Separable form of low-momentum realistic NN interaction

TL;DR

This paper presents a simplified, separable form of the low-momentum nucleon-nucleon interaction that accurately reproduces nuclear matter properties and facilitates easier calculations in nuclear physics.

Contribution

The authors develop a rank-2 separable representation of $V_{low-k}$ that maintains accuracy for nuclear matter calculations, simplifying its application in nuclear structure studies.

Findings

A rank-2 separable force accurately reproduces $V_{low-k}$ for $rac{1}{2}$ fm$^{-1}$ cutoff.

Higher ranks are needed for larger cutoffs to maintain accuracy.

The separable force is easily parameterized for practical use.

Abstract

The low-momentum interaction $V_{\text{low-k}}$ derived from realistic models of the nucleon-nucleon interaction is presented in a separable form. This separable force is supported by a contact interaction in order to achieve the saturation properties of symmetric nuclear matter. Bulk properties of nuclear matter and finite nuclei are investigated for the separable form of $V_{\text{low-k}}$ and two different parameterizations of the contact term. The accuracy of the separable force in Hartree-Fock calculations with respect to the original interaction $V_{\text{low-k}}$ is discussed. For a cutoff parameter $\Lambda$ of 2 fm$^{-1}$ a representation by a rank 2 separable force yields a sufficient accuracy, while higher ranks are required for larger cut-off parameters. The resulting separable force is parameterized in a simple way to allow for an easy application in other nuclear structure calculations.