Density dependence of two-body interactions for beyond–mean-field calculations

This paper deals with the theoretical foundation of effective two-body forces for the generator coordinate method and the projected mean-field method. The first aim of this paper is to reduce the in-medium content of a generalized G matrix, removing the hard-core problem in this extended context, into various local densities. Then, we consider the possible renormalization of multibody forces through a density-dependent two-body interaction in the context of configuration mixing calculations. A density dependence of the form ${\rho }^{\sigma },$ as used in Skyrme and Gogny forces, is successfully interpreted as doing so when the mixed density is used. Finally, we propose a simple extension of the Skyrme force dedicated to the calculation of matrix elements between nonorthogonal product states, which are needed to evaluate the correlated energy.