20MeV以下n+~（56）Fe核反应kerma系数的模型计算
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摘要
Kerma系数对于确定核工程中材料、元件的辐照损伤,热工系统的传热、载热,中子辐射保护以及核医学中确定放射治疗的辐照剂量等方面,都起着关键的作用。铁作为一种重要的核材料,在核能开发和利用方面有着重要的应用,如洁净核能驱动系统(ADS)的设计,裂变、聚变、中子反应堆等装置的设计。铁元素主要由54Fe(丰度占5.845%)、56Fe(丰度占91.754%)、57Fe(丰度占2.119%)、58Fe(丰度占0.282%)4种同位素组成,所以精确地评价铁元素的中子kerma系数必须同时对其所有的同位素进行精确评价。然而,4种同位素的实验数据(包括中子kerma系数以及对中子kerma系数有着非常大影响的弹性截面、弹性角分布、非弹性截面、非弹性角分布、中子及带电粒子的双微分截面等)都非常缺乏,特别是在20MeV以下的入射能区。所以在这个能区范围内,对n + 56Fe核反应的kerma系数进行精确的模型计算具有非常重要的参考价值。
尽管铁的中子Kerma系数非常重要,但实验数据比较缺乏,而且测量的误差比较大,特别是在20MeV以下的入射能区。如P.M.DeLuca等人所说,在测量kerma系数时,实验方法中的计数器气体影响铁的能量分布,所以必须考虑其对铁的中子kerma系数测量结果的影响。在15MeV以上,铁的中子kerma系数的误差有随着入射能量的增大而增大的趋势,有时误差竟达到90.9%。所以,R.S.Caswll等人说过,在应用15MeV以上铁的中子kerma系数时要特别谨慎。20MeV以下kerma系数的评价通常是利用数据处理程序对现有数据库进行处理,这些程序都是利用现有数据库能给出详细的出射中子和光子的能谱这样的事实。但是这种方法得到的kerma系数的精确性很大程度上取决于所处理数据库的好坏。而且56Fe的中子kerma系数只有M.B.Chadwick等人在1999年评价过。在14.5MeV以下,他们的结果是利用NJOY程序对ENDF/B-VI数据库进行处理得到的,在14.5MeV到20MeV之间,他们的评价值是通过线性插值得到的。然而在20MeV以下,ENDF/B-VI没有完整的带电粒子的信息。
本文利用统一的Hanser-Feshbach和激子模型,分析了20MeV以下n + 56Fe核反应开放的反应道,在严格保证能量守恒的前提下,给出了各反应道各出射的带电粒子在实验室系中的能量表示。在此基础上利用改进的UNF程序(2009版),得到了与实验数据符合很好的中子弹性散射角分布、总截面、弹性散射截面、(n,p)和(n,α)反应道截面,由此确定中子、质子和α等带电粒子的光参。由这些光参计算得到了与实验数据符合很好的中子、质子和α粒子的出射双微分截面。由此利用新的、包含更多参数信息的kerma系数计算公式(Phys.Rev.C,2008(78),054610)很自然的得到了20MeV以下n + 56Fe核反应总的kerma系数。在14.5MeV以下本文的结果较好的符合了实验数据,也和M.B.Chadwick等人的结果很接近,虽然在14.5MeV以上,本文的结果低于实验数据及M.B.Chadwick等人的结果,但本文给出了较为详细的与实验符合的较好的中子、带电粒子的信息,且本文所用的kerma系数的计算公式包含了更加全面详细的信息。故本文得到的20MeV以下n + 56Fe核反应的kerma系数的评价值具有一定的合理性,可为核技术及核工程等提供一定的参考。
Kerma coe?cients are important in many ?elds, such as determining the radia-tion damage in nuclear engineering, and the thermal conduction, and determining thedose delivery in therapy beams. iron is the main nuclear structural material, the datais of great signi?cance to the development of nuclear energy and nuclear engineeringconstruction. Such as accelerator driven clean power system (ADS) designs, ?ssiondesigns, fusion designs, neutron reactor designs and so on. Elemental iron consists offour isotopes, 54Fe (5.845% abundant), 56Fe (91.754% abundant), 57Fe (2.119% abun-dant), 58Fe (0.282% abundant). So each isotopes must be evaluated in order to obtainthe accurate kerma coe?cients of iron. However, the experimental data of four iso-topes (consist of neutron kerma coe?cients and others that have signi?cant in?uenceon neutron kerma coe?cients, such as elastic cross sections, elastic-scattering angu-lar distributions, inelastic cross sections, inelastic- scattering angular distributions,neutron double-di?erential cross sections and charged-particle double-di?erential crosssections) are very scarce, especially the incident neutron energy below 20 MeV. So atthis energy rang, it is signi?cantly referential value to accurately calculate the neutronkerma coe?cients using theory model for n + 56Fe reaction.
Despite the neutron kerma coe?cients of Fe is very important, the experimentaldata are absent, and the uncertainties of experimental data are relative big, especiallythe incident neutron energy below 20 MeV. As mentioned by P. M. DeLuca et al, thegas contribution changes the energy deposition spectrum for Fe and must be taken intoaccount in determining the kerma coe?cients. There is a general tendency that theuncertainties increase with increasing neutron energy for Iron element above 15 MeVincident neutron energy. sometimes, the uncertainty is up to 90.9%. Therefore, caremust be taken when the data are applied above 15 MeV, as mentioned by R. S. Caswell.The evaluated kerma coe?cients below 20 MeV were usually derived from ENDF/B-VIformat libraries using the data processing codes. These codes take advantage of the facts that many evaluation libraries give explicit energy distributions for the emittedneutrons and photons. The limitation using data processing codes on the accuracyof neutron kerma calculation is determined by the availability and accuracy of theevaluation libraries. Furthermore, the kerma coe?cients of Iron element were onlyevaluated by M. B. Chadwick in 1999. These kerma coe?cients below 14.5 MeVwere obtained from existing ENDF/B-VI evaluated library using NJOY code, and thevalues in 14.5-20 MeV region were linearly interpolated, However Below 20 MeV, theENDF/B-VI information on charged-particle emission is incomplete.
In this work, the reaction channels of n + 56Fe reaction are analyzed, on the basisof the Uni?ed Hauser-Feshbach and Excition Model, the energy formulas of all kindsof emitted particles in diversi?ed channels are given, and the energy balance is heldstrictly simultaneously. On the basis of this, the elastic scattering angle distributionsand cross section, total cross section, cross sections of (n,α) and (n, p) are calculatedused UNF(2009) code, these results are agree well with the experimental datas. So theoptical potential parameters of neutron, proton and charged particle are obtained. Anduseing these optical potential parameters, the double-di?erential cross sections of n, pandαparticle for n + 56Fe reaction below 20MeV are calculated. The calculations areagree well with the experimental data, so the total kerma coe?cient of n + 56Fe below20MeV is obtained naturally using the new formula of kerma coe?cient, which consistsmore parameter information. Below 14.5 MeV, the result of this work is agree withthe experimental data and the result of M. B. Chadwick. Although above 14.5 MeV,the result of this work is lower than the result of M. B. Chadwick and the measureddata. But, the more detailed information of neutron, proton and charged particlesare given in this work, and these information are agree well with the experimentaldata. Furthermore the formula of kerma coe?cient used in this work contains moredetailed, comprehensive information. So the result of total kerma coe?cients for n +56Fe nuclear reaction is reasonable to some extent, and these parameters can providesome reference to nuclear technology and nuclear engineering.
尽管铁的中子Kerma系数非常重要,但实验数据比较缺乏,而且测量的误差比较大,特别是在20MeV以下的入射能区。如P.M.DeLuca等人所说,在测量kerma系数时,实验方法中的计数器气体影响铁的能量分布,所以必须考虑其对铁的中子kerma系数测量结果的影响。在15MeV以上,铁的中子kerma系数的误差有随着入射能量的增大而增大的趋势,有时误差竟达到90.9%。所以,R.S.Caswll等人说过,在应用15MeV以上铁的中子kerma系数时要特别谨慎。20MeV以下kerma系数的评价通常是利用数据处理程序对现有数据库进行处理,这些程序都是利用现有数据库能给出详细的出射中子和光子的能谱这样的事实。但是这种方法得到的kerma系数的精确性很大程度上取决于所处理数据库的好坏。而且56Fe的中子kerma系数只有M.B.Chadwick等人在1999年评价过。在14.5MeV以下,他们的结果是利用NJOY程序对ENDF/B-VI数据库进行处理得到的,在14.5MeV到20MeV之间,他们的评价值是通过线性插值得到的。然而在20MeV以下,ENDF/B-VI没有完整的带电粒子的信息。
本文利用统一的Hanser-Feshbach和激子模型,分析了20MeV以下n + 56Fe核反应开放的反应道,在严格保证能量守恒的前提下,给出了各反应道各出射的带电粒子在实验室系中的能量表示。在此基础上利用改进的UNF程序(2009版),得到了与实验数据符合很好的中子弹性散射角分布、总截面、弹性散射截面、(n,p)和(n,α)反应道截面,由此确定中子、质子和α等带电粒子的光参。由这些光参计算得到了与实验数据符合很好的中子、质子和α粒子的出射双微分截面。由此利用新的、包含更多参数信息的kerma系数计算公式(Phys.Rev.C,2008(78),054610)很自然的得到了20MeV以下n + 56Fe核反应总的kerma系数。在14.5MeV以下本文的结果较好的符合了实验数据,也和M.B.Chadwick等人的结果很接近,虽然在14.5MeV以上,本文的结果低于实验数据及M.B.Chadwick等人的结果,但本文给出了较为详细的与实验符合的较好的中子、带电粒子的信息,且本文所用的kerma系数的计算公式包含了更加全面详细的信息。故本文得到的20MeV以下n + 56Fe核反应的kerma系数的评价值具有一定的合理性,可为核技术及核工程等提供一定的参考。
Kerma coe?cients are important in many ?elds, such as determining the radia-tion damage in nuclear engineering, and the thermal conduction, and determining thedose delivery in therapy beams. iron is the main nuclear structural material, the datais of great signi?cance to the development of nuclear energy and nuclear engineeringconstruction. Such as accelerator driven clean power system (ADS) designs, ?ssiondesigns, fusion designs, neutron reactor designs and so on. Elemental iron consists offour isotopes, 54Fe (5.845% abundant), 56Fe (91.754% abundant), 57Fe (2.119% abun-dant), 58Fe (0.282% abundant). So each isotopes must be evaluated in order to obtainthe accurate kerma coe?cients of iron. However, the experimental data of four iso-topes (consist of neutron kerma coe?cients and others that have signi?cant in?uenceon neutron kerma coe?cients, such as elastic cross sections, elastic-scattering angu-lar distributions, inelastic cross sections, inelastic- scattering angular distributions,neutron double-di?erential cross sections and charged-particle double-di?erential crosssections) are very scarce, especially the incident neutron energy below 20 MeV. So atthis energy rang, it is signi?cantly referential value to accurately calculate the neutronkerma coe?cients using theory model for n + 56Fe reaction.
Despite the neutron kerma coe?cients of Fe is very important, the experimentaldata are absent, and the uncertainties of experimental data are relative big, especiallythe incident neutron energy below 20 MeV. As mentioned by P. M. DeLuca et al, thegas contribution changes the energy deposition spectrum for Fe and must be taken intoaccount in determining the kerma coe?cients. There is a general tendency that theuncertainties increase with increasing neutron energy for Iron element above 15 MeVincident neutron energy. sometimes, the uncertainty is up to 90.9%. Therefore, caremust be taken when the data are applied above 15 MeV, as mentioned by R. S. Caswell.The evaluated kerma coe?cients below 20 MeV were usually derived from ENDF/B-VIformat libraries using the data processing codes. These codes take advantage of the facts that many evaluation libraries give explicit energy distributions for the emittedneutrons and photons. The limitation using data processing codes on the accuracyof neutron kerma calculation is determined by the availability and accuracy of theevaluation libraries. Furthermore, the kerma coe?cients of Iron element were onlyevaluated by M. B. Chadwick in 1999. These kerma coe?cients below 14.5 MeVwere obtained from existing ENDF/B-VI evaluated library using NJOY code, and thevalues in 14.5-20 MeV region were linearly interpolated, However Below 20 MeV, theENDF/B-VI information on charged-particle emission is incomplete.
In this work, the reaction channels of n + 56Fe reaction are analyzed, on the basisof the Uni?ed Hauser-Feshbach and Excition Model, the energy formulas of all kindsof emitted particles in diversi?ed channels are given, and the energy balance is heldstrictly simultaneously. On the basis of this, the elastic scattering angle distributionsand cross section, total cross section, cross sections of (n,α) and (n, p) are calculatedused UNF(2009) code, these results are agree well with the experimental datas. So theoptical potential parameters of neutron, proton and charged particle are obtained. Anduseing these optical potential parameters, the double-di?erential cross sections of n, pandαparticle for n + 56Fe reaction below 20MeV are calculated. The calculations areagree well with the experimental data, so the total kerma coe?cient of n + 56Fe below20MeV is obtained naturally using the new formula of kerma coe?cient, which consistsmore parameter information. Below 14.5 MeV, the result of this work is agree withthe experimental data and the result of M. B. Chadwick. Although above 14.5 MeV,the result of this work is lower than the result of M. B. Chadwick and the measureddata. But, the more detailed information of neutron, proton and charged particlesare given in this work, and these information are agree well with the experimentaldata. Furthermore the formula of kerma coe?cient used in this work contains moredetailed, comprehensive information. So the result of total kerma coe?cients for n +56Fe nuclear reaction is reasonable to some extent, and these parameters can providesome reference to nuclear technology and nuclear engineering.
引文
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