O ct 2 00 2 Density - Dependence of Two - Body Interactions Beyond the Mean - Field Approximation

This paper deals with the theoretical foundation of phenomenological effective two-body forces for beyond mean-field calculations such as the Generator Coordinate Method (GCM) or the projected mean-field method. Extending the Brueckner-Goldstone perturbation theory [34], a generalized G matrix removing the hard core problem by summing two-body correlations in the context of mixed non-orthogonal Slater-determinants has been derived. The aim of this paper is to reduce the in-medium content of this effective interaction into various local densities dependences. Thus an extension of the Skyrme force dedicated to the calculation of matrix elements between non-orthogonal product states is proposed. As an application, the derived density-dependence of the Skyrme force is shown to be well-defined for symmetry restoration.