Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes

TL;DR

This paper develops a method to calculate the energy of nuclear matter by resumming ladder diagrams using experimental nucleon-nucleon scattering data, providing a rigorous low-density reference.

Contribution

It introduces a ladder resummation approach expressed directly in terms of experimental phase shifts, applicable to symmetric and neutron matter, with convergence achieved including up to G waves.

Findings

Energy per particle and sound velocity calculated for symmetric and neutron matter.

Results expressed explicitly in terms of nucleon-nucleon phase shifts and mixing angles.

Convergence reached with inclusion of higher partial waves.

Abstract

Infinite nuclear matter is studied by resuming the series of ladder diagrams based on the results developed by us in Ann. Phys. 437, 168741 (2022). The master formula for the energy density is explicitly solved for the case of contact interactions, within a pionless description of the nucleon-nucleon interactions. Renormalized results are obtained which are directly expressed in terms of the nucleon-nucleon phase shifts and mixing angles in partial-wave amplitudes up to an including $G$ waves, with convergence reached under the inclusion of higher partial waves. The energy per particle, density and sound velocity resulting from the ladder series are given for symmetric and neutron matter. This resummation of the ladder diagrams provides a rigorous result that may be used as low-density reference for other parameterizations of $\bar{\cal{E}}$ for higher densities.