Effective shell-model hamiltonians from realistic nucleon-nucleon potentials within a perturbative approach
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 Q{sup -hat-}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 Z{sup -hat-}box vertex function recently introduced by Suzuki et al., is applied to the case of a non-degenerate (0+2)h{omega} model space. Finally, our shell-model results are compared with the exact ones obtained from no-core shell-model calculations. - Highlights: Black-Right-Pointing-Pointer The derivation of nuclear realistic shell-model effective hamiltonians is studied. Black-Right-Pointing-Pointer Perturbation theory. Black-Right-Pointing-Pointer Diagrammatics, intermediate-states and order-by-order convergences are investigated. Black-Right-Pointing-Pointer Shell-model calculations in degenerate and non-degenerate model spaces are presented. Black-Right-Pointing-Pointer Shell-model results are compared with the exact ones.