Effective shell-model hamiltonians from realistic nucleon–nucleon potentials within a perturbative approach

Abstract: This paper discusses the derivation of an effective shell-model hamiltonian starting from a realistic nucleon–nucleon potential by way of perturbation theory. More precisely, we present the state of the art of this approach when the starting point is the perturbative expansion of the -box vertex function. Questions arising from diagrammatics, intermediate-states and order-by-order convergences, and their dependence on the chosen nucleon–nucleon potential, are discussed in detail, and the results of numerical applications for the -shell model space starting from chiral next-to-next-to-next-to-leading order potentials are shown. Moreover, an alternative graphical method to derive the effective hamiltonian, based on the -box vertex function recently introduced by Suzuki et al., is applied to the case of a non-degenerate model space. Finally, our shell-model results are compared with the exact ones obtained from no-core shell-model calculations. [Copyright &y& Elsevier]