Implementing chiral three-body forces in terms of medium-dependent two-body forces

TL;DR

This paper reviews the derivation of medium-dependent two-body forces from chiral three-nucleon interactions and explores their applications in nuclear matter calculations, providing a practical approach to incorporate three-body forces efficiently.

Contribution

It introduces a simplified method to include chiral three-body forces via medium-dependent two-body interactions, facilitating more accurate nuclear structure calculations.

Findings

V_med accurately reflects three-body physics in two-body form

Differences observed between local and nonlocal regulators

Numerical results show V_med's effectiveness in nuclear matter calculations

Abstract

Three-nucleon (3N) forces are an indispensable ingredient for accurate few-body and many-body nuclear structure and reaction theory calculations. While the direct implementation of chiral 3N forces can be technically very challenging, a simpler approach is given by employing instead a medium-dependent NN interaction V_med that reflects the physics of three-body forces at the two-body normal-ordered approximation. We review the derivation and construction of V_med from the chiral 3N interaction at next-to-next-to-leading order (N2LO), consisting of a long-range $2\pi$-exchange term, a mid-range $1\pi$-exchange component and a short-range contact term. Several applications of V_med to the equation of state of cold nuclear and neutron matter, the nucleon single-particle potential in nuclear matter, and the nuclear quasiparticle interaction are discussed. We also explore differences in using local vs. nonlocal regulating functions on 3N forces and make direct comparisons to exact results at low order in perturbation theory expansions for the equation of state and single-particle potential. We end with a discussion and numerical calculation of the in-medium NN potential V_med from the next-to-next-to-next-to-leading order (N3LO) chiral 3N force, which consists of a series of long-range and short-range terms.