Low momentum shell model effective interactions with all-order core polarizations
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An all-order summation of core-polarization diagrams using the low-momentum nucleon-nucleon interaction Vlow-k is presented. The summation is based on the Kirson-Babu-Brown (KBB) induced interaction approach in which the vertex functions are obtained self-consistently by solving a set of nonlinear coupled equations. It is found that the solution of these equations is simplified using Vlow-k, which is energy independent, and using the Green's functions in the particle-particle and particle-hole channels. We have applied this approach to the sd-shell effective interactions and find that the results we calculated to all orders by using the KBB summation technique are remarkably similar to those of second-order perturbation theory, the average differences being less than 10%. 2005 The American Physical Society.