 0.16 (PVC) indicate a good agreement between the two measurements. To prove the consistency in a more detailed manner, Fig. 6 shows the two sets of data in the form of a common histogram of the residuals R in units of standard deviation [σ] for our two measurements, calculated as [10][11][12]: The fit of the data agrees at the 1.3σ level and the Gaussian centroid is shifted by −1.002, indicating a systematic effect. We assume that the large shift mainly originates from the lines at 774.8, 2179.1 and 2839.6 keV, only observed in the CeCl 3 sample. For these lines we found much less intensity compared to [14].
The fast-neutron spectrum-averaged partial cross sections for gamma-ray production calculated by means of Eq. (1) are given in column 5 of Tables 1 and 2. The values of the two datasets agree well with each other, taking into account the uncertainties except for the lines at 1219, 1572, 1726, 1763 and 1991 keV. For the latter the cross sections obtained from the CeCl 3 measurement are roughly higher by factors between 1.2 and 1.4 than these derived from the PVC measurement, thus, indicating possible interferences from cerium lines. For the line at 1219 keV we propose the cross section obtained from the PVC irradiation, while for all others the cross sections with the better R value, i.e. greater agreement in relative intensity with [14], are suggested. Proposed cross sections are written in bold in Tables 1 and 2.  Tables 3 and  4. No neutron capture lines from cerium were identified. Intensities of gamma lines were calculated relative to the 1596-keV line of 140 Ce. They are given along with the values determined in [14] in columns 3 and 6 of Tables 3  and 4. We detected 31 out of 45 lines given in [14], of which only 27 lines were originally assigned to fast-neutron reactions. The gamma rays listed at energies of 337.  [7,9]. The lines at 788.2 and 1958.5 keV are mainly associated to the neutron capture lines of 35 Cl and the lines at 774.8 and 2347.5 keV are essentially issued from the 35 Cl(n,p) 35 S reaction. The 1724.9-keV line was not identified uniquely due to strong interferences with the 1726.2-keV line of 37 Cl and the background lines of 207 Pb and 56 Fe at 1725 keV [9]. The line at 1899.3 keV listed in [14] is mainly related to the 1900.0-keV line of 37 Cl.
The DEs of the lines at 1762.9 keV ( 35 Cl) and 2645.2 keV ( 35 Cl) as well as the SE of the line at 3625.5 keV ( 37 Cl) were found to interfere significantly with the lines at 739.6, 1623.6 and 3118.2 keV, respectively. Their contributions to the net count rates were estimated with Eq. (4) to be (34.9 ± 3.3)%, (41.9 ± 4.9)% and (14.5 ± 2.5)%, respectively. The contribution of the DE of the background line at 2614 keV ( 208 Pb) [7,9]  On the other hand, in comparison to [14] we have iden-  Tables 3  and 4).
The correlation between the relative intensities measured in this work and these given in [14] is depicted in Fig. 7 for all lines. The values have been fitted with Eq. (5) yielding the coefficients a = 0.86 ± 0.06 and b = 0.98 ± 0.05. The average intensity ratio I R /I RD is 0.93 ± 0.23, indicating a reasonable agreement between the two measurements. Figure 8 shows the two sets of data in the form of a histogram of the residuals R in units of standard deviation [σ], calculated according to Eq. (6). The fit of the data agrees at the 1.2σ level and the Gaussian centroid is shifted by −0.671, indicating a probable systematic effect.

Prompt gamma ray of carbon
Since the PVC sample was irradiated for a relatively long time the Doppler-broadened peak at 4441.0 keV from the 12 C(n,n') 12 C reaction was also identified (see Fig. 2). It was exploited to confirm the result from our previous measurement on calcium carbonate (CaCO 3 ) [12]. A partial cross section of (12.8 ± 2.3) mb determined with Eq. (1) agrees well with that of (14.4 ± 3.3) mb derived in [12], thereby demonstrating reproducibility of our instrument. From our two measurements we derive an average value of (13.3 ± 1.9) mb for fast neutrons, compared to (2.6 ± 0.1) mb (4945.3-keV line of 12 C [28]) for thermal neutrons. Thus, in case of equal measurement conditions (i.e. same neutron flux and spectrometer set-up) FaNGaS offers greater sensitivity in the detection of carbon higher by a factor of approximately five.

Detection limit
The detection limit (DL) can be defined as the minimum mass of a pure element that has to be irradiated for a certain time in order to give a net signal with a certain standard deviation σ. For a certain counting time t c , neglecting any neutron and gamma beam attenuation effects, it can be calculated with Eq. (1) from the minimum peak area P Eγ (c) that might be estimated according to [42] as: where B Eγ is the area of the background below the gamma line of interest and c a predefined value for the relative uncertainty of the peak area.
For a counting live time of 12 h, the DL of cerium and chlorine were calculated for the most intense gamma line of each element by means of Eqs. (1) and (7). The value E γ is the gamma-ray energy, P Eγ (90°)/(ε Eγ ·f Eγ ) the net counts in the gamma-ray peak divided by the full-energy-peak efficiency and the gamma self-absorption factor, I R the relative intensity of the gamma ray and < σ Eγ (90°) > the fission-neutron spectrum-averaged partial cross section for gamma-ray production at an angle of 90° between neutron beam and detector determined with Eq. (1). R is the residual calculated by means of Eq. (6) a Reaction threshold for inelastic scattering is 0.56 MeV [41] of B Eγ was determined from the beam background with HYPERMET-PC [19]. For a value of c = 0.5, corresponding to a peak area uncertainty of 50%, the smallest quantity of pure element that can be detected is 1 mg for cerium ( 140 Ce, E γ = 1596.0 keV, < σ Eγ (90°) > = 666 mb) and 2 mg for chlorine ( 35 Cl, E γ = 1763.1 keV, < σ Eγ (90°) > = 70 mb).

Conclusions
Emission of prompt gamma rays following fast-neutron inelastic scattering (n,n'), (n,p) and (n,α) reactions on a CeCl 3 and a PVC sample were measured with the FaNGaS instrument operated at MLZ. In total, 29 and 58 prompt b Reaction threshold for inelastic scattering is 1.61 MeV [29,30] c Gamma ray of 136 Ce d Interference from 142 Ce(n,n'γ) 142 Ce possible with respect to [27] e Corrected for background interferences f Doublet with 142 Ce (see Table 4) g Corrected for escape peak interference h Somewhat cautious assignment, as relative intensities differ considerably compared to data given in [26] i Wrong level energy assigned by Demidov et al. [14]   E γ is the gamma-ray energy, P Eγ (90°)/(ε Eγ ·f Eγ ) the net counts in the gamma-ray peak divided by the full-energy-peak efficiency and the gamma self-absorption factor, I R the relative intensity of the gamma ray and < σ Eγ (90°) > the fission-neutron spectrum-averaged partial cross section for gamma-ray production at an angle of 90° between neutron beam and detector determined with Eq. (1). R is the residual calculated by means of Eq. (6) a Threshold for inelastic scattering is 0.65 MeV [29,30] gamma lines were identified for chlorine and cerium, respectively, and their relative intensities and fast-neutron spectrum-averaged partial gamma-ray production cross sections were determined. In comparison with the work of Demidov et al. [14], 37 gamma lines were detected additionally (10 for chlorine and 27 for cerium) owing to a better detector resolution and a higher mean excitation energy (2.30 MeV). However, 8 lines of chlorine and 14 lines of cerium, partly unassigned in [14], were not observed in our measurements either due to background interferences or lower sample-masses irradiated for a shorter time or were found to disagree with nuclear data provided in [20]. The relative intensities of the lines measured in our work agree reasonably well (1.3σ level for chlorine and 1.2σ level for cerium) with the values given in [14]. The detection limits of chlorine and cerium are determined as 2 and 1 mg, respectively, for a counting time of 12 h. In addition, the partial cross section of the 4.44-MeV line of carbon derived from the measurement of the PVC sample is found to be in good agreement with the value obtained in the previous measurement of CaCO 3 [12].
Funding Open Access funding enabled and organized by Projekt DEAL.

Competing interests
The authors have no competing interests to declare that are relevant to the content of this article.
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Fig. 7
Relationship between the relative intensities I R of the prompt gamma rays induced by fast-neutron inelastic scattering (n,n') reactions on cerium measured in this work and the relative intensities I RD tabulated in the Demidov Atlas [14]. The solid line represents the fit of the data with Eq. (5)