Nuclear matter calculations with the phenomenological three-nucleon interaction

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.