Density-dependent Two-body Interaction Research Articles

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 (GCM) and the projected mean-field method. The first aim of this paper is to reduce into various local-densities the in-medium content of a generalized $G$ matrix removing the hard core problem in this extended context. Then, we consider the possible renormalization of multi-body 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 non-orthogonal product states, which are needed to evaluate the correlated energy.

Equation of state of finite nuclei and liquid-gas phase transition

We construct the equation of state (EOS) of finite nuclei including surface and Coulomb effects in a Thomas-Fermi framework using a finite range, momentum and density dependent two-body interaction. We identify critical temperatures for nuclei below which the EOS so constructed shows clear signals for liquid-gas phase transition in these finite systems. Comparison with the EOS of infinite nuclear matter shows that the critical density and temperature of the phase transition in nuclei are influenced by the mentioned finite size effects.

Velocity-and density-dependent forces in hyperspherical formalism

The hyperspherical one-dimensional Schrodinger equation is derived for a velocity- and density-dependent two-body interaction of finite range. Consequences of newly appearing terms are discussed, application to a contact force is carried out and, as a numerical example, Skyrme force III is used in doubly magic nuclei to calculate energies, breathing modes, r.m.s. and transition radii, and densities.