中子输运本征值问题和γ射线探测效率的蒙特卡罗方法研究
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摘要
对于提供核能源或中子源的核裂变反应系统，需从理论上给出它的临界安全性和中子能谱，通常通过k本征值问题的计算来实现。由于蒙特卡罗方法(简称MC方法)被认为是处理粒子输运问题的精确计算方法，国外已发展出了计算k本征值问题的蒙特卡罗程序，例如KENO、MCNP等，但这些程序都不能计算除k本征值问题以外的其它诸如λ、α等本征值问题，而对于特定的核裂变系统，采用这些本征值比用k本征值问题更为重要，比如采用λ本征值问题可以得到比用k本征值问题更接近实际的中子能谱。为此，我们从对λ本征值问题计算模型的研究出发，在原有KENO程序的基础上，研制出了计算λ本征值问题的蒙特卡罗程序。
环境中放射性对健康的影响日益成为人们关心的问题。在放射性测量中，采用高纯锗γ谱仪可以方便地分析环境样品中放射性核素的种类和含量，但要准确地分析核素含量，需要准确知道各样品中的各种能量γ射线的探测效率，通常由一定密度和样品量的标准样品来得到这一效率。但由于待测环境样品的来源不同，其介质成份、密度和体积量可能相差很大，实验上又难以制作各种各样的标准样品，采用蒙特卡罗方法可以比较容易地解决这些问题，对此，我们采用蒙特卡罗方法，研究了高纯锗γ谱仪对不同环境样品的探测效率，解决了实验上制作各种标准样品的难题。
针对上述问题取得了如下创新结果：
1．在蒙特卡罗程序KENO-Ⅳ的基础上，建立了λ-k_(eff)迭代计算模型，从原理和方法上解决了λ本征值问题的计算。该模型把λ本征值问题的计算转化成带参数λ的一系列k本征值问题的计算，其参数λ值的调节通过上一次迭代计算的k_(eff)来实现。
2．研制出了计算入本征值问题的蒙特卡罗程序，并用该程序进行了入本征
值问题的计算。计算所得入本征值、入本征值能谱与理论预言吻合。为反应堆
等核裂变系统的核临界安全分析和中子核反应率的计算提供了有意义的结果。
3．利用蒙特卡罗程序MCmp－4B模拟计算了高纯锗Y谱仪对环境样品的探
测效率，并与标准样品的实验结果比较，检验了计算结果的正确性。
4．模拟计算了探测效率随环境样品成份、密度及样品体积的变化规律，得
出了具有实际意义的结果，解决了实验中制作各种标准样品的烦琐问题。
The nuclear fissile reaction system, which provides nuclear energy or neutrons, theoretically demands its criticality safety and neutron energy spectrum to be predicated. Generally, those are realized by calculating the k-eigenvalue problem. Because Monte Carlo Method, for short MC method, has been known as accurate numerical methods for calculating particle transport, a number of general Monte Carlo Code have been developed abroad, for example KENO and MCNP are MC code. But these code only can calculate the k eigenvalue problem, and not calculate such as the λ. and a eigenvalue problem. However, for some special nuclear fissile systems, those eigenvalue problem are more important comparing to the k eigenvalue problem, for instance, using λ -eignevalue problem may obtain more accurate neutron spectrum than using k-eigenvalue problem. Therefore, we have constructed the calculations model of λ -eignevalue problem, and on the basis of
KENO code, developed the MC code of λ -eigenvalue problem.
The unhealthful radioactivity in environment has increasingly been an interest problem. In the radioactivity measure of the environment samples, HPGe γ -spectrometer can expediently analyze the species and content of the radionuclide in the environment samples. Those demands the detection efficiency corresponding to the different energy y -ray in the various environment samples. We are used to gain the detection efficiency by making the standard samples, because of the different source of the environment samples, the component and density and volume of the samples can't entirely match those of the standard samples, so it is very difficult to make the standard samples, thereby, in order to conquered experiment difficulty, this article has calculated the detection efficiency of HPGe γ -spectrometer by existing Monte Carlo code.
Aim at the above problem, this article obtained following creative results:
1.Base on the KENO-IV code, λ-keff iteration model has been constructed in this thesis. By this model, the λ-eigenvalue problem can be treated as a series of k eigenvalue problems with a certain λ number which is adjusted by keff. The Monte Carlo code for calculating λ eigenvalue problem has been developed in this thesis. This code has been used to calculate the λ-eigenvalue problem and the calculation results of λ-eigenvalue, correspond spectra and correspond reaction rates are consistent with the predication of the theory, and gained the practical results.
2.Using the MCNP-4B code, this article has calculated the efficiency calibration curves of the HPGe -spectrometer ,compared with the results of experiment. The results have shown that the Monte Carlo simulation calculation has been a convenient and reliable method for the efficiency calibration of the HPGe γ, -spectrometer. We have calculated the variety rules of detection efficiency with the samples of various components and densities and sizes on different energy points, gained the factual results, and resolved the difficulty of the experiment.
环境中放射性对健康的影响日益成为人们关心的问题。在放射性测量中，采用高纯锗γ谱仪可以方便地分析环境样品中放射性核素的种类和含量，但要准确地分析核素含量，需要准确知道各样品中的各种能量γ射线的探测效率，通常由一定密度和样品量的标准样品来得到这一效率。但由于待测环境样品的来源不同，其介质成份、密度和体积量可能相差很大，实验上又难以制作各种各样的标准样品，采用蒙特卡罗方法可以比较容易地解决这些问题，对此，我们采用蒙特卡罗方法，研究了高纯锗γ谱仪对不同环境样品的探测效率，解决了实验上制作各种标准样品的难题。
针对上述问题取得了如下创新结果：
1．在蒙特卡罗程序KENO-Ⅳ的基础上，建立了λ-k_(eff)迭代计算模型，从原理和方法上解决了λ本征值问题的计算。该模型把λ本征值问题的计算转化成带参数λ的一系列k本征值问题的计算，其参数λ值的调节通过上一次迭代计算的k_(eff)来实现。
2．研制出了计算入本征值问题的蒙特卡罗程序，并用该程序进行了入本征
值问题的计算。计算所得入本征值、入本征值能谱与理论预言吻合。为反应堆
等核裂变系统的核临界安全分析和中子核反应率的计算提供了有意义的结果。
3．利用蒙特卡罗程序MCmp－4B模拟计算了高纯锗Y谱仪对环境样品的探
测效率，并与标准样品的实验结果比较，检验了计算结果的正确性。
4．模拟计算了探测效率随环境样品成份、密度及样品体积的变化规律，得
出了具有实际意义的结果，解决了实验中制作各种标准样品的烦琐问题。
The nuclear fissile reaction system, which provides nuclear energy or neutrons, theoretically demands its criticality safety and neutron energy spectrum to be predicated. Generally, those are realized by calculating the k-eigenvalue problem. Because Monte Carlo Method, for short MC method, has been known as accurate numerical methods for calculating particle transport, a number of general Monte Carlo Code have been developed abroad, for example KENO and MCNP are MC code. But these code only can calculate the k eigenvalue problem, and not calculate such as the λ. and a eigenvalue problem. However, for some special nuclear fissile systems, those eigenvalue problem are more important comparing to the k eigenvalue problem, for instance, using λ -eignevalue problem may obtain more accurate neutron spectrum than using k-eigenvalue problem. Therefore, we have constructed the calculations model of λ -eignevalue problem, and on the basis of
KENO code, developed the MC code of λ -eigenvalue problem.
The unhealthful radioactivity in environment has increasingly been an interest problem. In the radioactivity measure of the environment samples, HPGe γ -spectrometer can expediently analyze the species and content of the radionuclide in the environment samples. Those demands the detection efficiency corresponding to the different energy y -ray in the various environment samples. We are used to gain the detection efficiency by making the standard samples, because of the different source of the environment samples, the component and density and volume of the samples can't entirely match those of the standard samples, so it is very difficult to make the standard samples, thereby, in order to conquered experiment difficulty, this article has calculated the detection efficiency of HPGe γ -spectrometer by existing Monte Carlo code.
Aim at the above problem, this article obtained following creative results:
1.Base on the KENO-IV code, λ-keff iteration model has been constructed in this thesis. By this model, the λ-eigenvalue problem can be treated as a series of k eigenvalue problems with a certain λ number which is adjusted by keff. The Monte Carlo code for calculating λ eigenvalue problem has been developed in this thesis. This code has been used to calculate the λ-eigenvalue problem and the calculation results of λ-eigenvalue, correspond spectra and correspond reaction rates are consistent with the predication of the theory, and gained the practical results.
2.Using the MCNP-4B code, this article has calculated the efficiency calibration curves of the HPGe -spectrometer ,compared with the results of experiment. The results have shown that the Monte Carlo simulation calculation has been a convenient and reliable method for the efficiency calibration of the HPGe γ, -spectrometer. We have calculated the variety rules of detection efficiency with the samples of various components and densities and sizes on different energy points, gained the factual results, and resolved the difficulty of the experiment.
引文
[1] 杜书华等，输运问题非计算机模拟，湖南科技出版社，1988
[2] W.R.Martin and J.J.Duderstadt,Nucl.sci.Eng,62,371-390(1977)
[3] J.Pilkarauta and P.Snlvennoinen,Nucl,Sci.Eng.50,297-300)1973)
[4] J.J.Dorning,Nodal Transport Method After Five Years,The proc. Of an International topical Meeting Sponsored by the Math.and Comput. Division of the Am.Nucl.Soc. Knoxville,Tennessee,April 9-11 1985
[5] R.D.Lawrance and J.J.Dorning,New Coase-mesh Diffusion and Transport Theory Methods for the Efficient Numerical Calculation of Multi-Dimensional Reactor power Distfibutions,Proe.OECD NEA-CRP Specialists Meeting on Calculation of Three-Dimensional power Distributions in Operating Reactors,OECD,Paris P.383,(1979)
[6] 谢仲生，J.J.Dorning,三维中子输运方程节块数值解法，第二届反应堆数值计算专业组年会报告，1985．9
[7] Halton,J.H., A Retrospective and Prospective Survey of the Monte Carlo Method,SIAM Rev., 12,1,1970
[8] 谢仲生 等，核反应堆物理数值计算，原子能出版社，1996
[9] 许淑艳，蒙特卡罗方法在实验核物理中的应用，原子能出版社，1996．12
[10] D.G.Cacuci etc.,Eigenvalue Dependent Neutron Energy Spectra: Definitions,Ananlyses,and Applications,Nuc. Sci.Eng.,81,432-442(1982)
[11] Y.Ronen etc.,A Comparison of Some Eifenvalues in Reactor Theory, Nuc.Sci.Eng.,60,97(1976)
[12] 徐家云，中子输运理论的蒙特卡罗方法研究，2001
[13] 复旦大学，清华大学，北京大学合编，原子核物理实验方法，北京，原子能出版社，1997
[14] 庞巨丰编著，γ能谱数据分析，西安，陕西科学技术出版社，722～789，
[15] 《环境放射性监测方法》编写组，环境放射性监测方法，原子能出版社，1977，311～317，
[16] 向长兴，一组实用γ谱分析效率刻度曲线，核电子学与探测技术，1994．11，14(6)，363～366，
[17] Sharshar T, Elnomer T, et al,Efficient calibration of HPGe detectors for volume-source geometries, Applied Radiation and Isotopes, May 1997, 48(5),695～697,
[18] 徐家云 张一云，快中子核次临界的多群蒙特卡罗计算，四川大学学报，1999，36(6)，
[19] A.G.Frodesen et.al.,Probability and Statistics in Particle Physics,University forlaget, 1979
[20] D.H.Lehmer, Mathematical methods in largecal computing units, Proc.Sym.on largescale digital calcul, machinery, Harvard Univ. Press, 141(1951)
[21] 裴鹿成，张孝泽，蒙特卡罗方法及其在粒子输运中的应用，科学出版社(1980)
[22] B.Aavison,Neutron Transport Theory,Oxford University Press,1957
[23] 谢仲生，核反应堆物理分析，原子能出版社，1981
[24] G.I.贝尔，S.格拉斯登 第一章 原子能出版社
[25] R.V.梅弗雷布林等，反应堆分析(上、下)，科学出版社1976
[26] G.E.Whitesides,N.F.Cross,KENO-A mulyigroup Monte Carlo Criticality Program, CTC-5 1969
[27] F.Briesmeister, MCNP—A Generral Monte Carlo Code for Neutron and Photon Transport, Los Alamos National Laboratory, 1989
[28] G.Goertzel, M.H.Kalos,Monte Carlo Methods in Transport Problems,Progress in Nuclear Energy, Series 1,Physics & Mathematics, Vol.2(1958) 315
[29] W.A. Coleman, Mathematical Verification of a Certain Monte Carlo Sampling Technique and Applications of the Technique to Radiation Transport Problems,Nucl. Sci.Eng.,32(1968)76
[30] J.Spanier, E.M.Gelbard, Monte Carlo Principle and Neutron transport Problems(1V. A. Ambarzumian, Compt. rend Acad. Sci. URSS 38,299(1943)
[31] J.O.Mingle,The Invariant Imbedding Theory of Nuclear Transport,American Elsevier Publishing Company Inc. New York, London, Amsterdam(1973)
[32] R.Belman, Invariant Imbedding and Radiative Transfer in Spherical Shells, J.Comp.Physics 2,245(1967)
[33] T.Ohnishi,Finite-Element Solution Technique For Neutron Transport
[33] T.Ohnishi,Finite-Element Solution Technique For Neutron Transport Equations(Fn Approximation),Numerical Reactor Calculation,1972
[34] Lord Kelvin,Nineteenth century clouds over the dynamical theory of heat and light,Phil.Mag.(6)2,1-40,1905
[35] S.N.Cramer, Next Flight Estimation for the Fictitious Scattering Monte Carlo Method,Trans.ANS-18400 (1974)
[36] S.N.Cramer, Application of the Fictitious Scattering Model for Deep Penetration Monte Carlo Calculations,ORNL-TM-4880 (1978)
[37] R.R.Coveyou,et al., Adjoint and Importance in Monte Carlo Application, Nucl. Sci.Eng.,27(1967)219
[38] Yu.A.Shreider, et al., The Monte Carlo Method(The Method of Statistical trials),(1966)
[39] H.J.Amster, et al., Predication of Statistical in Monte Carlo Transport Calculations, Nucl.Sci.Eng., 60(1976)131
[40] I.Lux, Variance Versus Efficiency in Transport Monte carlo, Nucl.Sci.Eng., 73(1980)66
[41] 任光明等，NDP FORTRAN 486/386使用指南，电子工业出版社，1996
[42] 谭浩强等，FORTRAN 77结构化程序设计，清华大学出版社，1990
[2] W.R.Martin and J.J.Duderstadt,Nucl.sci.Eng,62,371-390(1977)
[3] J.Pilkarauta and P.Snlvennoinen,Nucl,Sci.Eng.50,297-300)1973)
[4] J.J.Dorning,Nodal Transport Method After Five Years,The proc. Of an International topical Meeting Sponsored by the Math.and Comput. Division of the Am.Nucl.Soc. Knoxville,Tennessee,April 9-11 1985
[5] R.D.Lawrance and J.J.Dorning,New Coase-mesh Diffusion and Transport Theory Methods for the Efficient Numerical Calculation of Multi-Dimensional Reactor power Distfibutions,Proe.OECD NEA-CRP Specialists Meeting on Calculation of Three-Dimensional power Distributions in Operating Reactors,OECD,Paris P.383,(1979)
[6] 谢仲生，J.J.Dorning,三维中子输运方程节块数值解法，第二届反应堆数值计算专业组年会报告，1985．9
[7] Halton,J.H., A Retrospective and Prospective Survey of the Monte Carlo Method,SIAM Rev., 12,1,1970
[8] 谢仲生 等，核反应堆物理数值计算，原子能出版社，1996
[9] 许淑艳，蒙特卡罗方法在实验核物理中的应用，原子能出版社，1996．12
[10] D.G.Cacuci etc.,Eigenvalue Dependent Neutron Energy Spectra: Definitions,Ananlyses,and Applications,Nuc. Sci.Eng.,81,432-442(1982)
[11] Y.Ronen etc.,A Comparison of Some Eifenvalues in Reactor Theory, Nuc.Sci.Eng.,60,97(1976)
[12] 徐家云，中子输运理论的蒙特卡罗方法研究，2001
[13] 复旦大学，清华大学，北京大学合编，原子核物理实验方法，北京，原子能出版社，1997
[14] 庞巨丰编著，γ能谱数据分析，西安，陕西科学技术出版社，722～789，
[15] 《环境放射性监测方法》编写组，环境放射性监测方法，原子能出版社，1977，311～317，
[16] 向长兴，一组实用γ谱分析效率刻度曲线，核电子学与探测技术，1994．11，14(6)，363～366，
[17] Sharshar T, Elnomer T, et al,Efficient calibration of HPGe detectors for volume-source geometries, Applied Radiation and Isotopes, May 1997, 48(5),695～697,
[18] 徐家云 张一云，快中子核次临界的多群蒙特卡罗计算，四川大学学报，1999，36(6)，
[19] A.G.Frodesen et.al.,Probability and Statistics in Particle Physics,University forlaget, 1979
[20] D.H.Lehmer, Mathematical methods in largecal computing units, Proc.Sym.on largescale digital calcul, machinery, Harvard Univ. Press, 141(1951)
[21] 裴鹿成，张孝泽，蒙特卡罗方法及其在粒子输运中的应用，科学出版社(1980)
[22] B.Aavison,Neutron Transport Theory,Oxford University Press,1957
[23] 谢仲生，核反应堆物理分析，原子能出版社，1981
[24] G.I.贝尔，S.格拉斯登 第一章 原子能出版社
[25] R.V.梅弗雷布林等，反应堆分析(上、下)，科学出版社1976
[26] G.E.Whitesides,N.F.Cross,KENO-A mulyigroup Monte Carlo Criticality Program, CTC-5 1969
[27] F.Briesmeister, MCNP—A Generral Monte Carlo Code for Neutron and Photon Transport, Los Alamos National Laboratory, 1989
[28] G.Goertzel, M.H.Kalos,Monte Carlo Methods in Transport Problems,Progress in Nuclear Energy, Series 1,Physics & Mathematics, Vol.2(1958) 315
[29] W.A. Coleman, Mathematical Verification of a Certain Monte Carlo Sampling Technique and Applications of the Technique to Radiation Transport Problems,Nucl. Sci.Eng.,32(1968)76
[30] J.Spanier, E.M.Gelbard, Monte Carlo Principle and Neutron transport Problems(1V. A. Ambarzumian, Compt. rend Acad. Sci. URSS 38,299(1943)
[31] J.O.Mingle,The Invariant Imbedding Theory of Nuclear Transport,American Elsevier Publishing Company Inc. New York, London, Amsterdam(1973)
[32] R.Belman, Invariant Imbedding and Radiative Transfer in Spherical Shells, J.Comp.Physics 2,245(1967)
[33] T.Ohnishi,Finite-Element Solution Technique For Neutron Transport
[33] T.Ohnishi,Finite-Element Solution Technique For Neutron Transport Equations(Fn Approximation),Numerical Reactor Calculation,1972
[34] Lord Kelvin,Nineteenth century clouds over the dynamical theory of heat and light,Phil.Mag.(6)2,1-40,1905
[35] S.N.Cramer, Next Flight Estimation for the Fictitious Scattering Monte Carlo Method,Trans.ANS-18400 (1974)
[36] S.N.Cramer, Application of the Fictitious Scattering Model for Deep Penetration Monte Carlo Calculations,ORNL-TM-4880 (1978)
[37] R.R.Coveyou,et al., Adjoint and Importance in Monte Carlo Application, Nucl. Sci.Eng.,27(1967)219
[38] Yu.A.Shreider, et al., The Monte Carlo Method(The Method of Statistical trials),(1966)
[39] H.J.Amster, et al., Predication of Statistical in Monte Carlo Transport Calculations, Nucl.Sci.Eng., 60(1976)131
[40] I.Lux, Variance Versus Efficiency in Transport Monte carlo, Nucl.Sci.Eng., 73(1980)66
[41] 任光明等，NDP FORTRAN 486/386使用指南，电子工业出版社，1996
[42] 谭浩强等，FORTRAN 77结构化程序设计，清华大学出版社，1990