Reducible chiral four-body interactions in nuclear matter

TL;DR

This paper evaluates the impact of reducible chiral four-nucleon interactions on nuclear matter energy, revealing that their net attraction is limited and involves complex diagrammatic cancellations.

Contribution

It provides a detailed first-order calculation of four-nucleon interactions in nuclear matter using unitary transformations, highlighting the magnitude and cancellations of these contributions.

Findings

Net attraction from four-nucleon interactions is less than -1.3 MeV at relevant densities.

Complex diagrammatic cancellations reduce the overall effect.

Method simplifies integrals over Fermi spheres to manageable forms.

Abstract

The method of unitary transformations generates five classes of leading-order reducible chiral four-nucleon interactions which involve pion-exchanges and a spin-spin contact-term. Their first-order contributions to the energy per particle of isospin-symmetric nuclear matter and pure neutron matter are evaluated in detail. For most of the closed four-loop diagrams the occurring integrals over four Fermi-spheres can be reduced to easily manageable one- or two-parameter integrals. One observes substantial cancelations among the different contributions arising from 2-ring and 1-ring diagrams. Altogether, the net attraction generated by the chiral four-nucleon interaction does not exceed values of $-1.3$\,MeV for densities $\rho<2\rho_0$.