New charge exchange model of GEANT4 for 9 Be(p,n) 9 B reaction
aa r X i v : . [ nu c l - e x ] O c t New charge exchange model of GEANT4for Be(p,n) B reaction
Jae Won Shin
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
Tae-Sun Park
Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea
Abstract
A new data-based charge exchange model of GEANT4 dedicated to the Be(p,n) B reaction is developed by taking the ENDF/B-VII.1 differentialcross-section data as input. Our model yields results that are in good agree-ment with the experimental neutron yield spectrum data obtained for protonbeams of energy (20 ∼
35) MeV. In particular, in contrast to all the con-sidered GEANT4 hadronic models, the peak structure resulting from thediscrete neutrons generated by the charge-exchange reaction is observed tobe accurately reproduced in our model.
Keywords:
GEANT4, Be(p,n) B, neutron yield, ENDF/B-VII.1
PACS:
1. Introduction
Neutron sources play essential roles in various industrial and scientificfields. In obtaining neutron beams with the desired energy spectrum, oneapproach that is commonly adopted is the use of neutron-emitting radioisotopes, such as
Cf and Be-coupled
Am. In this method, however, the
Email address: [email protected] (Tae-Sun Park)
Preprint submitted to Journal of Nucl. Instrum. Meth. B October 5, 2014 nergies of the neutrons are on the order of a few MeV and are determined bythe isotope. That is, the neutron spectra of
Cf and
Am-Be are smoothcurves with average energies of ∼ ∼ Be(p,n) B reaction is thus of great importance.For proton beams of energy (20 ∼
35) MeV impinged on a 0.1 cm thickberyllium target, we first performed a comparative study with GEANT4[1, 2] and PHITS [3], and observed that all the platforms substantially un-derestimate the neutron yields ( Y n ). This finding may not be too surprisingbecause the hadronic models of the platforms have been developed for wideuse, but none of the models is specialized for the Be(p,n) B reaction.In this work, we developed a charge exchange model of GEANT4 dedi-cated to the Be(p,n) B reaction, taking the ENDF/B-VII.1 differential cross-section data [6] as input. When combined with the G4BinaryCascade [7]model for continuum neutrons, the developed model is observed to accu-rately describe the experimental neutron yield spectra, see Figs. 8 and 10.In particular, the peak structure due to the discrete neutrons is well repro- There are also MCNPX [4] simulation results for 11 MeV protons impinged on a 0.2cm thick beryllium target [5]. The simulations show that although rather good agreementis achieved overall, the model overestimates the neutron yield near the end point (e.g.,E n ≃
2. Simulation tool
GEANT4 is a tool kit that allows for microscopic Monte Carlo simulationsof particles interacting with materials. The platform has been thoroughlytested and is widely used in many different scientific fields, such as medicalphysics [8, 9, 10], accelerator-based radiation studies [11, 12, 13], neutronshielding studies [14, 15, 16], and environment radiation detection [17, 18, 19].In this work, we simulated the neutrons produced by proton beams on a Be target by using GEANT4 v10.0. For the electromagnetic processes, weadopted “G4EmStandardPhysics option3”. For the hadronic inelastic pro-cesses, four different hadronic models were considered: “G4BertiniCascade”[20], “G4BinaryCascade” [7], “G4Precompound” [21] and “G4INCLCascade”[22], which will be hereafter referred to as “G4BERTI”, “G4BC”, “G4PRECOM”and “G4INCL”, respectively. The models are described in detail in thePhysics Reference Manual [23] and Refs. [24, 25].
3. Results
As mentioned in the Introduction, GEANT4 is not equipped with a spe-cialized routine for the Be(p,n) B reaction. To quantify the accuracy ofthe hadronic models of GEANT4, we simulated the neutron yields due to 35MeV protons directed toward a 0.1 cm thick Be target, whose experimentaldata are presented in Ref. [26] and in the EXFOR database [27]. Accordingto the experimental setup, the diameter of the proton beam was set to 0.4 cm(with a flat shape), and we placed a cylindrical scoring geometry measuring0.1 cm in thickness and 5.1 cm in diameter at a distance of 1.3 m from the3 .1 cm ( scorer )5.1 cm3 cm1.2 cm ( water )0.1 cm ( Be ) 130 cmprotonbeam
Figure 1: (Color online) Schematic diagram of the simulation geometry. target; see Fig. 1 for the simulation geometry. We also took into account theproton stopper of the experiment, i.e. , the 1.2 cm thick water layer placedbehind the target. We repeated our simulations for each of the four hadronicmodels mentioned above.Figure 2 shows the neutron energy spectra in the forward angle, θ lab = 0 ◦ ,where E p and E n represent for the energy of the incident protons and theoutgoing neutrons, respectively. The figure clearly shows that the consideredmodels do not reproduce the peak structure at E n ≃
32 MeV, where the peakis mainly due to discrete neutrons produced by the Be(p,n) B reaction.To confirm our findings, we simulated the total and angular differentialcross-sections of the Be(p,n) B reaction. The results are presented in Fig. 3,which indicate that enormous discrepancies exist among the models; indeed,4 Y i e l d ( / M e V / s r / C ) x E n ( MeV ) Be ( lab =0 o , E p = 35 MeV) Exp. G4BC G4BERTI G4INCL G4PRECOM Figure 2: (Color online) Energy spectra of neutrons at θ lab = 0 ◦ produced by 35 MeVprotons on a 0.1 cm Be target. The open squares represent the experimental data [26],the red squares G4BC, the green inverted triangles G4BERTI, the blue circles G4INCLand the orange triangles G4PRECOM. To gaina better microscopic understanding, we also plotted the double differentialcross-sections with respect to the neutron energy in the forward angle, asshown in Fig. 4. The figure clearly shows that the GEANT4 hadronic models(Fig. 4 (a)) fail to describe the sharp peak structure of the ENDF/B-VII.1data (Fig. 4 (b)).Indeed, without the peak structure, it is not possible to describe the neu-tron spectrum accurately. Therefore, we constructed a GEANT4 hadronicmodel dedicated to the Be(p,n) B reaction, a detailed description of whichis presented in the next section. Be(p,n) B charge exchange model
It should be noted that there is a GEANT4 hadronic model for chargeexchange reactions, G4ChargeExchange (“G4CE”). To demonstrate the ac-curacy of the model, we repeated the simulation under the same conditionsdescribed above. Noting that G4CE covers only the charge-exchange reac-tion but not other continuum neutrons, we studied three cases, G4CE, G4BCand G4BC+G4CE. For the G4BC+G4CE case, to avoid any possible doublecounting, we removed the neutrons produced by the Be(p,n) B reaction ofG4BC for the entire energy region by making use of the G4UserSteppingActionclass. The resulting neutron yields are plotted in Fig. 5, which shows thatadding G4CE on top of G4BC improves the accuracy remarkably. However,an error of approximately 20% in the height for the n peak remains, and then i (i ≥
1) peaks are still missing, where n and n i denote the neutrons withthe residual B in the ground and i-th excited states, respectively. In extracting the ENDF/B-VII.1 differential cross-section values, we combined theENDF MF=3 and MF=6 data using a software program that is currently under develop-ment [28, 29].
20 40 60 80 100050100150200250 (a) C r o ss s ec t i o n ( m b ) E p ( MeV ) ENDF/B-VII.1 G4BC G4BERTI G4INCL G4PRECOM -2 -1 (b) D i ff ere n t i a l cr o ss s ec t i o n ( m b / s r ) lab E p = 35 MeV ENDF/B-VII.1 G4BC G4BERTI G4INCL G4PRECOM Figure 3: (Color online) Total cross-sections with respect to the incident proton energy(a) and the differential cross-sections with respect to the angle θ lab at E p = 35 MeV (b)of the Be(p,n) B reaction. (a) D i ff ere n t i a l cr o ss s ec t i o n ( m b / M e V / s r ) E n ( MeV ) G4BC G4BERTI G4INCL G4PRECOM n n n n n n (b) D i ff ere n t i a l cr o ss s ec t i o n ( m b / M e V / s r ) E n ( MeV ) ENDF/B-VII.1
Figure 4: (Color online) Double differential cross-sections with respect to neutron energyat θ lab = 0 ◦ . (a) and (b) show the results obtained from the models of GEANT4 andENDF/B-VII.1, respectively. Y i e l d ( / M e V / s r / C ) x E n ( MeV ) E p = 35 MeV G4BC + G4CE Exp. G4CE G4BC Figure 5: (Color online) Energy spectra of neutron yields at θ lab = 0 ◦ for 35 MeV protonson a 0.1 cm Be target. The open squares, the blue triangles and the red squares representthe experimental data [26], the G4CE results and the G4BC results, respectively. Thedotted line represents the values of Y n calculated using G4BC + G4CE. Y i e l d ( / M e V / s r / C ) x E n ( MeV ) E p = 35 MeV Exp. G4CE DCE Figure 6: (Color online) Neutron energy spectra at θ lab = 0 ◦ produced by 35 MeV protons.The open squares represent the experimental data [26], the blue triangles with a dottedline represent the G4CE results, and the orange circles with a solid line represent theresults of our DCE model. Y i e l d ( / M e V / s r / C ) x E n ( MeV ) E p = 35 MeV Exp. n n n n DCE
Figure 7: (Color online) Neutron energy spectra at θ lab = 0 ◦ produced by 35 MeV protonson a Be target. The open squares represent the experimental data [26]. The greeninverted triangles, the red triangles, the cyan diamonds and the black squares denote thecalculated values of n , n , n and n +n +n , respectively, and the orange circles with asolid line represent the results of our DCE model. For an accurate description of discrete neutrons, we developed a data-based charge exchange (DCE) model. For the discrete neutrons from the Be(p,n) B reaction, the ENDF/B-VII.1 differential cross-section data [6] ofthe reaction were taken as input. The resulting Y n is plotted in Fig. 6, whichshows that the prediction of the DCE model is in good agreement with theexperimental data.The contribution of each n i to the yield is plotted in Fig. 7, which showsthat the contribution of n is quite substantial, without which the shoulder ofthe peak cannot be reproduced. In contrast, the contributions of n and n i ,with i ≥
3, are observed to be marginal. The figure also shows that the widthof each peak is approximately 3 MeV, which is mainly due to the energy loss11 (a) Y i e l d ( / M e V / s r / C ) x E n ( MeV ) E p = 20 MeV Exp. G4 G4* (this work) (b) Y i e l d ( / M e V / s r / C ) x E n ( MeV ) E p = 25 MeV Exp. G4 G4* (this work) (c) Y i e l d ( / M e V / s r / C ) x E n ( MeV ) E p = 30 MeV Exp. G4 G4* (this work) (d) Y i e l d ( / M e V / s r / C ) x E n ( MeV ) E p = 35 MeV Exp. G4 G4* (this work)
Figure 8: (Color online) Neutron energy spectra at θ lab = 0 ◦ produced by 20, 25, 30and 35 MeV incident proton beams on a Be target are plotted in (a), (b), (c) and (d),respectively. The open squares shown in black are the experimental data [26]. The greensquares with dotted lines and the red circles with solid lines denote the values of Y n calculated using G4 (G4BC + G4CE) and G4* (G4BC + DCE), respectively. of the incident protons. For 35 MeV protons, the calculated average energyloss of the incident protons in the 0.1 cm thick Be target is 2.58 ± able 1: The calculated-to-experimental ratio for the total neutron yields. E p (MeV) G4BC G4BC+G4CE this work20 0.67 ± ± ± ± ± ± ± ± ± ± ± ± Be target at θ lab = 0 ◦ are plotted in Fig. 8. A comparison of this figure with Fig. 2 revealsthat the agreement with the experimental data near the peak region – wherethe Be(p,n) B reaction plays a dominant role – is significantly improved.Below the peak region, the models show a tendency to underestimate theneutron yields, although their predictions are within the error of the data;see, for example, the E n = (15 ∼
24) MeV region for E p = 35 MeV plottedin Fig. 8 (d). This discrepancy may derive from the inaccuracy in treatingthe continuum neutrons emanating from other reaction channels, such as Be(p,pn) Be and Be(p,n α ) Li.The calculated-to-experimental (C/E) ratios for the total and peak neu-tron yields are tabulated in Table 1 and Table 2, respectively. Table 1 showsthat the error in the C/E ratio of G4BC for the total neutron yield is ap-proximately 30 %, which is not particularly different from the error yieldedby the G4CE model. However, when our DCE model is added, the error isreduced to approximately (0 ∼
16) %. The improvement for the peak neu-trons is observed to be more dramatic. That is, the results of G4BC – whichhardly covers the discrete neutrons that are responsible for the peaks – arecompletely unacceptable. By adding the G4CE model on top of the G4BCmodel, the error in the C/E ratio is reduced to (21 ∼
48) %. Moreover, byreplacing the G4CE model with our DCE model, the error is further reduced13 able 2: The calculated-to-experimental ratio for the peak neutron yield, where the peakregion of each E p is denoted in the 2nd column. E p (MeV) E n (MeV) G4BC G4BC+G4CE this work(peak region)20 11 ∼
19 0.38 ± ± ± ∼
24 0.20 ± ± ± ∼
29 0.14 ± ± ± ∼
34 0.10 ± ± ± ∼
16) %.The fraction of each peak contribution is plotted in Fig. 9, which showsthe relative importance of the peaks. At E p = 35 MeV, the fractions of n ,n , n and n are approximately 66%, 5.6%, 25% and 3%, respectively,and the G4BC contribution is observed to be negligibly small ( ∼ p = 20 MeV.We also performed PHITS simulations under the same conditions, explor-ing three hadronic models of PHITS, INCL [30, 31], Bertini [30] and QMD[30]. The results are plotted in Fig. 10. Below the peak region (e.g., E n .
4. Conclusion
We examined several hadronic models of GEANT4 for the neutrons pro-duced by proton beams impinging on a Be target and observed that noneof the models reproduces the peak structure of the neutron spectrum. Be-cause the peak structure is due to the discrete neutrons generated by the Be(p,n) B reaction, this finding suggests that the reaction is not properly14 F r a c t i o n ( % ) E p ( MeV ) n n n n G4BC
Figure 9: (Color online) Fraction of each contribution for the calculated peak neutronyield. implemented in the models considered.The charge exchange model of GEANT4, G4CE, was also studied; it wasobserved that the model reproduces the n peak, but its height is reduced toapproximately 80%, and n i peaks with i ≥ Be(p,n) B reaction by incorporating ENDF/B-VII.1 differential cross-section data of the reaction into G4CE. For proton beams of energy E p = (20 ∼
35) MeV, the resulting model predictions are in good agreement with theexperimental data. We also observed that noticeable discrepancies persistbelow the peak region. For an accurate reproduction of the neutron yieldsfor the entire energy region, it is extremely important to extend our workto take into account the ENDF data of all the p + Be channels, which iscurrently in progress. 15 Y i e l d ( / M e V / s r / C ) x E n ( MeV ) E p = 35 MeV Exp. G4* (This work) PHITS (INCL) PHITS (Bertini) PHITS (QMD) Figure 10: (Color online) Neutron energy spectra at θ lab = 0 ◦ for 35 MeV protons on a Be target. The open squares shown in black represent the experimental data [26], and thered solid line with circles represents the G4* (G4BC + DCE) results. The black dottedline with triangles, the cyan dashed line with inverted triangles and the green long-dashedline with squares represent the results obtained by the PHITS calculation using the INCL,Bertini and QMD models, respectively. cknowledgments This work was supported in part by the Basic Science Research Pro-gram through the Korea Research Foundation (NRF-2011-0025116, NRF-2012R1A1A2007826, NRF-2013R1A1A2063824).
References [1] S. Agostinelli, et al., GEANT4 − a simulation toolkit, Nucl. Instrum.Meth. A 506 (2003) 250–303. doi:10.1016/S0168-9002(03)01368-8 .[2] J. Allison, et al., Geant4 developments and applications, IEEE Trans.Nucl. Sci. 53 (2006) 270–278. doi:10.1109/TNS.2006.869826 .[3] T. Sato, K. Niita, N. Matsuda, S. Hashimoto, Y. Iwamoto, S. Noda,T. Ogawa, H. Iwase, H. Nakashima, T. Fukahori, K. Okumura, T. Kai,S. Chiba, T. Furuta, L. Sihver, Particle and Heavy Ion Transport CodeSystem PHITS, Version 2.52, J. Nucl. Sci. Technol. 50 (2013) 913–923. doi:10.1080/00223131.2013.814553 .[4] Monte Carlo Code MCNPX: Los Alamos National Laboratory, Availableonline at https://mcnp.lanl.gov/ .[5] S. Kamada, T. Itoga, Y. Unno, W. Takahashi, T. Oishi, M. Baba, Mea-surement of Energy-angular Neutron Distribution for Li, Be(p,xn) Re-action at EP = 70 MeV and 11 MeV, J. Korean Phys. Soc. 59 (2011)1676–1680. doi:10.3938/jkps.59.1676 .[6] ENDF/B-VII.1, Available online at .[7] G. Folger, V. N. Ivanchenko, J. P. Wellisch, The Binary Cascade, Eur.Phys. J. A 21 (2004) 407–417. doi:10.1140/epja/i2003-10219-7 .178] M. U. Bug, E. Gargioni, S. Guatelli, S. Incerti, H. Rabus, R. Schulte,A. B. Rosenfeld, Effect of a magnetic field on the track structure oflow-energy electrons: a Monte Carlo study, Eur. Phys. J. D 60 (2010)85–92. doi:10.1140/epjd/e2010-00145-1 .[9] J. W. Shin, S.-W. Hong, C.-I. Lee, T.-S. Suh, Application of a GEANT4Simulation to a Co Therapy Unit, J. Korean Phys. Soc. 59 (2011) 12–19. doi:10.3938/jkps.59.12 .[10] C. I. Lee, J. W. Shin, S.-C. Yoon, T. S. Suh, S.-W. Hong, K. J. Min,S. D. Lee, S. M. Chung, J.-Y. Jung, Percentage depth dose distributionsin inhomogeneous phantoms with lung and bone equivalent media forsmall fields of CyberKnife (2014). arXiv:1401.0692 .[11] J. K. Park, S. Kwon, S. W. Lee, J. T. Kim, J.-S. Chai, J. W. Shin,S.-W. Hong, Analysis of Single-event Upset for SRAM Devices by Us-ing the MC-50 Cyclotron, J. Korean Phys. Soc. 58 (2011) 1511–1517. doi:10.3938/jkps.58.1511 .[12] J. W. Shin, T.-S. Park, S. W. Hong, J. K. Park, J. T. Kim, J.-S.Chai, Estimates of SEU for Semiconductors Using MC50 Cyclotronand Geant4 Simulation, J. Korean Phys. Soc. 59 (2011) 2022–2025. doi:10.3938/jkps.59.2022 .[13] Y. Malyshkin, I. Pshenichnov, I. Mishustin, T. Hughes, O. Heid,W. Greiner, Neutron production and energy deposition in fissile spalla-tion targets studied with Geant4 toolkit, Nucl. Instrum. Meth. B 289(2012) 79–90. doi:10.1016/j.nimb.2012.07.023 .[14] S. Avery, C. Ainsley, R. Maughan, J. McDonough, Analytical shielding18alculations for a proton therapy facility, Radiat. Protect. Dosim. 131(2008) 167–179. doi:10.1093/rpd/ncn136 .[15] S. I. Bak, T.-S. Park, S.-W. Hong, J. W. Shin, I. S. Hahn, Geant4simulation of the shielding of neutrons from
Cf source, J. KoreanPhys. Soc. 59 (2011) 2071–2074. doi:10.3938/jkps.59.2071 .[16] J. W. Shin, S.-W. Hong, S.-I. Bak, D. Y. Kim, C. Y. Kim, GEANT4 andPHITS simulations of the shielding of neutrons from the
Cf source,J. Korean Phys. Soc. 65 (2014) 591–598. doi:10.3938/jkps.65.591 .[17] S. Hurtado, M. Garc´ıa-Le´on, R. Garc´ıa-Tenorio, GEANT4 code forsimulation of a germanium gamma-ray detector and its applicationto efficiency calibration, Nucl. Instrum. Meth. A 518 (2004) 764–774. doi:10.1016/j.nima.2003.09.057 .[18] K. Banerjee, et al., Variation of neutron detection characteristics withdimension of BC501A neutron detector, Nucl. Instrum. Meth. A 608(2009) 440–446. doi:10.1016/j.nima.2009.07.034 .[19] P. M. Joshirao, J. W. Shin, C. K. Vyas, A. D. Kulkarni, H. Kim, T. Kim,S.-W. Hong, V. K. Manchanda, Development of optical monitor of al-pha radiations based on CR-39, Appl. Radiat. Isot. 81 (2013) 184–189. doi:10.1016/j.apradiso.2013.06.012 .[20] A. Heikkinen, N. Stepanov, J. P. Wellisch, Bertini intra-nuclear cas-cade implementation in Geant4, Computing in High Energy and NuclearPhysics 2003 Conference Proceedings (2003). arXiv:nucl-th/0306008 .[21] K. K. Gudima, S. G. Mashnik, V. D. Toneev, Cascade-excitonmodel of nuclear reactions, Nucl. Phys. A 401 (1983) 329–361. doi:10.1016/0375-9474(83)90532-8 .1922] A. Boudard, J. Cugnon, J.-C. David, S. Leray, D. Mancusi, New poten-tialities of the Li`ege intranuclear cascade (INCL) model for reactions in-duced by nucleons and light charged particles (2012). arXiv:1210.3498 .[23] GEANT4 Physics Reference Manual, Available online at http://geant4.web.cern.ch/geant4/support/index.shtml .[24] J. Apostolakis, et al., Progress in hadronic physics modellingin Geant4, J. Phys.: Conf. Ser. 160 (2009) 012073, XIII Int.Conf. on Calorimetry in High Energy Physics (CALOR 2008). doi:10.1088/1742-6596/160/1/012073 .[25] J. Yarba, Recent Developments and Validation of Geant4 HadronicPhysics, J. Phys.: Conf. Ser. 396 (2012) 022060, Int. Conf. onComputing in High Energy and Nuclear Physics 2012 (CHEP2012). doi:10.1088/1742-6596/396/2/022060 .[26] Y. Uwamino, T. Ohkubo, A. Torii, T. Nakamura, Semi-monoenergeticneutron field for activation experiments up to 40 MeV, Nucl. Instrum.Meth. A 271 (1988) 546–552. doi:10.1016/0168-9002(88)90318-X .[27] EXFOR database, Available online at .[28] S. I. Bak, R. Brun, F. Carminati, J. S. Chai, A. Gheata, M. Gheata,S.-W. Hong, Y. Kadi, V. Manchanda, T.-S. Park, C. Tenreiro, A NewFormat for Handling Nuclear Data, J. Korean Phys. Soc. 59 (2011) 1111–1114. doi:10.3938/jkps.59.1111 .[29] T.-S. Park, “TNudy project”, unpublished.2030] K. Niita, N. Matsuda, Y. Iwamoto, H. Iwase, T. Sato,H. Nakashima, Y. Sakamoto, L. Sihver, PHITS: Parti-cle and Heavy Ion Transport code System, Version 2.23,JAEA-Data / Code 2010-022 (2010), Available online at http://jolissrch-inter.tokai-sc.jaea.go.jp/pdfdata/JAEA-Data-Code-2010-022.pdf (2010).[31] J. Cugnon, D. Mancusi, A. Boudard, S. Leray, New Features of theINCL4 Model for Spallation Reactions, J. Korean Phys. Soc. 59 (2011)955–958. doi:10.3938/jkps.59.955doi:10.3938/jkps.59.955