A New Analytical Derivation of Kernels in the Resonating Group Method for Composite-Particle Scattering and Molecule-Like Structures: Derivation from Kernels in the Generator Coordinate Method and Application to 16O +

Abstract

Exchange kernels in the resonating group method are derived analytically from those in the generator coordinate method without any use of inverse operators of Gauss transforma­ tion. The whole kernels of 160+a system with Coulomb interaction are given, divided into various exchange mechanisms. Derivation in the cases where two interacting nuclei have different oscillator parameters and where other channels are included is also presented. § I. Introduction The cluster structure and molecular aspect in nuclei have been studied ex­ tensively in terms of interaction between composite particles. 1l Recently, many attempts based on phenomenological and microscopic approaches have been made with the progress of experiments on composite-particle scattering and cluster transfer reactions. 2l It must be one of the main aims of such studies to investi­ gate the microscopic mechanism of interaction between composite nuclei by em­ ploying the many-body Hamiltonian and taking into account the Pauli principle exactly. The resonating group method3l (RGM) ·is very powerful to this aim. For instance, on the basis of the RGM a deep understanding was obtained concern­ ing the origin of the repulsive core of phenomenological a-a potential as a model representation of the existence of almost energy-independent behaviour of the nodal point.'l Saito 5l showed that the behaviour is understood as a result of or­ thogonality of the relative wave function to forbidden states and proposed an orthogonality condition model which describes the inner part of interaction be­ tween composite particles with the orthogonality condition and the outer part with a direct potential. This approximated model has obtained successful results for a-a scattering 5l' 6l and for a-decay widths of 160 +a system.7l Although the RGM approach is very powerful in extracting physical understandings from it­ self, its application to a system heavier than a+ a has been generally regarded as very much difficult.