Energy per particle of nuclear and neutron matter from subleading chiral three-nucleon interactions

TL;DR

This paper analytically derives the first-order energy contributions of subleading chiral three-nucleon interactions to nuclear and neutron matter, providing explicit formulas for various diagram types.

Contribution

It presents the first analytical evaluation of subleading chiral three-nucleon interaction contributions to nuclear matter energy per particle.

Findings

3-ring diagrams vanish by spin-trace

2-ring diagrams expressed with elementary functions

Most 1-ring diagrams reduced to one-parameter integrals

Abstract

We derive from the subleading contributions to the chiral three-nucleon interaction [published in Phys.~Rev.~C77, 064004 (2008) and Phys.~Rev.~C84, 054001 (2011)] their first-order contributions to the energy per particle of isospin-symmetric nuclear matter and pure neutron matter in an analytical way. For the variety of short-range and long-range terms that constitute the subleading chiral 3N-force the pertinent closed 3-ring, 2-ring, and 1-ring diagrams are evaluated. While 3-ring diagrams vanish by a spin-trace and the results for 2-ring diagrams can be given in terms of elementary functions of the ratio Fermi-momentum over pion mass, one ends up in most cases for the closed 1-ring diagrams with one-parameter integrals. The same treatment is applied to the subsubleading chiral three-nucleon interactions as far as these have been constructed up to now.