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.
Highlights
This article presents formal details of the derivation of effective shell-model Hamiltonians (Heff) and decay operators by a perturbative approach, and reviews a large sample of recent applications to the study of spectroscopic properties of atomic nuclei
This paper has presented a general overview of the perturbative approach to deriving effective shell model (SM) operators, in particular the SM Hamiltonian and decay operators
We described the theoretical framework, which is essentially based on the perturbative expansion of a vertex function—the Q -box for the effective Hamiltonian and the -box for effective decay operators—whose calculation is pivotal in the Lee-Suzuki similarity transformation
Summary
This article presents formal details of the derivation of effective shell-model Hamiltonians (Heff) and decay operators by a perturbative approach, and reviews a large sample of recent applications to the study of spectroscopic properties of atomic nuclei. Over more than 70 years of SM calculations, this approach has been very successful at reproducing a huge amount of data and describing some of the most fundamental physical properties of the structure of atomic nuclei In this regard, it is worth mentioning the review by Caurier et al [3], which contains an interesting discussion about the properties of the effective SM Hamiltonian; additional references will be given . Came the seminal paper by Tom Kuo and Gerry Brown [10], which represents a true turning point in nuclear structure theory It includes the first successful attempt at performing a shell-model calculation starting from the free nucleon-nucleon (NN) Hamada-Johnston (HJ) potential [11], and resulted in a quantitative description of the spectroscopic properties of sdshell nuclei. The final section gives a summary of the present work
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