预平衡裂变动力学研究及n+～（12）C反应的理论分析与中子核数据库的建立
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摘要
本论文主要包括两方面研究内容：一是应用裂变的扩散模型对n＋~(238)U和p＋~(208)pb的预平衡裂变过程进行研究；二是对n＋~(12)C反应的理论分析与中子评价核数据库的建立．
关于预平衡裂变，主要通过数值解Smoluchowski方程，对两个典型核反应n＋~(238)U和p＋~(208)pb的裂变过程进行了研究，并把结论推广到锕系核和重核的情况．对锕系核来说，在中低能的情况下，可以忽略预平衡裂变过程的影响；而对Pb等重核来说，即使在激发能比较高(GeV量级)的情况下，也可以忽略预平衡裂变的贡献．从而为利用平衡态理论计算裂变截面，在加速器洁净能源驱动次临界系统(ADS)等工程的靶物理模拟计算中忽略靶材料核的预平衡裂变提供了理论支持．在核温度较高的锕系核的裂变过程中，会出现裂变速率的Overshooting现象，该现象主要是由鞍点处的扩散流引起的．对于Pb等重核则不会出现类似的Overshooting现象．同时，还讨论了选择鞍点或断点作为裂变点在扩散模型中所引起的物理图像，并认为在扩散模型中选择鞍点作为裂变点是比较合理的．如裂变前及裂变过程中有轻粒子发射，则裂变速率的Overshooting现象将减弱甚至消失，这是因为发射的轻粒子总会带走母核的一些能量，子核的激发能或核温度将减少或降低，从而减弱了预平衡过程中裂变的几率．从定性的角度更加支持了在中低能情况下利用平衡态理论计算裂变截面及在高能情况下靶物理的模拟计算中忽略预平衡裂变过程的合理性．
当扩散项为常数、漂移项为一维谐振子势(包括谐振子势阱和谐振子位垒)的情况下，得到Smoluchowski方程的解析表达式．此解析解包含了目前已知其它势场形式的解析表达式，初始条件为δ(x—x_0)函数也只是此解析解的一种特例．其中重点讨论了谐振子势阱形式的解析解，分析了几率密度在不同的核温度及初始条件下随时间的变化特征，得到了定态解及稳定解的表示形式及其满足的条件．根据一维情况下的定态解及稳定解可知，在大粘滞性条件下的输运过程中，当扩散流受到谐振子势的束缚时，不管扩散流处于何种状态，最终会达到稳定．这个结论为扩散流稳定性条件的应用提供了一定的参考．同时，为研究大粘滞性的扩散过程(如天然气在煤颗粒中的扩散，乳胶质的悬浮等问题)的应用提供学术上的参考。
在轻核反应方面，角动量相关的跃迁矩阵元是该理论模型的一个关键问题．本文利用耦合表象与非耦合表象之间的转换技巧，详细地推导了跃迁几率角动量因子，得到的结果与文献给出的结果一致，且此推导方法简单，思路明了易懂．利用新轻核反应模型理论．重新对n＋~(12)C反应进行了研究，主要在四个方面进行了改进．第一，把入射能量提高到30MeV，以供核工程的需要；第二，在n＋~(12)C反应过程中，对靶核和各反应道剩余核能级纲图进行了更新；第三，在更新的能级纲图基础上，得到了一套新的中子及带电粒子的光学模型势参数；最后，重新对各个反应道进行了分析，并在此基础上，利用改进的LUNF程序，得到了出射总中子双微分截面，并很好地符合实验数据．通过对出射总中子双微分截面的理论分析可知，总谱(从出射能区的高能段起)的第一个峰值主要是弹性散射反应道的贡献，第二、第三个峰值主要分别是第一、第二激发态非弹散射反应道的贡献，而第四个峰值则主要是由第三激发态非弹散射反应道与(n，nα)反应道共同贡献的结果．由于~(12)C的第三激发态存在E3模式的γ退激和α粒子发射的竞争，而目前程序对E3模式的γ退激不能计算准确．为此，我们借鉴日本库JENDL-3．3中采用耦合道和统计模型计算的第三激发态非弹散射截面的结果，在配合中子角通量谱基准检验结果的基础上进行调整，得到了与中子角通量谱符合很好的基准检验结果，以确定第三激发态非弹散射截面值．在此基础上，建立了30MeV以下入射能区的中子评价核数据库，并截取20MeV以下能区的数据建立了更新版中子评价核数据库CENDL-3．1版．通过基准检验，可看到本文CENDL-3．1版的基准检验结果非常好地符合了中子角通量谱实验数据，且明显比ENDF／B-Ⅶ库的结果要好．特别是本文新建的两个核数据库都包含了伴随中子出射的全部带电粒子信息的双微分截面文档(file 6)，这在国际上同类核数据库(包括ENDF／B-Ⅶ库和JENDL-3．3库)是无法做到的．另外，由于目前理论计算的20MeV以上能区的非弹散射角分布不能很好地符合实验数据，且ENDF／B-Ⅶ库和JENDL-3．3库中也都没有给出这些数据，故本文利用最小二乘法拟合实验数据，给出了20MeV以上能区的第一激发态、第二激发态非弹散射角分布的Legendre系数，从而弥补了其它数据库中的不足．同时，在新轻核反应模型理论的基础上，为带电粒子Kerma(Kinetic Energy Released from Material)系数的研究提供了很好的理论基础．
This thesis is consists of two parts: first, the research of the pre-equilibrium fission processes for n＋~(238)U and p＋~(208)Pb reactions based on the diffusion model; second, the theoretical analysis and the establishment of nuclear databases for n＋~(12)C reaction based on light nuclear reaction model.
In pre-equilibrium fission fields, n＋~(238)U and p＋~(208)Pb reactions are studied by numerical solution of Smoluchowski equation, and their results can be extended to the fission reactions of those nuclei in actinium and sub-actinium family. It is suggested that the contributions of the pre-equilibrium fission can be ignored for the projectile with low or medium incoming energy to the target in actinium family, and even with high energy(GeV) to the target in sub-actinium family. The evidences are provided theoretically in this paper for overlooking the contributions of pre-equilibrium fission to calculating the fission cross sections used equilibrium statistics and to stimulating the nuclear material on target physics of the accelerator driven sub-critical system (ADS). In fission processes at higher nuclear temperature for fissile nuclei, the fission rates appear Overshooting phenomena, which are induced by the fission current at saddle. However, there is no Overshooting phenomenon for sub-actinium family nuclei. Simultaneously, the physical figures are obtained and analyzed by views saddle or scissor as the fission point in this paper. It is reasonable that the saddle is regarded as the fission point in the diffusion model. If the light particle emissions are considered in fission processes, Overshooting will weaken gradually, even vanish. The exited energy of compound nuclear decreases because of the light particles emission, so the contribution of pre-equilibrium fission decreases. It is proved more qualitatively that the contribution of the pre-equilibrium fission can be ignored in some fields at the suitable projectile energy mentioned above.
In this paper, the analytical solution of Smoluchowski equation, of which diffusive term is constant and drift term harmonic oscillator potential (including the well and the barrier potentials), is derived from a simple Gaussian distribution in a easy and wizard method. This analytical solution covers all analytical expressions published nowadays. The properties of probability density distributions and probability currents are analyzed with time evolution at the different nuclear temperatures or the different initial distributions. The stationary and the steady solution are derived from the analytical solution, and their bound conditions are given too. The stationary and the steady solutions offer some advices for the applied studies in some strong friction coefficient fields.
The angular momentum factors of all kinds of transition matrix elements, which are kernel of the light nuclear reaction model, are derived through the transformation from coupled and un-coupled representations each other. Based on the new light reaction model, four aspects of n＋~(12)C reaction are extended or modified. Firstly, the incident neutron energy extends up to 30 MeV. Secondly, more open reaction channels are considered, including (n, 2n), (n, t), (n, ~3He), (n, pα), (n, ~6Li) and (n, dα) channels, which are closed below 20 MeV. Thirdly, some updated level schemes are used, in stead of old and pseudo ones. Finally, we obtained a new set of neutron and charged particles optical potential parameters. On the basis of four improved aspects, LUNF code is modified to calculate the total outgoing neutron double-differential cross sections from the threshold energy to 30 MeV. The calculated results agree fairly well with the experimental measurements. The analysis of the total energy angular spectra shows that the elastic channel and the inelastic channels of the 1st and 2nd excited levels largely con tribute to the first three peaks, the third excited level of inelastic channel and (n, nα) channel commonly to the 4th peak of the total spectra at high outgoing energy region. Because theγde-excitation mechanism of the 3rd excited state belongs to E3 module, which is not described successfully in Systematics up to now and not calculated accurately in LUNF code in other way, the calculated total spectra are generally lower than the experimental data at the 4th peak region. Thus, the neutron angular flux spectra are low too at the same location. In order to improve this deficiency, the evaluation method is used to set up the neutron nuclear databases below 30 MeV and below 20 MeV (CENDL-3.1), whose 3rd excite level inelastic cross sections (MF=3, MT=53) are modified in virtue of the results of JENDL-3.3 calculated in coupled channel and statistic model. The validation of ~(12)C evaluation for the updated database CENDL-3.1 was performed with neutron angular flux experiment (FNS) in this paper. The results agree very well with the benchmark measurements, and have obvious improvement contrast to ENDF/B-Ⅶ. It is one of the great characteristics that the file-6, which is not included in ENDF/B-Ⅶ, JENDL-3.3 and so on, comprises the information of all charged particles in accompany with outgoing neutron. Simultaneously, using the method of least squares, a code is developed to stimulate the Legendre coefficients of the 1st and 2nd excited level inelastic angular distributions, which are absent in ENDF/B-Ⅶand JENDL-3.3 above 20 MeV for lacking suitable theory. Furthermore, the new light nuclear reaction model extended in this paper provides a good method, which can study the Kerma (Kinetic Energy Released from Material) coefficients of the charged particles.
关于预平衡裂变，主要通过数值解Smoluchowski方程，对两个典型核反应n＋~(238)U和p＋~(208)pb的裂变过程进行了研究，并把结论推广到锕系核和重核的情况．对锕系核来说，在中低能的情况下，可以忽略预平衡裂变过程的影响；而对Pb等重核来说，即使在激发能比较高(GeV量级)的情况下，也可以忽略预平衡裂变的贡献．从而为利用平衡态理论计算裂变截面，在加速器洁净能源驱动次临界系统(ADS)等工程的靶物理模拟计算中忽略靶材料核的预平衡裂变提供了理论支持．在核温度较高的锕系核的裂变过程中，会出现裂变速率的Overshooting现象，该现象主要是由鞍点处的扩散流引起的．对于Pb等重核则不会出现类似的Overshooting现象．同时，还讨论了选择鞍点或断点作为裂变点在扩散模型中所引起的物理图像，并认为在扩散模型中选择鞍点作为裂变点是比较合理的．如裂变前及裂变过程中有轻粒子发射，则裂变速率的Overshooting现象将减弱甚至消失，这是因为发射的轻粒子总会带走母核的一些能量，子核的激发能或核温度将减少或降低，从而减弱了预平衡过程中裂变的几率．从定性的角度更加支持了在中低能情况下利用平衡态理论计算裂变截面及在高能情况下靶物理的模拟计算中忽略预平衡裂变过程的合理性．
当扩散项为常数、漂移项为一维谐振子势(包括谐振子势阱和谐振子位垒)的情况下，得到Smoluchowski方程的解析表达式．此解析解包含了目前已知其它势场形式的解析表达式，初始条件为δ(x—x_0)函数也只是此解析解的一种特例．其中重点讨论了谐振子势阱形式的解析解，分析了几率密度在不同的核温度及初始条件下随时间的变化特征，得到了定态解及稳定解的表示形式及其满足的条件．根据一维情况下的定态解及稳定解可知，在大粘滞性条件下的输运过程中，当扩散流受到谐振子势的束缚时，不管扩散流处于何种状态，最终会达到稳定．这个结论为扩散流稳定性条件的应用提供了一定的参考．同时，为研究大粘滞性的扩散过程(如天然气在煤颗粒中的扩散，乳胶质的悬浮等问题)的应用提供学术上的参考。
在轻核反应方面，角动量相关的跃迁矩阵元是该理论模型的一个关键问题．本文利用耦合表象与非耦合表象之间的转换技巧，详细地推导了跃迁几率角动量因子，得到的结果与文献给出的结果一致，且此推导方法简单，思路明了易懂．利用新轻核反应模型理论．重新对n＋~(12)C反应进行了研究，主要在四个方面进行了改进．第一，把入射能量提高到30MeV，以供核工程的需要；第二，在n＋~(12)C反应过程中，对靶核和各反应道剩余核能级纲图进行了更新；第三，在更新的能级纲图基础上，得到了一套新的中子及带电粒子的光学模型势参数；最后，重新对各个反应道进行了分析，并在此基础上，利用改进的LUNF程序，得到了出射总中子双微分截面，并很好地符合实验数据．通过对出射总中子双微分截面的理论分析可知，总谱(从出射能区的高能段起)的第一个峰值主要是弹性散射反应道的贡献，第二、第三个峰值主要分别是第一、第二激发态非弹散射反应道的贡献，而第四个峰值则主要是由第三激发态非弹散射反应道与(n，nα)反应道共同贡献的结果．由于~(12)C的第三激发态存在E3模式的γ退激和α粒子发射的竞争，而目前程序对E3模式的γ退激不能计算准确．为此，我们借鉴日本库JENDL-3．3中采用耦合道和统计模型计算的第三激发态非弹散射截面的结果，在配合中子角通量谱基准检验结果的基础上进行调整，得到了与中子角通量谱符合很好的基准检验结果，以确定第三激发态非弹散射截面值．在此基础上，建立了30MeV以下入射能区的中子评价核数据库，并截取20MeV以下能区的数据建立了更新版中子评价核数据库CENDL-3．1版．通过基准检验，可看到本文CENDL-3．1版的基准检验结果非常好地符合了中子角通量谱实验数据，且明显比ENDF／B-Ⅶ库的结果要好．特别是本文新建的两个核数据库都包含了伴随中子出射的全部带电粒子信息的双微分截面文档(file 6)，这在国际上同类核数据库(包括ENDF／B-Ⅶ库和JENDL-3．3库)是无法做到的．另外，由于目前理论计算的20MeV以上能区的非弹散射角分布不能很好地符合实验数据，且ENDF／B-Ⅶ库和JENDL-3．3库中也都没有给出这些数据，故本文利用最小二乘法拟合实验数据，给出了20MeV以上能区的第一激发态、第二激发态非弹散射角分布的Legendre系数，从而弥补了其它数据库中的不足．同时，在新轻核反应模型理论的基础上，为带电粒子Kerma(Kinetic Energy Released from Material)系数的研究提供了很好的理论基础．
This thesis is consists of two parts: first, the research of the pre-equilibrium fission processes for n＋~(238)U and p＋~(208)Pb reactions based on the diffusion model; second, the theoretical analysis and the establishment of nuclear databases for n＋~(12)C reaction based on light nuclear reaction model.
In pre-equilibrium fission fields, n＋~(238)U and p＋~(208)Pb reactions are studied by numerical solution of Smoluchowski equation, and their results can be extended to the fission reactions of those nuclei in actinium and sub-actinium family. It is suggested that the contributions of the pre-equilibrium fission can be ignored for the projectile with low or medium incoming energy to the target in actinium family, and even with high energy(GeV) to the target in sub-actinium family. The evidences are provided theoretically in this paper for overlooking the contributions of pre-equilibrium fission to calculating the fission cross sections used equilibrium statistics and to stimulating the nuclear material on target physics of the accelerator driven sub-critical system (ADS). In fission processes at higher nuclear temperature for fissile nuclei, the fission rates appear Overshooting phenomena, which are induced by the fission current at saddle. However, there is no Overshooting phenomenon for sub-actinium family nuclei. Simultaneously, the physical figures are obtained and analyzed by views saddle or scissor as the fission point in this paper. It is reasonable that the saddle is regarded as the fission point in the diffusion model. If the light particle emissions are considered in fission processes, Overshooting will weaken gradually, even vanish. The exited energy of compound nuclear decreases because of the light particles emission, so the contribution of pre-equilibrium fission decreases. It is proved more qualitatively that the contribution of the pre-equilibrium fission can be ignored in some fields at the suitable projectile energy mentioned above.
In this paper, the analytical solution of Smoluchowski equation, of which diffusive term is constant and drift term harmonic oscillator potential (including the well and the barrier potentials), is derived from a simple Gaussian distribution in a easy and wizard method. This analytical solution covers all analytical expressions published nowadays. The properties of probability density distributions and probability currents are analyzed with time evolution at the different nuclear temperatures or the different initial distributions. The stationary and the steady solution are derived from the analytical solution, and their bound conditions are given too. The stationary and the steady solutions offer some advices for the applied studies in some strong friction coefficient fields.
The angular momentum factors of all kinds of transition matrix elements, which are kernel of the light nuclear reaction model, are derived through the transformation from coupled and un-coupled representations each other. Based on the new light reaction model, four aspects of n＋~(12)C reaction are extended or modified. Firstly, the incident neutron energy extends up to 30 MeV. Secondly, more open reaction channels are considered, including (n, 2n), (n, t), (n, ~3He), (n, pα), (n, ~6Li) and (n, dα) channels, which are closed below 20 MeV. Thirdly, some updated level schemes are used, in stead of old and pseudo ones. Finally, we obtained a new set of neutron and charged particles optical potential parameters. On the basis of four improved aspects, LUNF code is modified to calculate the total outgoing neutron double-differential cross sections from the threshold energy to 30 MeV. The calculated results agree fairly well with the experimental measurements. The analysis of the total energy angular spectra shows that the elastic channel and the inelastic channels of the 1st and 2nd excited levels largely con tribute to the first three peaks, the third excited level of inelastic channel and (n, nα) channel commonly to the 4th peak of the total spectra at high outgoing energy region. Because theγde-excitation mechanism of the 3rd excited state belongs to E3 module, which is not described successfully in Systematics up to now and not calculated accurately in LUNF code in other way, the calculated total spectra are generally lower than the experimental data at the 4th peak region. Thus, the neutron angular flux spectra are low too at the same location. In order to improve this deficiency, the evaluation method is used to set up the neutron nuclear databases below 30 MeV and below 20 MeV (CENDL-3.1), whose 3rd excite level inelastic cross sections (MF=3, MT=53) are modified in virtue of the results of JENDL-3.3 calculated in coupled channel and statistic model. The validation of ~(12)C evaluation for the updated database CENDL-3.1 was performed with neutron angular flux experiment (FNS) in this paper. The results agree very well with the benchmark measurements, and have obvious improvement contrast to ENDF/B-Ⅶ. It is one of the great characteristics that the file-6, which is not included in ENDF/B-Ⅶ, JENDL-3.3 and so on, comprises the information of all charged particles in accompany with outgoing neutron. Simultaneously, using the method of least squares, a code is developed to stimulate the Legendre coefficients of the 1st and 2nd excited level inelastic angular distributions, which are absent in ENDF/B-Ⅶand JENDL-3.3 above 20 MeV for lacking suitable theory. Furthermore, the new light nuclear reaction model extended in this paper provides a good method, which can study the Kerma (Kinetic Energy Released from Material) coefficients of the charged particles.
引文
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