Regularization of zero-range effective interactions in finite nuclei

TL;DR

This paper introduces a regularization scheme for zero-range effective interactions in finite nuclei, extending previous uniform matter methods to finite systems, and examines the validity of perturbative approaches in this context.

Contribution

The work develops a regularization procedure for zero-range interactions in finite nuclei, unifying the treatment with uniform matter and analyzing perturbative energy calculations.

Findings

Regularized zero-range interactions behave consistently in finite nuclei.

The proposed scheme effectively controls divergences in beyond mean-field calculations.

Perturbative approaches remain valid within the regularized framework.

Abstract

The problem of the divergences which arise in beyond mean-field calculations, when a zero-range effective interaction is employed, has not been much considered so far. Some of us have proposed, quite recently, a scheme to regularize a zero-range Skyrme-type force when it is employed to calculate the total energy, at second-order perturbation theory level, in uniform matter. Although this scheme looked promising, the extension for finite nuclei is not straightforward. We introduce such procedure in the current paper, by proposing a regularization procedure that is similar, in spirit, to the one employed to extract the so-called V_{\rm low-k} from the bare force. Although this has been suggested already by B.G. Carlsson and collaborators, the novelty of our work consists in setting on equal footing uniform matter and finite nuclei; in particular, we show how the interactions that have been regularized in uniform matter behave when they are used in a finite nucleus with the corresponding cutoff. We also address the problem of the validity of the perturbative approach in finite nuclei for the total energy.