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

Abstract

Microscopic calculations based on realistic nuclear Hamiltonians, while yielding accurate results for the energies of the ground and low-lying excited states of nuclei with $A\ensuremath{\leqslant}12$, fail to reproduce the empirical equilibrium properties of nuclear matter, that are known to be significantly affected by three-nucleon forces. We discuss a scheme suitable to construct a density-dependent two-nucleon potential, in which the effects of $n$-particle interactions can be included by integrating out the degrees of freedom of $(n\ensuremath{-}2)$ nucleons. Our approach, based on the formalism of correlated basis function and state-of-the-art models of the two- and three-nucleon potentials, leads to an effective interaction that can be easily employed in nuclear matter calculations, yielding results in good agreement with those obtained from the underlying three-body potential.