Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

TL;DR

This paper reviews the derivation of effective shell-model Hamiltonians and operators using many-body perturbation theory, emphasizing theoretical foundations, technical details, and applications to double-beta decay without empirical adjustments.

Contribution

It provides a comprehensive overview of deriving shell-model components from realistic potentials and assesses the perturbative approach's reliability in nuclear structure studies.

Findings

Shell-model ingredients can be derived from theory without empirical adjustments.

Perturbative expansion behavior influences the reliability of nuclear structure calculations.

Application to double-beta decay demonstrates the approach's practical relevance.

Abstract

The aim of this work is to present an overview of the derivation of the effective shell-model Hamiltonian and decay operators within many-body perturbation theory, and to show the results of selected shell-model studies based on their utilisation. More precisely, we report some technical details that are needed by non-experts to approach the derivation of shell-model Hamiltonians and operators starting from realistic nuclear potentials, in order to provide some guidance to 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. On the above grounds, we will present results of studies of double-beta decay of heavy-mass nuclei where shell-model ingredients are derived from theory, so to assess the reliability of such a way to shell-model investigations. Attention will be also focussed on the relevant aspects that are connected to the behavior of the perturbative expansion, whose knowledge is needed to establish limits and perspectives of this approach to nuclear structure calculations.