Second--order equation of state with the Skyrme interaction. Cutoff and dimensional regularization with the inclusion of rearrangement terms

TL;DR

This paper calculates the second--order equation of state for nuclear matter using Skyrme interactions, applying regularization techniques and including rearrangement terms, to develop improved effective forces for nuclear matter modeling.

Contribution

It introduces a method to incorporate second--order corrections with regularization and rearrangement terms into Skyrme interactions, creating new parameter sets for nuclear matter calculations.

Findings

Regularization effectively handles ultraviolet divergences.

Rearrangement terms significantly impact the second--order corrections.

New parameter sets improve the accuracy of nuclear matter models.

Abstract

We evaluate the second--order (beyond--mean--field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the zero--range character of this interaction. An adjustment of the force parameters is then performed in both cases to remove any double counting generated by the explicit computation of beyond--mean--field corrections with the Skyrme force. In addition, we include at second order the rearrangement terms associated to the density--dependent part of the Skyrme force and discuss their effect. Sets of parameters are proposed to define new effective forces which are specially designed for second--order calculations in nuclear matter.