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 Qˆ-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 p-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 Zˆ-box vertex function recently introduced by Suzuki et al., is applied to the case of a non-degenerate (0+2)ħω model space. Finally, our shell-model results are compared with the exact ones obtained from no-core shell-model calculations.