同位旋相关的相对论微观光学势研究
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摘要
光学模型势(OMP)是研究核反应和结构性质的重要理论工具。本工作将相对论Dirac Brueckner-Hartree-Fock得到的核子有效相互作用G矩阵应用于散射问题，研究了同位旋相关的相对论微观光学势(RMOP)。核子的光学势等价于核子在核介质中的自能，论文中RMOP的实部用G=V+AG在DBHF方法下计算得到，虚部则采用二级G矩阵极化图的虚部。用定域密度近似结合等效介子交换方法得到有限核的光学势，计算了入射能量小于200MeV的质子入射弹性散射的物理可观测量，得到了与实验值相一致的结果。我们分析了RMOP的同位旋相关性，并将其推广用于研究不稳定核反应，预言了质子与一些远离β稳定线核散射的实验可观测量。
DBHF方法从符合核子-核子(NN)散射相移和氘核性质的自由的NN相互作用出发，考虑核物质中核子的多体短程关联，得到核子有效相互作用G矩阵，因而G矩阵包含了核子有效相互作用的同位旋依赖信息。我们采用Schiller和Muether最近提出的将G矩阵分解成裸相互作用尸和由关联效应引起的修正ΔG两部分的新方法，其中V采用单玻色子交换势(OBEP)，ΔG部分通过投影方法得到，用交换四种质量无穷大的赝介子来描述短程关联并给出参数化的耦合常数。这种方法可以给出对称和不对称核物质中核子自能的Dirac结构，消除了投影方法对结果带来的不确定因素，分析不对称核物质和有限核的性质能够得到合理的结果。
G矩阵包含了核子有效相互作用的同位旋信息，同位旋矢量介子对质子和中子的作用不同，在计算中我们区分核物质中的质子和中子，这样得到的RMOP是同位旋相关的。通过分析不同的介子交换过程我们可以发现，来自能量无关的DBHF的直接项的贡献在核子自能中占主要的部分，自能的动量相关来自交换项的贡献，而G矩阵中的短程关联项ΔG减小了自能的强度。论文重点讨论了不同密度和不对称系数(β值)对不对称核物质中质子和中子的光学势的影响，分析表明，质子和中子的光学势随β值的变化规律相反。在低能量范围处，质子的标量势和矢量势随着β的增大而减弱，而且由于核子自能随能量增大而减弱，对质子这种减弱的趋势随着β的增大变得缓
中国原子能科学研究院
博卜学位论文
慢，因此到一定的能量时，质子的标量势和矢量势强度会比它们在对称核物质中的强
度强。中子的情况正好相反，低能处中子的标量势和矢量势随着刀的增大而增强，能
量相关性也随着刀的增大而增强，因此当能量大于某一值时，它在不对称核物质中的
标量势和矢量势实部的强度会比它们在对称核物质中的强度弱。
论文着重讨论了有限核的同位旋相关RMOP。由于直接用G矩阵计算很低密度核
物质时会给出发散的结果，为了在有限核光学势的研究中利用其基本特征和所包含的
同位旋信息，我们引入了等效介子交换，就是要求用cT、必、占和p四种介子在对不
同的密度和不对称参数的核物质中RIJF计算得到的核子自能和核子平均结合能与在
同样条件下DBHF计算的结果一致，通过拟合的方法得到有效介子一核子的藕合常数，
并采用合理的外推方法得到低密度区核物质中的有效介子一核子藕合常数。这样的等效
介子交换得到的有效相互作用包含了DBHF的基本特征和同位旋相关性，能够用于有
限核研究。
我们用有效介子交换的方法结合定域密度近似计算了有限核的RMOP，并且讨论
了有限核ROMP的性质。分析表明光学势的实部的强度随着能量升高缓慢变弱，虚部
强度则随能量增加的很快。将得到的光学势代入核子的Dirac方程中，消去Dirac旋
量的小分量后，推导出Dirac旋量的大分量满足的Schroedinger等价方程，得到了
Schroedinger等价势。计算结果表明，有限核的schroedinger等价势的中心势实部在
低能时为吸引势，随能量升高，向排斥势过渡，在核的表面会形成明显的“酒瓶底”
形状，其虚部则为随能量升高而增强的吸引势。由于采用了相对论方法，结果中自然
的包含了自旋轨道藕合势片口.，我们得到的代。.的实部提供吸引的相互作用，虚部提
供排斥的相互作用，随着入射能量的升高，其实部作用减弱虚部加强。这些性质和唯
象光学势分析的结论是一致的。
采用这一RMOP我们计算了2口口几介v以下质子入射甲oca和“0争b核的弹性散射角
分布和自旋可观测量，计算值与实验数据符合的比较好，应该强调的是我们计算的
R.MOP是从DBHFG矩阵得到的，没有可调的自由参数，它能够对一个相对较宽的能
区(<2口口人了已均的核反应作出合理的描述。我们进一步讨论了有限核RMOP的同位旋相
关问题，并将其推广用于不稳定核的计算中。我们计算了质子与Ca同位素链的散射，
并比较和分析了区分和不区分中子和质子密度分布的弹性散射实验可观察量。结果表
同位旋相关的相对论微观光学势研究
作者:荣健/导师:马中玉研究员
明，远离刀稳定线核的中子皮或晕结构对计算结果会产生明显的影响。这说明对同位
旋明显不对称的不稳定核研究，ROMP的同位旋相关性是必须考虑的。
关键词:同位旋相关性，相对论微观光学势，Dirac Brueckne卜Hartree一Fock，相互作用
G矩阵，定域密度近似，弹性散射角分布，自旋可观测量，远离刀稳定线核
The Optical Model Potential (OMP) is one of the most powerful tools to investigate the nuclear reaction and the nuclear structure. In this work, the new decomposition of the Dirac Brueckner-Hartree-Fock (DBHF) G-matrix is adopted to investigate the isospin-dependent relativistic microscopic optical potential (RMOP). The optical potential of a nucleon in the nuclear medium is identified with the nucleon self-energy. The real part of the RMOP is evaluated in the DBHF approximation by adopting the decomposition of G = V + AG , and the imaginary part is contributed by the imaginary part of the second-order G-matrix exchange diagram. The optical potential for the finite nucleus is obtained by means of the local density approximation (LDA), where the space dependence of RMOP is directly connected with the density and asymmetric parameter (β) of theasymmetric nuclear matter. The differential cross sections and the analyzing powers in the p+40Ca and p+208Pb at Ep less than 200MeV are also calculated with the RMOP. The isospin dependence of the RMOP is analyzed. Applying this RMOP, we also studied the elastic scattering reaction of the unstable nuclei and come to some predictions on the proton-unstable nucleus scatterings.The DBHF method adopts the realistic nucleon-nucleon (NN) interaction, which is fitted to the NN scattering phase shifts and deuteron properties. The nucleon in-medium short-range correlation effect is taken into account in the DBHF by summing up all ladder diagrams. We adopted the new decomposition approach of the DBHF G-matrix, which was recently proposed by Schiller and Muether and calculate the Dirac structure of the nucleon self-energy. T he G -matrix i s s eparated i nto a b are N N i nteraction V and the s hort-range correction term G. The projection method is only applied to the correction term, which is fitted by four psaudo-mesons. The ambiguities in the usual projection method are removed and a satisfactory description for the asymmetric nuclear matter (ASNM) and finite nucleus is achieved in this scheme.
The D BHF G -matrix w ith i sovector m esons c ontains t he i nformation o f t he i sospin dependence of the effective interaction. The proton and neutron are distinguished in this work. Therefore, the RMOP obtained by the G-matrix is isospin dependent. It is found that the direct term is the dominant part in the nucleon self-energy, which is energy-independent. The exchange term produces an energy dependent quantum correlation to the nucleon self-energy, which contribution is smaller than that from direct term. The contribution of the correlation term AG to the nucleon self-energies characterized by pseudo-meson exchanges is also energy independent due to the zero-range interactions adopted in this approach, and it reduces the intensity of the nucleon self-energies. At a fixed nucleondensity > 0 corresponds to the neutron-rich nuclear matter. It is found that at low energies both scalar and vector potentials of the proton decrease as increases.Interestingly, their energy dependence in the ASNM gets weaker than that in the symmetric one. Therefore, at a certain energy the strengths of scalar and vector potentials of the proton become stronger than those in the symmetric nuclear matter (SNM), and vise versa for the neutron optical potential. The absolute values of scalar and vector potentials of the neutron in the ASNM at low energies are larger than those in the SNM, and their energy dependencebecomes stronger as increases.The DBHF calculation can not be directly extended to very low density region because the phase transition may occur. Therefore, the method of effective meson exchanges is introduced to study the RMOP of finite nuclei. We impose the condition that the nucleon self-energy and the binding energy per nucleon at each density and each asymmetricparameter o btained in the DBHF is reproduced by fourk inds of meson ( and )exchanges in the RHF calculation. Then the coupling constants of those mesons can be determined by the fitting method. With the suitable approach, the coupling cons
DBHF方法从符合核子-核子(NN)散射相移和氘核性质的自由的NN相互作用出发，考虑核物质中核子的多体短程关联，得到核子有效相互作用G矩阵，因而G矩阵包含了核子有效相互作用的同位旋依赖信息。我们采用Schiller和Muether最近提出的将G矩阵分解成裸相互作用尸和由关联效应引起的修正ΔG两部分的新方法，其中V采用单玻色子交换势(OBEP)，ΔG部分通过投影方法得到，用交换四种质量无穷大的赝介子来描述短程关联并给出参数化的耦合常数。这种方法可以给出对称和不对称核物质中核子自能的Dirac结构，消除了投影方法对结果带来的不确定因素，分析不对称核物质和有限核的性质能够得到合理的结果。
G矩阵包含了核子有效相互作用的同位旋信息，同位旋矢量介子对质子和中子的作用不同，在计算中我们区分核物质中的质子和中子，这样得到的RMOP是同位旋相关的。通过分析不同的介子交换过程我们可以发现，来自能量无关的DBHF的直接项的贡献在核子自能中占主要的部分，自能的动量相关来自交换项的贡献，而G矩阵中的短程关联项ΔG减小了自能的强度。论文重点讨论了不同密度和不对称系数(β值)对不对称核物质中质子和中子的光学势的影响，分析表明，质子和中子的光学势随β值的变化规律相反。在低能量范围处，质子的标量势和矢量势随着β的增大而减弱，而且由于核子自能随能量增大而减弱，对质子这种减弱的趋势随着β的增大变得缓
中国原子能科学研究院
博卜学位论文
慢，因此到一定的能量时，质子的标量势和矢量势强度会比它们在对称核物质中的强
度强。中子的情况正好相反，低能处中子的标量势和矢量势随着刀的增大而增强，能
量相关性也随着刀的增大而增强，因此当能量大于某一值时，它在不对称核物质中的
标量势和矢量势实部的强度会比它们在对称核物质中的强度弱。
论文着重讨论了有限核的同位旋相关RMOP。由于直接用G矩阵计算很低密度核
物质时会给出发散的结果，为了在有限核光学势的研究中利用其基本特征和所包含的
同位旋信息，我们引入了等效介子交换，就是要求用cT、必、占和p四种介子在对不
同的密度和不对称参数的核物质中RIJF计算得到的核子自能和核子平均结合能与在
同样条件下DBHF计算的结果一致，通过拟合的方法得到有效介子一核子的藕合常数，
并采用合理的外推方法得到低密度区核物质中的有效介子一核子藕合常数。这样的等效
介子交换得到的有效相互作用包含了DBHF的基本特征和同位旋相关性，能够用于有
限核研究。
我们用有效介子交换的方法结合定域密度近似计算了有限核的RMOP，并且讨论
了有限核ROMP的性质。分析表明光学势的实部的强度随着能量升高缓慢变弱，虚部
强度则随能量增加的很快。将得到的光学势代入核子的Dirac方程中，消去Dirac旋
量的小分量后，推导出Dirac旋量的大分量满足的Schroedinger等价方程，得到了
Schroedinger等价势。计算结果表明，有限核的schroedinger等价势的中心势实部在
低能时为吸引势，随能量升高，向排斥势过渡，在核的表面会形成明显的“酒瓶底”
形状，其虚部则为随能量升高而增强的吸引势。由于采用了相对论方法，结果中自然
的包含了自旋轨道藕合势片口.，我们得到的代。.的实部提供吸引的相互作用，虚部提
供排斥的相互作用，随着入射能量的升高，其实部作用减弱虚部加强。这些性质和唯
象光学势分析的结论是一致的。
采用这一RMOP我们计算了2口口几介v以下质子入射甲oca和“0争b核的弹性散射角
分布和自旋可观测量，计算值与实验数据符合的比较好，应该强调的是我们计算的
R.MOP是从DBHFG矩阵得到的，没有可调的自由参数，它能够对一个相对较宽的能
区(<2口口人了已均的核反应作出合理的描述。我们进一步讨论了有限核RMOP的同位旋相
关问题，并将其推广用于不稳定核的计算中。我们计算了质子与Ca同位素链的散射，
并比较和分析了区分和不区分中子和质子密度分布的弹性散射实验可观察量。结果表
同位旋相关的相对论微观光学势研究
作者:荣健/导师:马中玉研究员
明，远离刀稳定线核的中子皮或晕结构对计算结果会产生明显的影响。这说明对同位
旋明显不对称的不稳定核研究，ROMP的同位旋相关性是必须考虑的。
关键词:同位旋相关性，相对论微观光学势，Dirac Brueckne卜Hartree一Fock，相互作用
G矩阵，定域密度近似，弹性散射角分布，自旋可观测量，远离刀稳定线核
The Optical Model Potential (OMP) is one of the most powerful tools to investigate the nuclear reaction and the nuclear structure. In this work, the new decomposition of the Dirac Brueckner-Hartree-Fock (DBHF) G-matrix is adopted to investigate the isospin-dependent relativistic microscopic optical potential (RMOP). The optical potential of a nucleon in the nuclear medium is identified with the nucleon self-energy. The real part of the RMOP is evaluated in the DBHF approximation by adopting the decomposition of G = V + AG , and the imaginary part is contributed by the imaginary part of the second-order G-matrix exchange diagram. The optical potential for the finite nucleus is obtained by means of the local density approximation (LDA), where the space dependence of RMOP is directly connected with the density and asymmetric parameter (β) of theasymmetric nuclear matter. The differential cross sections and the analyzing powers in the p+40Ca and p+208Pb at Ep less than 200MeV are also calculated with the RMOP. The isospin dependence of the RMOP is analyzed. Applying this RMOP, we also studied the elastic scattering reaction of the unstable nuclei and come to some predictions on the proton-unstable nucleus scatterings.The DBHF method adopts the realistic nucleon-nucleon (NN) interaction, which is fitted to the NN scattering phase shifts and deuteron properties. The nucleon in-medium short-range correlation effect is taken into account in the DBHF by summing up all ladder diagrams. We adopted the new decomposition approach of the DBHF G-matrix, which was recently proposed by Schiller and Muether and calculate the Dirac structure of the nucleon self-energy. T he G -matrix i s s eparated i nto a b are N N i nteraction V and the s hort-range correction term G. The projection method is only applied to the correction term, which is fitted by four psaudo-mesons. The ambiguities in the usual projection method are removed and a satisfactory description for the asymmetric nuclear matter (ASNM) and finite nucleus is achieved in this scheme.
The D BHF G -matrix w ith i sovector m esons c ontains t he i nformation o f t he i sospin dependence of the effective interaction. The proton and neutron are distinguished in this work. Therefore, the RMOP obtained by the G-matrix is isospin dependent. It is found that the direct term is the dominant part in the nucleon self-energy, which is energy-independent. The exchange term produces an energy dependent quantum correlation to the nucleon self-energy, which contribution is smaller than that from direct term. The contribution of the correlation term AG to the nucleon self-energies characterized by pseudo-meson exchanges is also energy independent due to the zero-range interactions adopted in this approach, and it reduces the intensity of the nucleon self-energies. At a fixed nucleondensity > 0 corresponds to the neutron-rich nuclear matter. It is found that at low energies both scalar and vector potentials of the proton decrease as increases.Interestingly, their energy dependence in the ASNM gets weaker than that in the symmetric one. Therefore, at a certain energy the strengths of scalar and vector potentials of the proton become stronger than those in the symmetric nuclear matter (SNM), and vise versa for the neutron optical potential. The absolute values of scalar and vector potentials of the neutron in the ASNM at low energies are larger than those in the SNM, and their energy dependencebecomes stronger as increases.The DBHF calculation can not be directly extended to very low density region because the phase transition may occur. Therefore, the method of effective meson exchanges is introduced to study the RMOP of finite nuclei. We impose the condition that the nucleon self-energy and the binding energy per nucleon at each density and each asymmetricparameter o btained in the DBHF is reproduced by fourk inds of meson ( and )exchanges in the RHF calculation. Then the coupling constants of those mesons can be determined by the fitting method. With the suitable approach, the coupling cons
引文
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