Dimensional regularization applied to nuclear matter with a zero--range interaction

TL;DR

This paper demonstrates how dimensional regularization can effectively remove ultraviolet divergences in nuclear matter calculations with zero-range interactions, leading to a consistent and cutoff-independent equation of state.

Contribution

The study introduces dimensional regularization to handle divergences in nuclear matter models with zero-range interactions, enabling a unique parameter set without cutoff dependence.

Findings

Ultraviolet divergence is successfully removed using dimensional regularization.

Regularized second-order corrections are independent of cutoff parameters.

The method shows promise for application in finite nuclei beyond mean-field models.

Abstract

We apply the dimensional regularization procedure to treat an ultraviolet divergence occurring in the framework of the nuclear many-body problem. We consider the second--order correction (beyond the mean-field approximation) to the equation of state of nuclear matter with a zero-range effective interaction. The unphysical ultraviolet divergence that is generated at second order by the zero range of the interaction is removed by the regularization technique and the regularized equation of state (mean-field + second-order contributions) is adjusted to a reference equation of state. The main practical advantage of this procedure, with respect to a cutoff regularization, is to provide a unique set of parameters for the adjusted effective interaction. This occurs because the regularized second-order correction does not contain any cutoff dependence. The encouraging results found in this work indicate that such an elegant technique to generate regularized effective interactions is likely to be applied in future to finite nuclei in the framework of beyond mean-field models.