Nuclear Science and Engineering ISSN: 0029-5639 (Print) 1943-748X (Online) Journal homepage: http://www.tandfonline.com/loi/unse20 Calculations and Evaluations of n + Reactions up to 200 MeV 113,115,nat. In Xinwu Su, Zhengjun Zhang & Yinlu Han To cite this article: Xinwu Su, Zhengjun Zhang & Yinlu Han (2015) Calculations and Evaluations of 113,115,nat. n+ In Reactions up to 200 MeV, Nuclear Science and Engineering, 181:3, 272-288, DOI: 10.13182/NSE15-1 To link to this article: http://dx.doi.org/10.13182/NSE15-1 Published online: 12 May 2017. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=unse20 Download by: [University of Florida] Date: 27 October 2017, At: 01:46 NUCLEAR SCIENCE AND ENGINEERING: 181, 272–288 (2015) Calculations and Evaluations of n þ 113,115,nat.In Reactions up to 200 MeV Xinwu Su Shanxi Datong University, School of Physics and Electronic Science, Datong 037009, China Downloaded by [University of Florida] at 01:46 27 October 2017 Zhengjun Zhang Northwest University, Department of Physics, Xi’an of Shaanxi 710069, China and Yinlu Han* China Institute of Atomic Energy, P.O. Box 275(41), Beijing 102413, China Received December 24, 2014 Accepted February 27, 2015 http://dx.doi.org/10.13182/NSE15-1 Abstract – All cross sections of neutron-induced reactions, angular distributions, energy spectra, and double-differential cross sections for n þ 113,115,nat.In reactions are consistently calculated and analyzed at incident neutron energies below 200 MeV by using nuclear theoretical models. The isomeric cross section is especially calculated. The theoretical results are further compared with the available experimental data and the evaluated results in ENDF/B-VII, JENDL-4, and TENDL-2012. for indium. Natural indium consists of two isotopes: 113In (4.29%) and 115In (95.71%). The evaluated data for n þ 113,115In reactions were provided over the incident neutron energy range from 10211 to 20 MeV in JENDL-4 and ENDF/B-VII. The cross sections, angular distributions, and double-differential spectra were calculated utilizing the nuclear reaction model in JENDL-4 (Ref. 5), while the cross sections, angular distributions, and energy distributions of secondary neutrons emitted were evaluated and calculated in the ENDF/B-VII database,6,7 which was largely adopted from an earlier JENDL-3.3 evaluation. The evaluated data are also given over the incident neutron energy range from 10211 to 200 MeV for n þ 113,115In reactions in TENDL2012. The cross sections, angular distributions, doubledifferential spectra, isomeric production, discrete and continuum photon production cross sections, residual production cross sections, and recoils8 are included. The double-differential cross sections were also obtained from I. INTRODUCTION Understanding nucleon-induced reactions is a crucial step for the further development of nuclear reaction theory. Complete information in this field is strongly needed for a large amount of applications, such as the accelerator-driven system,1–4 which is supposed to use intense high-energy protons that induce spallation reactions on heavy targets. Such applications require accurate neutron- and proton-induced nuclear reaction data of cross sections, the energy-angle correlated spectra of secondary light particles (neutrons, protons, deuterons, tritons, helium, and alpha particles), double-differential cross sections, gamma-ray production cross sections, and gamma-ray production energy spectra. Since indium plays an important role in the structure materials used in nuclear reactors, it is essential to develop high-quality nuclear data *E-mail: [email protected] 272 Downloaded by [University of Florida] at 01:46 27 October 2017 NEUTRON-INDIUM REACTIONS the energy spectra calculated using the Kalbach systematics.9 Because the experimental data of neutron-induced reactions are scarce and there are some discrepancies in these experimental data from different laboratories, selfconsistent calculation and analysis by nuclear theoretical models are very important and interesting. Moreover, better nuclear data libraries for n þ 113,115,nat.In reactions are also required of applications over the incident neutron energy up to 200 MeV. In the present work, all reaction cross sections, the angle-integrated spectra, and the double-differential cross sections of neutron, proton, deuteron, triton, helium, and alpha-particle emission for n þ 113,115,nat.In reactions are calculated in the incident neutron energy region of En # 200 MeV. The optical model, the unified HauserFeshbach and exciton model including the improved Iwamoto-Harada model, the distorted wave Born approximation, the intranuclear cascade model, and recent experimental data are used. The calculated results are analyzed and compared with the available experimental data and the evaluated results in JENDL-4, ENDF/B-VII, and TENDL-2012. Section II describes the theoretical models used in this work. Section III analyzes and compares the calculated results with the experimental data. Section IV gives simple conclusions. 273 where Vr(r) ¼ real part potential Ws(r), Wv(r) ¼ imaginary part potential of surface absorption and volume absorption, respectively Vso(r) ¼ spin-orbit potential Vc(r) ¼ coulomb potential. The energy dependencies of potential depths and optimum neutron optical potential parameters are expressed as follows: Real part of optical potential: V r ¼ V 0 þ V 1 E þ V 2 E 2 þ V 3 ðN 2 ZÞ=A , (2) Imaginary part of the surface absorption: W s ¼ max{0:0,W 0 þ W 1 E þ W 2 ðN 2 ZÞ=A} , (3) and Imaginary part of the volume absorption: W y ¼ max{0:0,U 0 þ U1 E þ U2 E 2 } , (4) where Z, N, A ¼ charge, neutron, and mass numbers of the target, respectively II. THEORETICAL MODELS AND PARAMETERS The optical model is used to describe measured neutron-induced total, nonelastic, elastic cross sections and elastic scattering angular distributions, as well as to calculate the transmission coefficient of the compound nucleus and the preequilibrium emission process. The optical model potentials considered here are WoodsSaxon10 form for the real part; Woods-Saxon and derivative Woods-Saxon form for the imaginary parts corresponding to the volume and surface absorptions, respectively; and the Thomas form for the spin-orbit part. The APMN theoretical model code11 is used to obtain a set of neutron optical model potential parameters. By this code the best neutron optical model potential parameters can be automatically searched to fit the experimental data of total, nonelastic, and elastic cross sections and elastic scattering angular distributions. In the procedure, the adjustment of optical potential parameters is performed to minimize a quantity called x2, which represents the deviation of the theoretically calculated results from the experimental values. The optical potential is expressed by VðrÞ ¼ V r ðrÞ þ i½W s ðrÞ þ W v ðrÞ þ V so ðrÞ þ V c ðrÞ , (1) NUCLEAR SCIENCE AND ENGINEERING VOL. 181 E ¼ incident neutron energy in the center of mass system. The spin-orbit couple potential is Uso. The radius of the real part, the surface absorption, the volume absorption, and the spin-orbit couple potential are rr, rs, rv, and rso. The diffuseness width of the real part, the surface absorption, the volume absorption, and the spin-orbit couple potential are ar, as, av, and aso, respectively. The units of the potentials Vr, Ws, Wv, and Uso are in megaelectron-volts; the lengths rr, rs, rv, rso, ar, as, av, and aso are in fermis; and the energy E is in mega-electron-volts. The experimental data of neutron total cross sections were obtained at different laboratories, and they are basically in agreement at incident energies below 300 MeV for natural indium. The total cross-section experimental data,12 which were obtained at the Los Alamos Neutron Science Center Weapons Neutron Research white neutron source facility and extend from 5 to 600 MeV, are used to guide theoretical calculation. There are some experimental data of elastic scattering cross sections and elastic scattering angular distributions for 113,115,nat.In at incident neutron energies below 15.0 MeV. There are no experimental data for nonelastic scattering cross sections of 113,115In. We use the experimental data of total cross sections,12 all elastic NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 274 SU et al. scattering cross sections and elastic scattering angular distributions, and the experimental data of the nonelastic cross section for nat.Sn to obtain a set of neutron optical model potential parameters of 115In in incident neutron energy from 0.1 to 300 MeV. The optical model potential parameter obtained is given in Table I. V3, W2, and Uso are taken from the Becchetti and Greenlees results.10 The direct inelastic scattering angular distributions to low-lying states are important in nuclear data theoretical calculations. The DWUCK4 code13 of the distorted wave Born approximation theory is used to precalculate the direct inelastic scattering cross sections and angular distributions of discrete levels for 113,115In. The discrete levels are taken from Nuclear Data Sheets; levels above the highest excited state are assumed to be overlapping, and the level density formula is used. The discrete levels are taken into account from the ground (4.5þ) to 40th (2.4820 3.5þ) excited state for 113In and the ground (4.5þ) to 40th (2.4797 3.5þ) excited state for 115In. The optical model potential parameters obtained are used in the DWUCK4 code. The optical potential parameters for protons are taken from Wu and Han’s results.14 The optical potential parameters for deuterons are taken from Han’s results.15 The 3He global optical model potential parameters16 are applied and also used as triton and alpha-particle optical potential parameters. The experimental data of total, nonelastic, elastic scattering cross sections, and elastic scattering angular distributions are taken from the EXFOR library. The unified Hauser-Feshbach and exciton model with parity and angular momentum conservation was TABLE I Neutron Optical Model Potential Parameters Parameter Value V0 (MeV) V1 V2 (MeV21) V3 (MeV) W0 (MeV) W1 W2 (MeV) U0 (MeV) U1 U2 (MeV21) VSO (MeV) aR (fm) aS (fm) aV (fm) aSO (fm) rR (fm) rS (fm) rV (fm) rSO (fm) 54.51207 2 0.27974 0.00016775 224.0 9.96613 2 0.085786 212.0 2 1.67187 0.18790 2 0.000388 6.2 0.76707 0.44672 0.62887 0.75 1.16869 1.32905 1.16828 1.01 developed.17 The light composite particles such as deuteron, triton, helium, and alpha emissions will take place at an excitation energy of several tens megaelectron-volts in nucleon-induced reactions. Iwamoto and Harada18 developed a composite particle model based on the statistical phase-space integration method within the framework of the exciton model. Zhang et al.,19 Zhang,20 and Shen21 improved the Iwamoto-Harada model to reduce the preformation probabilities. The unified Hauser-Feshbach and exciton model17 is used to describe the nuclear reaction equilibrium and preequilibrium decay processes at incident neutron energies below 20 MeV. The Hauser-Feshbach model with width fluctuation correction describes the emissions from the compound nucleus to the discrete levels and continuum states of the residual nuclei in an equilibrium process, while the preequilibrium process is described by the angular momentum and parity dependent exciton model. The emissions to the discrete level and continuum states in the multiparticle emissions for all opened channels are included. The secondary particle emissions are described by the multistep Hauser-Feshbach model at incident neutron energies below 20 MeV. The improved Iwamoto-Harada model18 – 21 is used to describe the composite particle (deuteron, triton, 3He, alpha) emission in the compound nucleus. The improved Iwamoto-Harada model is included in the exciton model for the light composite particle emissions. The recoil effects in multiparticle emissions from continuum state to discrete level as well as from continuum to continuum state are taken into account strictly, so the energy balance is held accurately in every reaction channel. The double-differential cross section can be calculated by a generalized master equation17,22 to get the angular momentum dependent lifetime with the Legendre expansion form. The formula forms of the doubledifferential cross section for the first and second particle emissions and the residual nucleus are similar, whereas the expressions are different and given in Refs. 17 and 23. The exact Pauli exclusion effect and the Fermi motion of a nucleon in the exciton state densities24 are taken into account. The partial wave coefficients of single nucleon emission are calculated by the linear momentum dependent exciton state density model.25 The intranuclear cascade model is used at incident neutron energies above 20 MeV. In order to simplify the calculations, the angular dependent formula form of the Kalbach phenomenological approach9 is used in present calculations of the double-differential cross sections for neutron, proton, deuteron, triton, helium, and alphaparticle emission at incident neutron energies above 20 MeV. The UNF code26 is used at incident neutron energies below 20 MeV, and the MEND code27 is used up to 200 MeV. The angular momentum and parity NUCLEAR SCIENCE AND ENGINEERING VOL. 181 NOV. 2015 NEUTRON-INDIUM REACTIONS 275 dependent exciton model is used in the UNF code; other models are the same as the MEND code. The level density parameters and pair correction parameters of the backshifted Fermi gas level density28 for low energy are used. The Ignatyuk nuclear level densities29 are also used, which include the washing-out of shell effects with increasing excitation energy, collective excitations, and single-particle excitations; depart from more traditional ones; and are matched continuously onto a low-lying experimental discrete level. The Ignatyuk model for describing the statistical level density properties of excited nuclei is particularly appropriate for the relatively high energies. Downloaded by [University of Florida] at 01:46 27 October 2017 III. THEORETICAL RESULTS AND ANALYSIS The total cross sections, nonelastic scattering cross sections, elastic scattering cross sections, and elastic scattering angular distributions for n þ 113,115,nat.In reactions are calculated and compared with the experimental data. The calculated results of total cross sections agree well with the experimental data12,30 – 32 for the n þ nat.In reaction. The calculated elastic scattering cross sections pass through the existing experimental data33 – 39 at incident energies below 10.0 MeV. Figures 1 and 2 give the comparisons of total and elastic scattering cross sections with the experimental data for only the n þ 115In reaction. Moreover, the results of the nonelastic scattering cross sections also fit with the existing experimental data of natural In at incident energies below 20.0 MeV. Our present results of total cross sections, the evaluated data from JENDL-4, and TENDL-2012 are in Fig. 1. Calculated neutron total cross section (solid line) compared with the experimental data (symbols) for n þ 115In reaction. NUCLEAR SCIENCE AND ENGINEERING VOL. 181 Fig. 2. Calculated neutron elastic scattering cross section (solid line) compared with the experimental data (symbols) for n þ 115In reaction. good agreement with the experimental data below incident neutron energy 200.0 MeV. The evaluated data from ENDF/B-VII are lower than the experimental data31,32 below incident neutron energy 1.5 MeV. The calculated results of elastic scattering cross sections are in good agreement with the experimental data for lower energies. The calculated results of nonelastic cross sections are inconsistent with ENDF/B-VII and TENDL-2012. The theoretical results of the elastic scattering angular distributions for the n þ 113,115,nat.In reactions are also in good agreement with the experimental data. The comparisons of the elastic scattering angular distributions for the n þ 115In reactions with the experimental data from different laboratories are, respectively, presented in Figs. 3 to 7. The calculated results of the elastic scattering angular distributions for the n þ 115In reactions are compared with the experimental data38 at incident neutron energies 3.0 to 8.05 MeV as shown in Fig. 3. They are also compared with the experimental data31 as shown in Figs. 4 to 6 at incident neutron energies 1.5 to 3.75 MeV. In addition, Fig. 7 shows the comparisons with the experimental data40 at incident neutron energies 4.5 to 9.99 MeV. The comparisons of the calculated results of the n þ 113In reaction with the experimental data are similar to those of the n þ 115In reaction. The present results of the elastic scattering angular distributions for the n þ 113,115,nat.In reactions are in good agreement with the evaluated results from JENDL-4 and TENDL-2012. The calculated results for the 113,115In(n,g) reaction cross sections are in good agreement with the experimental data. The calculated results of the inelastic scattering cross sections of the first and second excited states for the NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 276 SU et al. Fig. 3. Calculated neutron elastic scattering angular distribution (solid lines) compared with the experimental data (symbols) for n þ 115In reaction. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. Fig. 5. Calculated neutron elastic scattering angular distribution (solid lines) compared with the experimental data (symbols) for n þ 115In reaction. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. Fig. 4. Calculated neutron elastic scattering angular distribution (solid lines) compared with the experimental data (symbols) for n þ 115In reaction. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. n þ 115In reaction are compared with the experimental data.41 The calculated results are in agreement with the experimental data. Figure 8 gives the comparisons only for the second excited state. The experimental data42 – 45 of the inelastic scattering cross sections for the n þ 113,115,nat.In reactions are given. The comparisons of the calculated results with the experimental data are presented in Figs. 9 and 10. The calculated results agree with the experimental data. Furthermore, the comparisons of the 115In(n,n0 )115MIn (0.33624 1/2–) reaction cross sections with the experimental data46 – 67 are shown in Fig. 11. The calculated curves pass through some experimental data within error bars. The comparisons of the calculated results for the 113In(n,n0 )113MIn (0.391691 1/2 – ) reaction with the experimental data are similar to those of the 115In(n,n0 )115MIn (0.33624 1/2 – ) reaction. The calculated results for the 115In(n,p)115GCd and 115 In(n,p)115MCd (0.181000 11/2–) reactions are compared with the experimental data as shown in Figs. 12 and 13. The calculated results of the 115In(n,p)115GCd reaction NUCLEAR SCIENCE AND ENGINEERING VOL. 181 NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 NEUTRON-INDIUM REACTIONS 277 Fig. 6. Calculated neutron elastic scattering angular distribution (solid lines) compared with the experimental data (symbols) for n þ 115In reaction. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. Fig. 7. Calculated neutron elastic scattering angular distribution (solid lines) compared with the experimental data (symbols) for n þ 115In reaction. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. cross sections are in good agreement with some experimental data47,50,56,65,68,69 and are larger than the experimental data from Refs. 70 to 73. The calculated results of the 115In(n,p)115MCd (0.181000 11/2–) reaction cross sections pass through the experimental data56,70,71 but are only smaller than the experimental data from Ref. 68. In addition, the comparisons of the calculated results for the 115In(n,p)115Cd reaction with the experimental data are further given in Fig. 14. The calculated results are in good agreement with some experimental data,56,70,71 while are smaller than the experimental data from Refs. 68 and 74. The 113,115In(n,t) reaction cross sections are calculated and compared with the experimental data.75,76 The theoretical results are consistent with the existing experimental data. The comparisons of the calculated results for only the 115In(n,t) reaction with the experimental data76 are given in Fig. 15. The 113,115In(n,a) reaction cross sections are also compared with the available experimental data. The calculated results are in good agreement with the experimental data. Figure 16 Fig. 8. Calculated inelastic scattering cross section (solid line) of the second excited state compared with the experimental data (symbols) for n þ 115In reaction. NUCLEAR SCIENCE AND ENGINEERING VOL. 181 NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 278 SU et al. Fig. 9. Calculated 113In(n,n0 ) reaction cross section (solid line) compared with the experimental data (symbols). Fig. 11. Calculated 115In(n,n0 )115MIn reaction cross section (solid line) compared with experimental data (symbols). Fig. 10. Calculated 115In(n,n0 ) reaction cross section (solid line) compared with the experimental data (symbols). Fig. 12. Calculated 115In(n,p)115GCd reaction cross section (solid line) compared with the experimental data (symbols). presents the comparisons of only the 115In(n,a) reaction cross sections with the experimental data.47,50,56,68,70 – 73,77,78 The comparisons of the calculated results of the 113 In(n,2n)112GIn reaction cross section with the experimental data72,79 – 82 are given in Fig. 17. The calculated results are in agreement with the experimental data72,80 – 82 but are only larger than the experimental data from Ref. 79. The comparisons of the calculated results of the 113 In(n,2n)112MIn (0.156590 4þ) reaction cross section with the experimental data47,50,72,73,79 – 85 are given in Fig. 18. The calculated results pass through the experimental data within error bars.72,80,81,83 – 85 Furthermore, the comparisons of the calculated results of the 113 In(n,2n) reaction cross section with the experimental data50,79 – 82,86,87 are also given in Fig. 19. The calculated results are in agreement with the experimental data within error bars80 – 82,86,87 and are larger than the experimental data.50,79 Similarly, the cross sections for the 115In(n,2n)112GIn and 115In(n,2n)114MIn (0.190290 5þ) reactions are also calculated and compared with the existing experimental data. The cross sections of the 115In(n,2n)114GIn reaction have only the experimental data from Ref. 65. The calculated curves pass through the experimental data within error bars. The comparisons of the calculated results of the 115 In(n,2n)114MIn (0.190290 5þ) reaction cross section NUCLEAR SCIENCE AND ENGINEERING VOL. 181 NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 NEUTRON-INDIUM REACTIONS Fig. 13. Calculated 115In(n,p)115MCd reaction cross section (solid line) compared with the experimental data (symbols). Fig. 14. Calculated 115In(n,p)115Cd reaction cross section (solid line) compared with the experimental data (symbols). with the experimental data47,49,50,54,56,65,69,72,73,82,85,88 – 90 are given in Fig. 20. The calculated results are in agreement with the experimental data.54,56,65,69,72,73,82,85,90 The comparisons of the calculated results of the 115In(n,2n) reaction cross section with the experimental data65,91 are also given in Fig. 21. The calculated results are in agreement with the experimental data within error bars65 and are smaller than the experimental data.91 The experimental data92 of the 113In(n,3n) reaction cross sections were proposed. The calculated results are in reasonable agreement with the experimental data as shown in Fig. 22. NUCLEAR SCIENCE AND ENGINEERING VOL. 181 279 Fig. 15. Calculated 115In(n,t) reaction cross section (solid line) compared with experimental data (symbols). Fig. 16. Calculated 115In(n,a) reaction cross section (solid line) compared with the experimental data (symbols). There have been no experimental data for other reaction cross sections up to now; all reaction cross sections have been predicted by theoretical models. The present calculated results of all reaction cross sections for all channels are similar to the evaluated results in JENDL-4, ENDF/B-VII, and TENDL-2012 as concerns curve shapes but much better fit the experimental data for some channels. Based on the agreement of the calculated results with the experimental data for all reaction cross sections and angular distributions, the energy spectra as well as the double-differential cross sections for neutron, proton, deuteron, triton, helium, and alpha emission, the gammaray production cross sections and the gamma-ray NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 280 SU et al. Fig. 17. Calculated 113In(n,2n)112GIn reaction cross section (solid line) compared with the experimental data (symbols). Fig. 19. Calculated 113In(n,2n) reaction cross section (solid line) compared with the experimental data (symbols). Fig. 18. Calculated 113In(n,2n)112MIn reaction cross section (solid line) compared with the experimental data (symbols). Fig. 20. Calculated 115In(n,2n)114MIn reaction cross section (solid line) compared with the experimental data (symbols). production energy spectrum are calculated by the theoretical models. The experimental data42 of the neutron emission double-differential cross sections of the 113,115In(n,n0 ) reaction at incident neutron energy from 5.0 to 8.6 MeV and emission angle of 31.0 to 151.0 deg were given. The calculated results of the 113,115In(n,n0 ) reaction cross sections are compared with the experimental data. The calculated results of the neutron emission doubledifferential cross sections for the 113In(n,n0 ) reaction are in good agreement with the experimental data42 at incident neutron energies 7.49 and 8.53 MeV as shown in Figs. 23 and 24. The contributions of the elastic scattering cross section are included in the calculated results. Moreover, the experimental data45 of the neutron emission double-differential cross sections of the nat. In(n,n0 ) reaction at incident neutron energies 5.981 and 6.97 MeV and emission angle of 90.0 deg were given. The calculated results are in good agreement with the experimental data for the 113In(n,n0 ) reaction as shown in Fig. 25. The calculated results of the neutron emission doubledifferential cross sections for the 115In(n,n0 ) reaction are compared with the experimental data42 at incident neutron NUCLEAR SCIENCE AND ENGINEERING VOL. 181 NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 NEUTRON-INDIUM REACTIONS 281 Fig. 21. Calculated 115In(n,2n) reaction cross section (solid line) compared with the experimental data (symbols). Fig. 23. Calculated double-differential cross sections of neutron emission (solid lines) compared with the experimental data for 113In(n,n0 ) reaction at incident energy 7.49 MeV. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. Fig. 22. Calculated 113In(n,3n) reaction cross section (solid line) compared with the experimental data (symbols). energies 5.19, 6.47, 7.49, and 8.53 MeV. The contributions of the elastic scattering cross section are included in the calculated results. The calculated results are in good agreement with the experimental data at incident neutron energies 7.49 and 8.53 MeV. The calculated results are in good agreement with the experimental data from the contributions of the inelastic scattering cross sections of the continuum states of the residual nuclei and are lower than those of the experimental data from the contributions of the inelastic scattering cross sections of discrete levels at incident neutron energies 5.19 and 6.47 MeV. The comparisons of the calculated neutron emission doubledifferential cross sections with the experimental data at NUCLEAR SCIENCE AND ENGINEERING VOL. 181 Fig. 24. Calculated double-differential cross sections of neutron emission (solid lines) compared with the experimental data for 113In(n,n0 ) reaction at incident energy 8.53 MeV. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. incident neutron energies 6.47, 7.49, and 8.53 MeV are plotted in Figs. 26, 27, and 28. The calculated results of the neutron emission double-differential cross sections of the 115In(n,n0 ) reaction at incident neutron energies 5.981 NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 282 SU et al. Fig. 25. Calculated double-differential cross sections of neutron emission (solid lines) compared with the experimental data for 113In(n,n0 ) reaction at incident energies 5.981 and 6.97 MeV. The curve and data points at the top represent true values, while the other is offset a factor of 10. Fig. 26. Calculated double-differential cross sections of neutron emission (solid lines) compared with the experimental data for 115In(n,n0 ) reaction at incident energy 6.47 MeV. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. and 6.97 MeV and emission angle of 90.0 deg are also in good agreement with the experimental data of the nat. In(n,n0 ) reaction.45 The calculated results of the neutron emission doubledifferential cross sections of the 115In(n,xn) reaction at incident neutron energy 14.6 MeV are lower than those of the experimental data93 for all emission angles. The Fig. 27. Calculated double-differential cross sections of neutron emission (solid lines) compared with the experimental data for 115In(n,n0 ) reaction at incident energy 7.49 MeV. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. Fig. 28. Calculated double-differential cross sections of neutron emission (solid lines) compared with the experimental data for 115In(n,n0 ) reaction at incident energy 8.53 MeV. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. experimental data94 – 96 of the neutron emission doubledifferential cross sections of the nat.In(n,xn) reaction at incident neutron energies 14.0, 14.4, and 14.1 MeV were given. The calculated results of the neutron emission NUCLEAR SCIENCE AND ENGINEERING VOL. 181 NOV. 2015 Downloaded by [University of Florida] at 01:46 27 October 2017 NEUTRON-INDIUM REACTIONS double-differential cross sections of the 113,115In(n,xn) reactions at incident neutron energies 14.0 and 14.4 MeV are lower than those of the experimental data94,95 for all emission angles, but they are in good agreement with the experimental data96 at incident neutron energy 14.1 MeV. The comparisons of the calculated results with the experimental data for the n þ 115In reaction at incident neutron energy 14.1 MeV are only given in Fig. 29. The experimental data97 of the proton emission double-differential cross sections of the 115In(n,xp) reaction at incident neutron energy 14.8 MeV were given. The calculated results are in good agreement with the experimental data. The comparisons of the calculated results with the experimental data are shown in Fig. 30. The calculated results of the double-differential cross sections of proton emission are from the contributions of the (n,p) reaction above proton emission energy 6.0 MeV and the (n,np) reaction below proton emission energy 6.0 MeV. The experimental data98 of the alpha emission double-differential cross sections of the 115In(n,xa) reaction at incident neutron energy 14.4 MeV and emission angle of 0.0 deg were provided. The calculated results are in good agreement with the experimental data. 283 Fig. 30. Calculated double-differential cross sections of proton emission (solid lines) compared with the experimental data at incident energy 14.8 MeV for 115In(n,xp) reaction. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, and 1000. The comparisons of the calculated results with the experimental data are plotted in Fig. 31. The calculated results of the double-differential cross sections of alpha emission are from the contribution of the (n,a) reaction. Furthermore, the experimental data42 of the neutron emission spectra of the 113,115In(n,n0 ) reaction at incident neutron energy from 5.0 to 8.6 MeV were also given. The contributions of the elastic scattering cross section are included in the calculated results. The calculated results agree well with the experimental data at incident neutron Fig. 29. Calculated double-differential cross sections of neutron emission (solid lines) compared with the experimental data for 115In(n,xn) reaction at incident energy 14.1 MeV. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, etc. NUCLEAR SCIENCE AND ENGINEERING VOL. 181 Fig. 31. Calculated double-differential cross section of alpha emission (solid line) compared with the experimental data at incident energy 14.4 MeV for 115In(n,xa) reaction. NOV. 2015 284 SU et al. Downloaded by [University of Florida] at 01:46 27 October 2017 energies 7.49 and 8.53 MeV. Furthermore, the calculated results are in good agreement with the experimental data from the contributions of the inelastic scattering cross sections of the continuum states of the residual nuclei and are lower than those of the experimental data from the contributions of the inelastic scattering cross sections of discrete levels at incident neutron energies 5.19, 5.34, and 6.47 MeV. These results are shown in Figs. 32 and 33. Since the experimental data42 of the spectra and double- Fig. 32. Calculated spectra of neutron emission (solid lines) compared with the experimental data for 113In(n,n0 ) reaction. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, and 1000. Fig. 33. Calculated spectra of neutron emission (solid lines) compared with the experimental data for 115In(n,n0 ) reaction. The curve and data points at the top represent true values, while the others are offset by factors of 10, 100, and 1000. differential cross sections for the 113,115In(n,n0 ) reactions at incident neutron energies 5.19, 5.34, and 6.47 MeV are larger than those of the calculated results, the calculated results of the inelastic scattering cross sections are lower than the corresponding experimental data as shown in Figs. 11 and 12. The experimental data96,99 of the neutron emission spectra of the nat.In(n,xn) reaction at incident neutron energy 14.1 and 14.625 MeV were also provided. The calculated results of the 113,115In(n,xn) reactions are in good accord with the experimental data. The comparisons of the calculated results with the experimental data for the n þ 115In reaction are only given in Fig. 34. The experimental data100 of the neutron emission double-differential cross sections of the nat.In(n,xn) reaction at incident neutron energy 100.0 MeV were given. The calculated results of the neutron emission double-differential cross sections for the 113,115In(n,xn) reactions are compared with the experimental data. The calculated results are in good agreement with the experimental data below emission angle 70.0 deg. The comparisons of the calculated results with the experimental data for the 115In(n,xn) reaction are only given in Fig. 35. The calculated results at very low neutron emission energy (0 to 10 MeV) are mainly from the contributions of the equilibrium reaction, while for the other neutron emission energy region, the calculated results are from the contributions of the preequilibrium reaction. Some structures in the higher emission neutron energy are from the contributions of direct reaction of inelastic scattering cross sections of discrete levels. The calculated results of the double-differential cross sections of neutron emission also show that the contribution of Fig. 34. Calculated spectra of neutron emission (solid lines) compared with the experimental data for 115In(n,xn) reaction. The curve and data points at the top represent true values, while the others are labeled. NUCLEAR SCIENCE AND ENGINEERING VOL. 181 NOV. 2015 285 NEUTRON-INDIUM REACTIONS can be used in radiation transport calculations for simulations of accelerator-driven systems. ACKNOWLEDGMENTS This work is part of National Basic Research Program of China (973 Program) entitled Key Technology Research of Accelerator Driven Sub-critical System for Nuclear Waste Transmutation and is supported by China Ministry of Science and Technology under contract 2007CB209903. REFERENCES Downloaded by [University of Florida] at 01:46 27 October 2017 1. R. C. HAIGHT, M. B. CHADWICK, and D. J. VIEIRA, Los Alamos Sci. Mag., 30, 52 (2006). 2. A. J. KONING, J.-P. DELAROCHE, and O. BERSILLON, “Nuclear Data for Accelerator Driven Systems: Nuclear Models, Experiments and Data Libraries,” Nucl. Instrum. Methods Phys. Res. A, 414, 49 (1998); http://dx.doi.org/10.1016/S0168-9002 (98)00528-2. Fig. 35. Calculated double-differential cross sections of neutron emission (solid lines) compared with the experimental data at incident energy 100.0 MeV for 115In(n,xn) reaction. 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