arXiv:nucl-th/0504058·v1·Nuclear Theory
Low momentum shell model effective interactions with all-order core polarizations
Jason D. Holt (1) · Jeremy W. Holt (1) · T. T. S. Kuo (1) · G. E. Brown (1) · S. K. Bogner (2) ((1) State University of New York at Stony Brook · (2) The Ohio State University)
Abstract
An all-order summation of core polarization diagrams using the low-momentum nucleon-nucleon interaction, V_low-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 non-linear coupled equations. It is found that the solution of these equations is simplified by using V_low-k, which is energy independent, and by employing Green 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 calculated to all orders using the KBB summation technique are remarkably similar to those of second-order perturbation theory, average differences being less than 10%.
Comments: 4 pages, 4 figures