Gamma-ray spectra from thermal neutron capture on gadolinium-155 and natural gadolinium

155 Gd and 157 Gd. We measured the γ -ray spectra produced from the thermal neutron capture on targets comprising a natural gadolinium ﬁlm and enriched 155 Gd (in Gd 2 O 3 powder) in the energy range from 0.11 MeV to 8.0 MeV, using the ANNRI germanium spectrometer at MLF, J-PARC. The freshly analyzed data of the 155 Gd( n , γ ) reaction are used to improve our previously developed model (ANNRI-Gd model) for the 157 Gd( n , γ ) reaction and its performance conﬁrmed with the independent data from the nat Gd( n , γ ) reaction. This article completes the development of an efﬁcient Monte Carlo model required to simulate and analyze particle interactions involving the thermal neutron captures on gadolinium in any relevant future experiments....................................................................................................................


Introduction
Gadolinium (Gd) has become an important element of consideration in a number of neutrino experiments for enhanced detection of electron anti-neutrinos (ν e ). The presence of Gd boosts the tagging of neutrons in the inverse beta decay reaction (IBD),ν e + p → e + + n, in organic liquid scintillator and water-Cherenkov detectors. This is primarily due to its large capture cross PTEP 2020, 043D02 T. Tanaka et al. Table 1. Relative abundances of gadolinium isotopes in natural gadolinium [20] and their radiative thermal neutron capture cross sections [1]. section for thermal neutrons and the large energy released by γ rays of ∼ 8 MeV for the Gd(n, γ ) reactions [1][2][3][4]: n + 155 Gd → 156 Gd * → 156 Gd + γ rays (8.536 MeV total), and n + 157 Gd → 158 Gd * → 158 Gd + γ rays (7.937 MeV total).
Therefore, it is of paramount importance to establish a precise Monte Carlo (MC) model for the γ -ray energy spectrum from the radiative thermal neutron capture on Gd. It is an essential prerequisite for MC studies aiming to evaluate the neutron tagging efficiency in a Gd-loaded detector. Precise modeling is especially important for those detectors that lack hermetic acceptance and/or have a high energy threshold for γ rays, since some of the γ rays emitted in the capture reaction may not be detected.
In most cases, detector materials are doped with the natural Gd ( nat Gd). Isotopic adundances are listed in Table 1.
The most frequent isotopes, 155 Gd and 157 Gd, also feature large thermal neutron capture cross sections. Therefore, the required MC model for nat Gd requires the modeling of the γ -ray emission from not only 157 Gd [21] but also 155 Gd.
We measured the γ -ray energy spectrum from the radiative thermal neutron capture on an enriched 155 Gd sample and a nat Gd film with the germanium (Ge) spectrometer of the Accurate Neutron-Nucleus Reaction Measurement Instrument (ANNRI) [22][23][24][25][26]. The incident pulsed neutron beam from the Japan Spallation Neutron Source (JSNS) at the Material and Life Science Experimental Facility (MLF) of the Japan Proton Accelerator Research Complex (J-PARC) [27] and the good γray energy resolution, high statistics, and low background makes ANNRI a favorable spectrometer for our intended study [21,22].
The Detector for Advanced Neutron Capture Experiments (DANCE) at the Los Alamos Neutron Science Center (LANSCE) has extensively studied the γ -ray energy spectra from the radiative neutron capture reaction at various multiplicities in the neutron kinetic energy range from 1 to 300 eV for both 155 Gd and 157 Gd targets [28][29][30]. They compared their γ -ray spectra to MC simulations with the DICEBOX package [31] and showed fair agreement. Concerning the measurements in the 2/15 PTEP 2020, 043D02 T. Tanaka et al. thermal energy region, Groshev et al. [32][33][34] measured prompt γ rays from the neutron capture on 155 Gd and 157 Gd and tabulated the γ -ray energy, intensity values and decay schemes in great detail. Valenta et al. [35] measured the two-step cascade (TSC) γ rays, following the thermal neutron capture on 155 Gd and 157 Gd, with a pair of HPGe detectors and studied the effect of the M 1 or E2 transitions in addition to the E1 transitions in the TSC spectra.
We performed a series of measurements of the prompt γ rays covering almost the full spectrum from 0.11 MeV to 9 MeV from the capture reaction on 155,157 Gd and nat Gd at thermal neutron energies. As we demonstrated in Fig. 12 of the previous publication [21] and also Fig. 7 of this report, it is very important to measure the full γ -ray spectrum from the capture in order to study the photon strength function and the nuclear level density, which are the important properties of the Gd nucleus 1 . Based on our data and a Geant4-based detector simulation [36,37] of our setup, we developed a Monte Carlo (MC) model to generate the full γ -ray spectrum from the thermal 157,155,nat Gd(n,γ ) reaction. The γ -ray spectrum and its corresponding MC model (ANNRI-Gd model) for 157 Gd has already been discussed in Ref. [21].
In this report, we present the γ -ray energy spectra from the 155 Gd(n, γ ) and nat Gd(n, γ ) reactions, modify our ANNRI-Gd model with the contribution from 155 Gd, and present our final MC performance for nat Gd(n, γ ) to be used by any neutrino or other experiments involving the measurement of γ -ray signals from the thermal neutron capture on Gd.

Experiment and data analysis
A 300 kW beam of 3 GeV protons from the JSNS facility in double-bunch mode at a frequency of 25 Hz was incident on a primary target of mercury, producing neutrons. The neutron beam thus produced consists of neutron pulses in double-bunch mode, each 100 ns wide, with 600 ns spacing every 40 ms. The ANNRI spectrometer is located 21.5 m away from the neutron beam source. It comprises two germanium cluster detectors with anti-coincidence shields made of bismuth germanium oxide (BGO) and eight co-axial germanium detectors. The target for neutron capture is positioned in line with the beam, 13.4 cm from each of the two cluster detectors on either side along the vertical plane.
In this report, we used only data taken with the cluster detectors, which cover 15% of the solid angle. Each cluster consists of seven Ge crystals in a hexagonal arrangement, details of which can be found in Ref. [21].
From the neutron time-of-flight T TOF recorded for each event we calculated the neutron kinetic energy E n as where m n is the neutron mass and L is the 21.5 m distance between neutron source and target. The resulting neutron energy spectra are shown in Fig. 1. Since we study the γ -ray spectrum solely from thermal neutron capture on 155 Gd and nat Gd, we only selected events from neutrons in the kinetic energy range [4,100] meV for the present analysis. The obtained data cover the energy region of γ rays from 0.11 MeV to about 9 MeV with observed γ -ray multiplicities (M ) one to three. The energies of the emitted γ rays are recorded by each of the PTEP 2020, 043D02 T. Tanaka et al.  crystals. A threshold of 100 keV is set for each of the cluster detectors. For the event classification, we assign a multiplicity value M and a hit value H to each recorded event. We defined the multiplicity M as the combined number of isolated sub-clusters of hit Ge crystals at the upper and lower clusters. A sub-cluster is formed by the neighboring hit Ge crystals and can be of size ≥ 1. The hit value H describes the total number of Ge crystals hit in the event. The multiplicity M represents the number of observed γ rays, while the hit value H is a measure of the lateral spread of γ rays. The details of the event class are described in Ref. [21]. The fraction of the data collected in each event class is reflected in the bar charts in Fig. A.1. We used radioactive sources ( 60 Co, 137 Cs, and 152 Eu) and 35 Cl(n,γ ) to calibrate the detector, and determined the detection efficiency of the spectrometer for γ rays at energies from 0.3 to 8.5 MeV, as described in detail in Ref. [21].
We measured the thermal neutron capture on a gadolinium (Gd 2 O 3 ) target enriched with 155 Gd (91.85%) in December 2014 and natural Gd (99.9% pure metal film) in March 2013. The weights of the targets, i.e., 155 Gd and 157 Gd powder, were 26.4 mg and 28.9 mg respectively, spread across an area of 1 × 1 cm in a Teflon envelope. The film of the natural gadolinium target was 5 mm × 5 mm × 10 μm (and 20 μm) in dimensions. The isotopic composition of our enriched gadolinium sample is given in Table 2.
In 2014, an additional layer of LiF (∼1 cm thickness) was included in the beam pipe to reduce the γ rays from neutron capture on the aluminum of the beam pipe. Therefore, the data-taking with nat Gd was subject to more background events (without the LiF layer) than that of 155,157 Gd. The background γ -ray energy spectra that were observed by one of the crystals (C6) for M1H1 events (one γ and one hit) with the empty target holder at two different periods in the neutron beam are shown in Fig. 2. The γ -ray energy spectra for M1H1 events with the three target materials, 155   to the differences in the target masses (× cross section) used for the three measurements. The size of the background is less than 0.1% for the data for the 155 Gd target and less than 1% for those for the nat Gd target. The background is accordingly subtracted for each data set and the resulting energy spectra for the three targets are shown in Fig. 3. The γ -ray energy spectrum from neutron capture on natural gadolinium is dominated by that from its two main isotopes, 155 Gd and 157 Gd, with fractions of 18.5% and 81.5%, respectively. The contributions of other isotopes are negligible.
The spectra taken separately for the pure 155 Gd and 157 Gd samples must be consistent with that of the nat Gd film, when they are combined in the corresponding proportions. This was checked and confirmed in Fig. 4, where excellent agreement is found between the two spectra (red and black).

Update for the ANNRI-Gd model
The MC model for 157 Gd has already been described in Ref. [21]. We now develop a MC model for 155 Gd, following the same approach of separate treatment for the discrete and continuum parts of the spectrum [21,38].
For the thermal neutron capture on 155 Gd in an s-wave, the resonance state is 8.536 MeV (J π = 2 − ) of 156 Gd. The resonance energy for the neutron is 26.8±0.2 meV and the radiative width is 108±1 meV [1]. We identified and measured the photo peak intensities of 12 discrete γ rays for 155 Gd(n, γ )  above 5 MeV as listed in Table 3. The single and double escape peaks were excluded before analyzing these peaks. The direct transition of the resonance state (J π = 2 − ) to the ground state (J π = 0 + ) is largely suppressed compared to the transition from 8.536 MeV (J π = 2 − ) to 0.089 MeV (J π = 2 + ), emitting a 8.448-MeV γ ray. The tabulated values of the energies are taken from Ref. [39]. In the case of overlapping peaks in our data spectrum, we mention the means of the primary γ -ray energies with their combined intensities. The discrete γ -ray emissions above 5 MeV are expected to arise mostly from the first transition and are hence referred to as "primary" γ rays. By tagging the events with each of these primary γ rays, we obtained the intensities of the secondary γ rays. We found them in fair agreement with the values published in Nuclear Data Sheets for A = 156 [39], as displayed in Fig. 5. Details of the comparison methods are described in Ref. [21]. The relative intensities of these discrete peaks add up to 2.78±0.02% of the data spectrum. For the modeling of the continuum part, we compute the probability P(E a , E b ) for E1 transitions with E γ = E a − E b in terms of the transmission coefficient T E1 (E γ ) and the number of levels ρ(E b )δE b as 6/15 PTEP 2020, 043D02 T. Tanaka et al. Table 3. List of the 12 discrete peaks from primary γ rays that we identified in our data. The stated energies are taken from Ref. [39], rounded to the nearest keV. In four cases the table lists the unweighted mean energy of known peaks that overlap in our data: (i) 6474 keV, combining 6482 keV and 6466 keV; (ii) 6348 keV, combining 6349 keV and 6345 keV; (iii) 5885 keV, combining 5889 keV and 5884 keV; as well as (iv) 5779 keV, combining 5774 keV and 5786 keV.
where δE is a finite energy step in our computations. T E1 (E γ ) refers to the E1 photon strength function f E1 (E γ ) (PSF) depending on cross section (σ i ), the width ( i ), and energy (E i ) of the resonances. It is written as where values of E i , σ i , and width i are mentioned in Table 4 and ρ(E b ) is the nuclear level density (NLD). We note that we add two small (pygmy) E1 resonances of the same Lorentzian type (i = 3, 4) to the PSF in Eq. (3) in order to check the effect of those two resonances on the γ -ray spectrum [40,42,43] 2 , while we used only the first two major E1 resonances in the previous publication [21]. Since PTEP 2020, 043D02 T. Tanaka et al.  these four resonances are all E1-type, we can construct probability tables according to Eq. (2) to generate the γ -ray spectrum 3 . The corresponding NLD [43][44][45] and the PSF [40] used for 156 Gd are shown in Fig. 6 (left and right respectively). Recent reviews on the NLD and the PSF can be found in Refs. [43,46].

Final model performance
We first generate the continuum part of the γ -ray spectrum in 156 Gd according to Eq. (2). The result is shown in Fig. 7. We then generate the discrete part according to the relative intensities listed in Table 3 and then compare these two parts with the observed spectrum. We determine the fraction of the discrete part in the total number of events to be 2.78±0.02% of the data above 0.11 MeV. The remaining dominant contribution of 97.22±0.02% comes from the continuum part of the energy levels in 156 Gd. The continuum and discrete components generated by our MC model are shown separately here for 155 Gd, along with the data in Fig. 8. They are added in the corresponding fractions in Fig. 9 (left). The data spectrum matches our MC spectrum well. The MC-generated spectrum for nat Gd(n, γ ) should naturally comprise the spectra for 155 Gd(n, γ ) and 157 Gd(n, γ ), as is obvious with the data spectra in Fig. 4. So, the spectrum for nat Gd(n, γ ) is obtained by adding the MC spectra generated for 155 Gd(n, γ ) and 157 Gd(n, γ ) in the required ratio of their relative cross sections and abundances, as is shown in Fig. 9 (right).
The spectra shown above are single energy spectra (M1H1), which constitute the most dominant (∼70%) fraction of the data. In fact, good agreement is found between all the MC-generated spectra and the subsamples of data for different observed multiplicities M . As examples, the M2H2 and M3H3 spectra are shown in Appendix A.

Conclusion
The γ -ray spectra generated by our ANNRI-Gd model agree not only with the individual 155 Gd and 157 Gd data set, but also with the nat Gd data set, which are entirely independent 4 . We show the ratio of data/MC in bins of 200 keV for 155 Gd, 157 Gd, and nat Gd in Fig. 10, for the single γ -ray M = 1 events as an approximate representation of the goodness of our model. For the presented single γ -ray spectrum with the 200 keV binning, the mean deviation of the single ratios from the mean ratio is about 17% for each of 157 Gd, 155 Gd, and nat Gd spectra. The same ratios for the M = 2 and M = 3 samples are shown in Fig. A.4. They are all in good agreement at a similar level to those published for the 157 Gd(n, γ ) reaction [21]. With this article, we have completed a consistent model (the ANNRI-Gd model) to generate the gross spectrum for the thermal 155 Gd, 157 Gd, and nat Gd(n, γ ) reaction.
In comparison, the more sophisticated model [35] tries to include a small contribution of the M 1 (scissors mode) or E2 resonance around 3 MeV in the PSF in order to explain the energy spectra in the sample of two-step cascade γ rays from the thermal neutron capture reactions. The DANCE experiment [28,29] also suggested a need for small resonances (M 1 or E2) around 3 MeV in addition PTEP 2020, 043D02 T. Tanaka et al. to the major E1 PSFs in order to explain the γ -ray energy spectra of the multiplicity M = 2, though the data of the 155,157 Gd(n, γ ) reactions were taken in neutron kinetic energies in values of tens of eV. To further refine the present modeling, we intend to work on a sample of 2γ rays including strong discrete cascade transitions. We note that those samples constitute a few % of the total number of capture events. As these previous articles point out, we must handle the positive-parity states and negative-parity states separately in the NLD or in any discrete levels in order to take into account the E1 transition or M 1/E2 transition correctly during the cascade.
After we submitted this article in August 2019, the Daya Bay Collaboration, one of the most advanced reactor-neutrino experiments, reported a Monte Carlo study of the γ -ray spectra from the thermal neutron capture on 155 Gd and 157 Gd and showed large discrepancies in the γ -ray spectra generated by various Monte Carlo models [47]. We compare our spectrum with their result in Appendix B. It shows clearly that our data and our MC model will help resolve such discrepancies in the gross γ -ray spectrum generated by various MC models for the thermal 155 Gd, 157 Gd, and nat Gd(n, γ ) reactions.  disagrees with Model 1 below 2 MeV. Other models generate spectra that are very different from ours in shape. We would like to stress again that we can discuss small structures at 2-3 MeV such as the scissors mode only after we understand the gross spectrum over the entire energy region.