Density-dependent effective nucleon-nucleon interaction from chiral three-nucleon forces

TL;DR

This paper derives density-dependent corrections to the nucleon-nucleon interaction from chiral three-nucleon forces, providing analytic expressions and an effective interaction for nuclear structure calculations.

Contribution

It introduces a method to incorporate chiral three-nucleon forces into in-medium nucleon-nucleon interactions with explicit density dependence.

Findings

Derived analytic expressions for in-medium scattering T-matrix

Combined results with V(low-k) for effective interactions

Applicable to nuclear structure calculations with reduced computational cost

Abstract

We derive density-dependent corrections to the in-medium nucleon-nucleon interaction from the leading-order chiral three-nucleon force. To this order there are six distinct one-loop diagrams contributing to the in-medium nucleon-nucleon scattering T-matrix. Analytic expressions are presented for each of these in both isospin-symmetric nuclear matter as well as nuclear matter with a small isospin asymmetry. The results are combined with the low-momentum nucleon-nucleon potential V(low-k) to obtain an effective density-dependent interaction suitable for nuclear structure calculations. The in-medium interaction is decomposed into partial waves up to orbital angular momentum L = 2. Our results should be particularly useful in calculations where an exact treatment of the chiral three-nucleon force would otherwise be computationally prohibitive.