Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

This article presents an overview of the derivation of effective shell-model Hamiltonian and decay operators within the framework of many-body perturbation theory, and discusses the results of selected shell-model studies based on these operators. More precisely, we give technical details that non-experts will need in order to derive shell-model Hamiltonians and operators starting from realistic nuclear potentials, and provide some guidance for shell-model calculations where the single-particle energies, two-body matrix elements of the residual interaction, effective charges, and decay matrix elements are all obtained without resorting to empirical adjustments. We report results of studies of double-β decay of heavy-mass nuclei where the shell-model ingredients are derived from theory, so as to assess the reliability of such an approach to shell-model investigations. Attention will be also focused on aspects relating to the behavior of the perturbative expansion, knowledge of which is needed for establishing limits and applying this approach to nuclear structure calculations.