Coarse graining the Bethe-Goldstone equation: nucleon-nucleon high momentum components

TL;DR

This paper introduces a simplified method using delta-shell representation to solve the Bethe-Goldstone equation, enabling efficient calculation of high-momentum nucleon pairs in nuclear matter and confirming the dominance of neutron-proton pairs due to tensor forces.

Contribution

It presents a novel coarse-grained approach to solving the Bethe-Goldstone equation using delta-shell potentials, simplifying the computation of high-momentum components in nuclear matter.

Findings

High-momentum neutron-proton pairs are about 18 times more probable than proton-proton pairs.

The method confirms the strong tensor force's role in nucleon correlations.

Efficient calculation of high-momentum distributions across all partial waves.

Abstract

The delta-shell representation of the nuclear force allows a simplified treatment of nuclear correlations. We show how this applies to the Bethe-Goldstone equation as an integral equation in coordinate space with a few mesh points, which is solved by inversion of a 5-dimensional square matrix in the single channel cases and a $10\times10$ matrix for the tensor-coupled channels. This allows us to readily obtain the high momentum distribution, for all partial waves, of a back-to-back correlated nucleon pair in nuclear matter. We find that the probability of finding a high-momentum correlated neutron-proton pair is about 18 times that of a proton-proton one, as a result of the strong tensor force, thus confirming in an independent way previous results and measurements.