Introduction to low-momentum effective interactions with Brown–Rho scaling and three-nucleon forces

Abstract

Model-space effective interactions Veff derived from free-space nucleon–nucleon interactions VNN are reviewed. We employ a double decimation approach: first we extract a low-momentum interaction from VNN using a T-matrix equivalence decimation method. Then Veff is obtained from by way of a folded-diagram effective interaction method. For decimation momentum , the interactions derived from different realistic VNN models are nearly model independent, and so are the resulting shell-model effective interactions. For nucleons in a low-density nuclear medium like valence nucleons near the nuclear surface, such effective interactions derived from free-space VNN are satisfactory in reproducing experimental nuclear properties. But it is not so for nucleons in a nuclear medium with density near or beyond nuclear matter saturation density. In this case it may be necessary to include the effects from Brown–Rho (BR) scaling of hadrons and/or three-nucleon forces V3N, effectively changing the free-space VNN into a density-dependent one. The density-dependent effects from BR scaling and V3N are compared with those from empirical Skyrme effective interactions.