Density-dependent NN-interaction from subleading chiral 3N-forces: short-range terms and relativistic corrections

TL;DR

This paper derives a density-dependent two-nucleon interaction from subleading chiral three-nucleon forces, including short-range and relativistic effects, to improve nuclear many-body calculations.

Contribution

It provides explicit analytical and numerical forms of the density-dependent potential derived from subleading chiral 3N-forces, aiding their implementation in nuclear physics models.

Findings

Derived $V_{med}$ in closed form or with minimal numerical integration.

Expressed potentials for various isospin and spin structures.

Facilitates inclusion of subleading chiral 3N-forces in many-body calculations.

Abstract

We derive from the subleading contributions to the chiral three-nucleon force (short-range terms and relativistic corrections, published in Phys. Rev. C84, 054001 (2011)) a density-dependent two-nucleon interaction $V_\text{med}$ in isospin-symmetric nuclear matter. The momentum and $k_f$-dependent potentials associated with the isospin operators ($1$ and $ \vec\tau_1\!\cdot\!\vec\tau_2$) and five independent spin-structures are expressed in terms of loop functions, which are either given in closed analytical form or require at most one numerical integration. Our results for $V_\text{med}$ are most helpful to implement subleading chiral 3N-forces into nuclear many-body calculations.