Microscopic Derivation of the Nucleus-Nucleus Potential by the Use of the Density-Dependent Effective Interaction

Abstract

A method to construct the microscopic nucleu!?·nucleus potential by the use of the density· dependent effective nucleon·nucleon interaction is presented based on the resonating group method in a semiclassical manner. The method is applied to the two:alpha system, where it is shown that the potential is obtained to be very attractive due to the antisymmetrization effect between the two alpha nuclei though the direct potential is even repulsive. Through the experimental and theoretical efforts, the study of the interaction between light composite nuclei is now in the stage of highly quantitative discussion. Phenomenological analyses of the elastic scattering of alpha nucleus from some target nuclei provide us with the unambiguous optical model potentials which are deep and which become slightly shallower as the bombarding energy gets higher. I) Further­ more the elastic scattering of alpha nucleus from the closed shell nuclei has been shown to be successfully described by the resonating group method (RGM) by incor­ porating phenomenological imaginary potential. 2 ) The equivalent local potentials for these RGM non-local potentials are very much similar to the corresponding phenomenological optical model potentials. It is now possible to investigate, as the origin of the energy-dependence of the nucleus-nucleus potential, the properties of the effective nucleon-nucleon interaction in the scattering process separating the effect of the antisymmetrization between the proJectile and target nuclei. As for the effective NN interaction in the scattering process, the nucleon-nucleus optical potential has come to be explained quantitatively starting from the G-matrix theory with local density approximation. The effective NN interaction thus obtained depends on the incident energy and the Fermi momentum of surrounding nucleons, and is complex reflecting the particle-hole excitation process during the propagation through the nuclear matter. In this paper we will develop the framework to derive the nucleus-nucleus potential by the use of the realistic, density-dependent, nucleon­ nucleon interaction. It is based on the extension of the method to construct the microscopic local nucleus-nucleus potential from the RGM non-local potential. In the construction of the equivalent local potential due to Refs. 3) and 4), what is necessary is the classical Hamiltonian of the nucleus-nucleus relative motion, heR, P), which is defined by