Kirson-Babu-Brown core polarization diagrams and low-momentum shell model effective interactions

The Kirson-Babu-Brown (KBB) induced interaction approach is applied to the derivation of the sd-shell nucleon effective interactions. We start from a low-momentum NN interaction Vlow-k obtained by integrating out the high-momentum components of modern realistic NN potentials beyond a decimation momentum λ. Then a large class of core polarization diagrams are summed up to all orders by way of the KBB self-consistent equations. It is found that the solution of these equations is simplified by the use of Vlow-k, which is energy independent, and by treating them in terms of the Green's fuctions in the particle-particle and the particle-hole channels. The effective interactions calculated with the all-order KBB core polarizations and those with the polarization in second-order perturbation theory are found to be rather similar to each other, typical difference between them being less than 10%.

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