Improved STEREO simulation with a new gamma ray spectrum of excited gadolinium isotopes using FIFRELIN
H. Almazán, L. Bernard, A. Blanchet, A. Bonhomme, C. Buck, A. Chebboubi, P. del Amo Sanchez, I. El Atmani, J. Haser, F. Kandzia, S. Kox, L. Labit, J. Lamblin, A. Letourneau, D. Lhuillier, M. Lindner, O. Litaize, T. Materna, A. Minotti, H. Pessard, J.-S. Réal, C. Roca, T. Salagnac, V. Savu, S. Schoppmann, V. Sergeyeva, T. Soldner, A. Stutz, L. Thulliez, M. Vialat
aa r X i v : . [ phy s i c s . i n s - d e t ] O c t Improved STEREO simulation with a new gamma rayspectrum of excited gadolinium isotopes using FIFRELIN
H. Almazán , L. Bernard , A. Blanchet , A. Bonhomme a , C. Buck , A. Chebboubi , P. del Amo Sanchez ,I. El Atmani b , J. Haser , F. Kandzia , S. Kox , L. Labit , J. Lamblin , A. Letourneau , D. Lhuillier , M. Lindner ,O. Litaize , T. Materna , A. Minotti c , H. Pessard , J.-S. Réal , C. Roca , T. Salagnac d , V. Savu , S. Schoppmann ,V. Sergeyeva e , T. Soldner , A. Stutz , L. Thulliez and M. Vialat Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 38000 Grenoble, France IRFU, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France Univ. Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, LAPP, 74000 Annecy, France Institut Laue-Langevin, CS 20156, 38042 Grenoble Cedex 9, France CEA, DEN, DER, SPRC, F-13108 Saint Paul Lez Durance, France
Abstract
The
Stereo experiment measures the electron antineutrino spectrum emitted in a researchreactor using the inverse beta decay reaction on H nuclei in a gadolinium loaded liquid scintillator. Thedetection is based on a signal coincidence of a prompt positron and a delayed neutron capture event.The simulated response of the neutron capture on gadolinium is crucial for the comparison with data,in particular in the case of the detection efficiency. Among all stable isotopes,
Gd and
Gd havethe highest cross sections for thermal neutron capture. The excited nuclei after the neutron capture emitgamma rays with a total energy of about 8 MeV. The complex level schemes of
Gd and
Gd are achallenge for the modeling and prediction of the deexcitation spectrum, especially for compact detectorswhere gamma rays can escape the active volume. With a new description of the Gd(n, γ ) cascades obtainedusing the Fifrelin code, the agreement between simulation and measurements with a neutron calibrationsource was significantly improved in the
Stereo experiment. A database of ten millions of deexcitationcascades for each isotope has been generated and is now available for the user.
PACS. γ transitions and level energies – 95.55.Vj Neutrino detectors – 28.20.-v Neutron physics The
Stereo experiment [1] detects electron antineu-trinos produced in a compact research reactor at the In-stitut Laue-Langevin (ILL) in Grenoble, France. With the
Stereo data, it is possible to test the hypothetical exis-tence of a sterile neutrino in the eV mass range [2]. An-tineutrinos are detected via the inverse beta decay reac-tion (IBD) ¯ ν e + p → e + + n in a gadolinium (Gd) loadedorganic liquid scintillator (LS) [3]. The positron ionizationgives rise to a prompt signal – related to the antineutrinoenergy –, while the neutron thermalizes and diffuses inthe liquid. The gamma emission following the radiative a Corresponding author: [email protected] b Present address: Hassan II University, Faculty of Sciences,Aïn Chock, BP 5366 Maarif, Casablanca 20100, Morocco c Present address: Univ. Grenoble Alpes, Université SavoieMont Blanc, CNRS/IN2P3, LAPP, 74000 Annecy, France d Present address: IPNL, CNRS/IN2P3, Univ. Lyon, Univer-sité Lyon 1, 69622 Villeurbanne, France e Present address: IPN Orsay, CNRS/IN2P3, 15 rue GeorgesClemenceau, 91406 Orsay, France capture of the neutron creates a delayed signal after typi-cal coincidence time of a few tens of µ s.The capture time can be strongly reduced by the ad-dition of Gd with its very high cross section for thermalneutron capture ( ∼ barn for some of the isotopes) tothe LS. At a Gd-concentration of 0.2 wt.% in Stereo ,the average capture time is µ s , one order of magni-tude lower than for an unloaded scintillator where cap-ture is mainly by hydrogen (H). More than 80% of theneutrons are captured on Gd. The resulting excited Gd-nuclei decay to the ground state by emitting on averagefour gammas with a total energy of about 8 MeV. Thisis well above the typical energies of the natural radioac-tivity backgrounds and the 2.2 MeV line of H(n, γ ), pro-viding a clean detection channel. Therefore, several past,present, and upcoming neutrino detectors take advantageof the Gd-loaded LS technology. All of these experimentsrely on a precise knowledge of the Gd-deexcitation process,where the gamma multiplicity and single energies are es-pecially relevant for segmented and/or compact detectorssuch as Stereo . These quantities play a crucial role inthe reconstructed spectrum of the experiments, since high
H. Almazán et al.: Improved STEREO simulation with a γ -ray spectrum of excited Gd isotopes using FIFRELIN energy gammas are more likely to escape the detector orleave only a part of their energy via Compton scattering,and populate thereby the tail of the reconstructed peak.The DANSS experiment, for example, reported some ten-sion between calibration and simulation data in the lowenergy part of the Gd spectrum [4]. To determine theneutron detection efficiency in the Daya Bay experiment,four different models are used to estimate the gamma en-ergy and multiplicity distributions [5]. An accurate mod-eling of these distributions is also of major relevance inwater Cherenkov detectors with Gd-loading [6], since thelight production is very sensitive to the energies of the sin-gle gammas due to the Cherenkov threshold. Therefore,a good understanding of the cascade for the most rele-vant isotopes Gd and
Gd is of primary importanceto reduce the systematic uncertainties. However, none ofthese isotopes have complete experimentally known nu-clear level schemes and branching ratios up to 8 MeV. Thecause of small discrepancies between the
Stereo data andsimulation was identified to be largely due to an inaccuratedescription of the gamma deexcitation of the Gd nuclei.By using Gd ∗ and Gd ∗ gamma cascades from thenucleus deexcitation code Fifrelin developed at CEA-Cadarache (France) these discrepancies are reduced.The
Fifrelin code is developed for the evaluation offission data and has already proven its ability to makeaccurate predictions regarding neutron and gamma prop-erties [7–9]. It provides important information on crucialparameters like the gamma multiplicity and the particleenergies. The code is made of two parts: one is the assign-ment of the initial state of the fission fragment and theother is the deexcitation process. For the
Stereo experi-ment, only the deexcitation part is used. Once the initialstates are given, a set of nucleus level schemes is sam-pled allowing to take into account nuclear structure un-certainties. The deexcitation processes are then performedwithin a Monte-Carlo Hauser-Feschbach framework, basedon Bečvář’s algorithm [10], and extended to the n/ γ emis-sion by Régnier [11].Figure 1: Sketch of a γ -cascade simulated in Fifrelin . After a thermal neutron capture (E n =25 meV), the Gd* and
Gd* nuclei have an excitation energy ap-proximately equal to the compound nucleus neutron sep-aration energy S n (E n ≪ S n ), equal to 8.536 MeV and7.937 MeV, respectively. Knowing the Gd,
Gd groundstate spin-parity J π =3/2 − , the selection rules give to theexcited nuclei a parity -1 and two allowed spins of 1 ~ and2 ~ . Following the latest nuclear data evaluations [12–14] a2 ~ spin is assigned to both nuclei, corresponding to theirfirst resonance spin. In Fifrelin , a realization of the nu-clear level scheme (fig. 1) uses all the experimental knowl-edge and the missing information comes from nuclear mod-els: – for E ≤ E RIPL , all the energy levels are known and areretrieved from the Reference Input Parameter Library(RIPL-3) database [15]. If a spin and/or a parity aremissing, the code samples them from the momentumand parity theoretical distributions detailed below. – for E RIPL < E ≤ E limit , only a few levels are experimen-tally determined. Additional discrete levels are thensampled until the level number matches the theoreti-cal level density. This is done until E limit , defined bya nuclear level density set to 5 · MeV − (defaultvalue). – for E > E limit , the number of levels is innumerableand corresponds to the continuum. Therefore, levelsare gathered in energy bins (dE=10 keV by default)having a specific J π given by a model.The values of E RIPL , E limit and E M for the relevant Gdisotopes are given in Table 1. The theoretical nuclear leveldensity ρ ( E,J, π ) used to complete the level scheme is ρ ( E,J, π ) = ρ tot ( E ) P(J|E) P( π ) (1)with ρ tot ( E ) the total nuclear level density, P(J|E) the en-ergy dependent angular momentum distribution and P( π )the parity distribution. The positive and negative paritiesare assumed to be equiprobable, P( π = ± = σ ( E ) exp (cid:18) − ( J+1/2 ) σ ( E ) (cid:19) (2)with σ (E) the spin cut-off parameter defining the dis-persion of the nucleus angular momentum. More informa-tion on its origin and its parametrization can be foundin [15,16]. The total nuclear level density follows the Com-posite Gilbert Cameron Model (CGCM) [17], using theConstant Temperature Model (CTM) at low energy andthe Fermi Gas Model (FGM) at high energy ρ CGCMtot ( E ) = (cid:26) ρ CTMtot ( E ) , for E ≤ E M ρ FGMtot ( E ) , for E > E M (3)with E M the energy where the CTM and FGM nuclearlevel densities match along with their derivatives. TheCGCM parametrizations used here can be found in [15]. . Almazán et al.: Improved STEREO simulation with a γ -ray spectrum of excited Gd isotopes using FIFRELIN 3 Table 1:
Threshold energies for
Gd and
Gd used in
FIFRELIN . E RIPL (MeV) E limit (MeV) E M (MeV) Gd 1.366 5.306 6.605
Gd 1.499 5.402 6.376
During a deexcitation step, all the transition probabil-ities Γ p ( i → f, α ) to go from a given initial state ( i ) toa final state ( f ) in emitting a particle p with given prop-erties ( α ) are computed. Then, one transition is sampledamong all of them. Generally, models only give access tothe average partial width Γ p ( I → F, α ) associated to atransition from an initial set of levels ( I ≡ [E, J π ] i ) to afinal set ( F ≡ [E, J π ] f ), having both a given J π : Γ p ( I → F, α ) = * X f ∈ F Γ p ( i → f, α ) + i ∈ I . (4)Finally, the partial width to go from I to F is Γ p ( I → F, α ) = Γ p ( ǫ p , α ) δ ( α, J πi , J πf ) y ( I → F ) ρ ( E f , J πf ) dE(5)where ǫ p is the transition energy, and with δ ( α, J πi , J πf ) accounting for spin and parity selection rules, y ( I → F ) the Porter-Thomas factor simulating the transition prob-ability fluctuation described by a χ distribution with[ ρ ( E i , J πi ) dE × ρ ( E f , J πf ) dE] degrees of freedom [18] and ρ ( E f , J πf ) dE the number of levels in F .At S n , neutron emission is unlikely. Conversion elec-trons are taken into account using BrIcc code [19]. Forgamma emission, the average partial width ( Γ γ ( ǫ γ , XL ) )depends on the emitted gamma energy ( ǫ γ ), its type X(electric or magnetic), its multipolarity L and the radia-tive strength function model ( f XL ): Γ γ ( ǫ γ , XL ) = ǫ γ f XL ( ǫ γ ) /ρ ( E i , J πi ) (6)The E1 transition is described by the Enhanced General-ized Lorentzian Model (EGLO) which is a Lorentzian func-tion where an asymptotic term is added to better repro-duce low energy experimental data [15, 20]. The other XLtransitions are best described by a Standard LorentzianModel (SLO) [21] defined by: f XL ( ǫ γ ) = f EGLOE1 ( B n ) R f
SLOXL ( ǫ γ ) f SLOXL ( B n ) (7)where B n is the neutron binding energy and R a nucleusmass dependent ratio. More details can be found in [15].The Stereo simulation is based on
Geant4 libraries[22] and includes the detailed geometry of the detector, thedescription of its response with special emphasis on lightemission and collection [1]. Neutron transportation is han-dled by the
NeutronHP libraries, in which microscopic in-teraction cross-sections are from the ENDF/B-VII.1 evalu-ation. Standard deexcitation processes in
Geant4 do notoffer a satisfactory treatment on an event-by-event basis regarding energy conservation. As a consequence, when aneutron is captured on a Gd isotope, standard
NeutronHP processes are bypassed and an user-defined process is usedin the
Stereo simulation. An empirical gamma-cascadetreatment was initially performed using an additional sup-port for the GLG4sim package [23], developed specificallyfor neutrino detection in LS. This implementation gavesatisfactory results in larger detectors for well containedenergy depositions. In the new
Stereo simulation, thedeexcitation cascades from
Fifrelin are directly used.In both cases, the deexcitation products are generatedisotropically. For natural Gd, the gamma multiplicity percascade is about 4, and differs only by a few percents be-tween GLG4sim and
Fifrelin . The major difference be-tween the codes can be seen in the energy distributionof single deexcitation products, presented in fig. 2. About15 % of the gammas generated in the
Fifrelin simula-tion have an energy higher than 3.5 MeV, while they onlyaccount for 7 % in the GLG4sim modeling. Recently, in-dependent measurements [6] have shown that these high-energy gammas are needed for an accurate descriptionof the cascade. This is of primary importance for the
Stereo detector since at such energies around 5 MeV, themean free path of a gamma in the LS is 40 cm, compara-ble to the characteristic size of a
Stereo cell. Conversionelectrons are present in about 70 % of the cascades with amost probable energy of 70 keV. Due to very low emissionprobability, electrons of more than 200 keV represent lessthan 1 % of the sample. energy [MeV] − − − − − −
10 1 no r m a li z ed c oun t s γ GLG4sim: γ FIFRELIN: - FIFRELIN: e
Figure 2:
Energy distribution of the cascade deexcitationproducts: the GLG4sim simulation provides only gammas(dashed blue), whereas both gammas (red) and conversionelectrons (gray) are generated in the
Fifrelin simulation.
In the
Stereo experiment, the neutron response –characterizing the delayed signal – is monitored using anamericium-beryllium (AmBe) source deployed regularly in5 of the 6 identical 91 cm high target cells at 5 differentvertical levels (10, 30, 45, 60 and 80 cm from the bottom).Neutrons are produced at a · s − rate through thereaction: α + Be → C + n. In about 60% of the cases [24],the neutron emission is accompanied by a 4.4 MeV gamma H. Almazán et al.: Improved STEREO simulation with a γ -ray spectrum of excited Gd isotopes using FIFRELIN from carbon deexcitation. A coincidence selection is thenapplied to isolate the neutrons from these gammas and toget a clean and pure neutron capture sample without back-ground: delayed signals are searched in a time window of µ s after a prompt 4.4 MeV gamma signal, and contribu-tions from random coincidences (accidental background)are statistically subtracted. The resulting delayed energyspectrum is presented in fig. 3, where both the 2.2 MeVpeak from H(n, γ ) and the ∼ γ ) arevisible, along with the simulations. The shape of the tailover all the energy range is greatly improved with the Fifrelin description, for central positions, as well as forborder positions, more sensitive to escaping gammas. Per-forming a Kolmogorov-Smirnov test on the tail from 3 to7 MeV, we find an agreement with a probability of 11%,providing no indication for a systematic effect in the de-scription at the central position, whereas the test showedclear incompatibility between data and the GLG4sim spec-trum at more than 5 standard deviations. As expected,the presence of higher energy gammas tends to correctthe balance between low and high energy events in thetail. The
Stereo energy scale being anchored to the lowenergy gamma of Mn [1], the mean positions of the re-constructed peaks are artificially higher than literaturevalues, due to quenching effects. These non-linearity ef-fects are calibrated and taken into account in the
Stereo simulation. In order to assess the improvement of this newsimulation without considerations on any residual linearsystematic effect on the energy scale, the reconstructedenergy of both simulations is scaled such that the meanposition of the H(n, γ ) peak from the simulation matchesthe data. In this way, the agreement for the Gd(n, γ ) peakis evaluated relatively to the H capture peak at 2.2 MeV,and an agreement for the Gd mean peak position at thesub-percent level is achieved with the Fifrelin simula-tion.The neutrino detection uncertainty in
Stereo is dom-inated by the systematic uncertainty on the delayed neu-tron detection efficiency. Beyond selection cuts related tothe event topology [2], the delayed event of an IBD candi-date is required in this article to be within a time windowof (0.5–70) µ s after the prompt signal. The largest inef-ficiency is coming from the (4.5 – 10) MeV energy cut onthe delayed event set in order to select only Gd events.The lower threshold is chosen to maximize the signal-to-background ratio and to minimize the systematic uncer-tainties, and it is clear from fig. 3 that a significant partof the Gd events – with large energy leakage – is not in-cluded. The correct description of the spectrum over thefull energy range is therefore essential.To quantify the impact of the event selection cuts, theneutron capture spectra are divided in two parts: a H win-dow (1.5 – 3) MeV and a Gd window (3 – 10) MeV. The ra-tio of events in the Gd window (N Gd ) and the total sum(N Gd +N H ) is defined as the Gd-fraction ( ε Gd ): ε Gd = N Gd N H + N Gd (8)The impact on the delayed selection cuts (time and energy)are evaluated by defining the IBD efficiency ε IBD , fraction Figure 3:
Reconstructed energy spectra from neutron cap-tures from an AmBe source in a central (upper plot) anda top position (lower plot). Data points are in black, andGLG4sim (
Fifrelin ) simulation is in blue (red). of events in the (N Gd ) passing the tighter delayed selectionused in the neutrino analysis: ε IBD = N (4 . − MeV and (0 . µ s <∆ T < µ s ) N Gd (9)The total delayed detection efficiency ε tot is then the prod-uct of these two terms: ε tot = ε Gd · ε IBD (10)The numbers in Table 2 illustrate that the
Stereo data favor the Gd spectrum from the
Fifrelin events ascompared to the GLG4sim simulation. Using GLG4sim,the ratio R= ε Datatot / ε MCtot quantifying the agreement betweendata and MC for the total efficiency was found to be 0.9537at the most central calibration point as shown in Table 2.In the new simulation, ε MCtot matches the data within 1%(R=0.9953). For ε Gd , small discrepancies remain, mainlyin the border positions. The data/MC ratio of ε Gd is verysensitive to the treatment of the neutron propagation. Inparticular the modeling of neutron scattering and ther-mal diffusion in the detector as well as the neutron de-tection cross-section could induce an additional mismatch. . Almazán et al.: Improved STEREO simulation with a γ -ray spectrum of excited Gd isotopes using FIFRELIN 5 The border regions are more sensitive to such inaccura-cies. Therefore, as an extreme case, the calibration dataat the top of cell 1 was investigated, for which the sourcewas located only 12 cm (8 cm) from the target wall (celltop). Overall very good data/MC agreement is achievedfor ε IBD due to the improvements related to the new sim-ulation input of
Fifrelin (see fig. 3).Table 2:
Ratios Data/MC of the partial ( ε Gd , ε IBD ) andtotal efficiencies for GLG4sim and
Fifrelin simulations,in the case of the deployment of the AmBe cell at a centralposition (second column) and at a border position (thirdcolumn). Only statistical uncertainties are quoted.
Cell 4 (central) Cell 1 (border)Central position Top position ε DataGd / ε MCGd
GLG4sim . ± . . ± . Fifrelin . ± . . ± . ε DataIBD / ε MCIBD
GLG4sim . ± . . ± . Fifrelin . ± . . ± . ε Datatot / ε MCtot
GLG4sim . ± . . ± . Fifrelin . ± . . ± . In summary, the correct description of the deexcita-tion process of the Gd nuclei after neutron capture is cru-cial for neutrino detection experiments using Gd in gen-eral. In particular, this is the case for small detectors sen-sitive to gamma escape such as
Stereo . Since nuclearlevel schemes are not completely experimentally known,nuclear models are needed. The
Stereo description ofthe Gd cascade was greatly improved using the
Fifre-lin nuclear code, making benefit of the most updated nu-clear databases and user feedback on nuclear evaluations.We make available ten millions of deexcitation cascadesfor each isotope [25], since other running and upcomingprojects might profit from these data as well.
This work is supported by the French National Research Agency(ANR) within the Project No. ANR-13-BS05-0007 and the pro-grams P2IO LabEx (ANR-10-LABX-0038) and ENIGMASSLabEx (ANR-11-LABX-0012). We acknowledge the support ofthe CEA, CNRS/IN2P3, the ILL and the Max-Planck-Gesellschaft.
References
1. N. Allemandou et al. , “The
Stereo
Experiment,”
JINST ,vol. 13, no. 07, p. P07009, 2018.2. H. Almazán et al. , “Sterile Neutrino Constraints from the
Stereo
Experiment with 66 Days of Reactor-On Data,”
Phys. Rev. Lett. , vol. 121, no. 16, p. 161801, 2018.3. C. Buck, B. Gramlich, M. Lindner, C. Roca, and S. Schopp-mann, “Production and Properties of the Liquid Scintilla-tors used in the
Stereo
Reactor Neutrino Experiment,”
JINST , vol. 14, no. 01, p. P01027, 2019.4. I. Alekseev et al. , “Search for sterile neutrinos at theDANSS experiment,”
Phys. Lett. B7 , vol. 87, pp. 56–63,2018. 5. D. Adey et al. , “Improved Measurement of the ReactorAntineutrino Flux at Daya Bay,” 2018arXiv:1808.10836.6. K. Hagiwara et al. , “Gamma Ray Spectrum from ThermalNeutron Capture on Gadolinium-157,”
PTEP , vol. 2019,no. 2, p. 023D01, 2019.7. O. Litaize et al., “Investigation of n+
U Fission Observ-ables,”
Nuclear Data Sheets , vol. 118, pp. 216–219, 2014.8. O. Litaize et al., “Fission modelling with FIFRELIN,”
Eur.Phys. J. A , vol. 51, no. 177, pp. 1–14, 2015.9. O. Litaize et al., “Influence of primary fragment excitationenergy and spin distributions on fission observables,”
EPJWeb of Conf. , vol. 169, p. 00012, 2018.10. F. Bečvář, “Simulation of γ cascades in complex nuclei withemphasis on assessment of uncertainties of cascade-relatedquantities,” Nucl. Instr. Meth. Phys. Res. A , vol. 417, no. 2-3, pp. 434–449, 1998.11. D. Regnier et al., “An improved numerical method to com-pute neutron/gamma deexcitation cascades starting froma high spin state,”
Comput. Phys. Commun. , vol. 201,pp. 19–28, 2016.12. D. Brown, M. Chadwick, R. Capote, et al. , “ENDF/B-VIII.0: The 8 th major release of the nuclear reactiondata library with CIELO-project cross sections, new stan-dards and thermal scattering data,” Nuclear Data Sheets ,vol. 148, pp. 1 – 142, 2018. Special Issue on Nuclear Reac-tion Data.13. K. K. Shibata et al., “"jendl-4.0: A new library for nuclearscience and engineering,” " J. Nucl. Sci. Technol. , vol. 48,no. 1, pp. 1–30, 2011.14. S. F. Mughabghab,
Atlas of Neutron Resonances: Reso-nance Parameters and Thermal Cross Sections Z=1-100.
Elsevier Science, 2006.15. R. Capote et al., “Reference input parameter library for cal-culation of nuclear reactions and nuclear data evaluations,”
Nuclear Data Sheets , vol. 110, pp. 3107–3214, 2009.16. H. A. Bethe, “An attempt to calculate the number of en-ergy levels of heavy nucleus,”
Phys. Rev. , vol. 50, no. 4,pp. 332–341, 1936.17. A. Gilbert and A. G. W. Cameron, “A composite nuclear-level density formula with shell corrections,”
CanadianJournal of Physics , vol. 43, pp. 1446–1496, 1965.18. E. Porter and C. R. G. Thomas, “Fluctuations of nuclearreaction widths,”
Phys. Rev. , vol. 104, p. 483, 1956.19. T. Kibédi et al., “Evaluation of theoretical conversion co-efficients using BrIcc,”
Nucl. Instr. Meth. Phys. Res. A ,vol. 589, pp. 202–228, 2008.20. J. Kopecky and M. Uhl, “Test of gamma-ray strength func-tions in nuclear reaction model calculations,”
Phys. Rev. C ,vol. 41, no. 5, pp. 1941–1955, 1990.21. D. M. Brink, “Individual particle and collective aspects ofthe nuclear photoeffect,”
Nucl. Phys. , vol. 4, pp. 215–220,1957.22. S. Agostinelli et al., “Geant4—a simulation toolkit,”
Nucl.Instr. Meth. Phys. Res. A , vol. 506, pp. 250–303, 2003.23. http://neutrino.phys.ksu.edu/~GLG4sim/Gd.html .24. J. Scherzinger et al. , “Tagging fast neutrons from an Am / Be source,”
Applied Radiation and Isotopes ,vol. 98, pp. 74 – 79, 2015.25. H. Almazán et al. , “Data from: Improved
Stereo simula-tion with a new gamma ray spectrum of excited gadoliniumisotopes using