Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

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.

arXiv comment39 pages, 18 figures, 3 tables, to be published in Frontiers in Physics as a contribution to the Research Topic "The Future of Nuclear Structure: Challenges and Opportunities in the Microscopic Description of Nuclei"

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• Shell-model study of titanium isotopic chain with chiral two- and three-body forces
• Uncovering the mechanism of chiral three-nucleon force in driving spin-orbit splitting
• Estimation of nuclear matrix elements of double-$\beta$ decay from shell model and quasiparticle random-phase approximation
• Puzzling $B(E2;0^{+}\to 2^{+})$ strength in the proton dripline nucleus ${}^{36}$Ca
• Electric dipole response of sd-shell nuclei within the Configuration-Interaction Shell Model approach
• Modeling Ultra-High-Energy Cosmic Rays propagation using the input from Configuration Interaction Shell Model
• A glimpse into an effective world
• Towards shell model interactions with credible uncertainties
• Structure evolution of ground and excited states in the exotic nucleus ${}^{22}$Al
• Nuclear structure study with two- and three-nucleon contact interactions derived within low-energy EFT