A study of the Gaussian overlap approach in the two-center shell model

Abstract

The Gaussian overlap approach (GOA) to the generator coordinate method (GCM) is carried through up to fourth order in the derivatives. By diagonalizing the norm overlap, a collective Schrödinger equation is obtained. The potential therein contains the usual potential energy surface (PES) plus correction terms, which subtract the zero-point energies (ZPE) in the PES. The formalism is applied to BCS states obtained from a two-center shell model (TCSM). To understand the crucial role of the pairing contributions in the GOA a schematic picture, the multi-level model, is constructed. An explicit numerical study of the convergence of the GOA is given for the TCSM, with the result that the GOA seems to be justified for medium heavy and heavy nuclei but critical for light nuclei.