Partial wave decomposition of finite-range effective tensor interaction

TL;DR

This paper analyzes the finite-range tensor interactions in nuclear physics, extracting parameters from microscopic results and showing their relation to Skyrme pseudo-potentials, with implications for modeling finite nuclei.

Contribution

It introduces a method to derive tensor parameters from microscopic nucleon-nucleon interactions and connects finite-range interactions to the N3LO Skyrme pseudo-potential.

Findings

Finite-range tensor interactions can be characterized via partial wave decomposition.

The zero-range limit of these interactions resembles the N3LO Skyrme pseudo-potential.

Tensor parameters can be fixed using Brueckner-Hartree-Fock results.

Abstract

We perform a detailed analysis of the properties of the finite-range tensor term associated with the Gogny and M3Y effective interactions. In particular, by using a partial wave decomposition of the equation of state of symmetric nuclear matter, we show how we can extract their tensor parameters directly from microscopic results based on bare nucleon-nucleon interactions. Furthermore, we show that the zero-range limit of both finite-range interactions has the form of the N3LO Skyrme pseudo-potential, which thus constitutes a reliable approximation in the density range relevant for finite nuclei. Finally, we use Brueckner-Hartree-Fock results to fix the tensor parameters for the three effective interactions.