Nuclear matter calculations with the phenomenological three-nucleon interaction

TL;DR

This paper investigates how phenomenological three-nucleon forces influence nuclear matter properties using variational methods and two-body correlations, improving agreement with empirical data especially for Urbana v14 potential.

Contribution

It introduces a method to incorporate three-body forces into nuclear matter calculations and compares their effects with two different nucleon-nucleon potentials.

Findings

Inclusion of TBF improves agreement with empirical saturation density and symmetry energy.

TBF causes additional attraction at higher densities for Argonne potential.

Results highlight the importance of three-body forces in nuclear matter modeling.

Abstract

Employing the concept of three-body radial distribution function and using the two-body correlation functions, calculated based on the lowest order constrained variational method, we investigated the effect of the three-body force (TBF) on the nuclear matter properties, for Argonne and Urbana $\it{v_{14}}$ potentials. As such, the results for nuclear matter density, incompressibility, energy per nucleon, and symmetry energy are presented at the saturation point. The inclusion of a phenomenological TBF resulted in closer values of the saturation density, incompressibility, and symmetry energy to the empirical ones for the symmetric nuclear matter. This is especially the case for the Urbana $\it{v_{14}}$ potential. In addition, an empirically-verified parabolic approximation of the interaction energy was utilized to perform an approximate study of the nuclear matter with neutron excess. Hence, at densities higher than about 0.3~fm$^{-3}$ and for proton-to-neutron density ratios close to the symmetric nuclear matter, the inclusion of TBF resulted in an extra attraction for the Argonne as compared to the Urbana $\it{v_{14}}$ potential.