Implementing Chiral Three-Body Forces in Terms of Medium-Dependent Two-Body Forces

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 Vmed that reflects the physics of three-body forces at the two-body normal-ordered approximation. We review the derivation and construction of Vmed from the chiral 3N interaction at next-to-next-to-leading order (N2LO), consisting of a long-range 2π-exchange term, a mid-range 1π-exchange component, and a short-range contact-term. Several applications of Vmed 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. non-local 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 Vmed 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.