Isospin Dependent Relativistic Microscopic Optical Potential

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...