Introduction to low-momentum effective interactions with Brown-Rho scaling and three-nucleon forces
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2016 The Royal Swedish Academy of Sciences. Model-space effective interactions V eff derived from free-space nucleon-nucleon interactions V NN are reviewed. We employ a double decimation approach: first we extract a low-momentum interaction from V NN using a T-matrix equivalence decimation method. Then V eff is obtained from by way of a folded-diagram effective interaction method. For decimation momentum , the interactions derived from different realistic V NN 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 V NN 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 V 3N, effectively changing the free-space V NN into a density-dependent one. The density-dependent effects from BR scaling and V 3N are compared with those from empirical Skyrme effective interactions.