The calculation of the neutrinoless double-beta decay matrix element within the realistic shell model

TL;DR

This paper calculates the neutrinoless double-beta decay nuclear matrix element using a realistic shell model, incorporating perturbation theory, short-range correlations, and Pauli-principle corrections to improve prediction reliability.

Contribution

It introduces a method to derive effective decay operators from realistic nucleon-nucleon potentials within the shell model, including key correlation effects.

Findings

Effective decay operators show improved reliability.

Short-range correlations significantly impact matrix elements.

Results are compared with previous shell-model calculations.

Abstract

We approach the calculation of the nuclear matrix element of the neutrinoless double-beta decay process, considering the light-neutrino-exchange channel, by way of the realistic shell model. To this end, we start from a realistic nucleon-nucleon potential and then derive the effective shell-model Hamiltonian and neutrinoless double-beta decay operator within the many-body perturbation theory. We focus on investigating the perturbative properties of the effective shell-model operator of such a decay process, aiming to establish the degree of reliability of our predictions. The contributions of the so-called short-range correlations and of the correction of Pauli-principle violations to the effective shell-model operator, the latter introduced in many-valence nucleon systems, are also taken into account. The subjects of our study are a few candidates to the neutrinoless double-beta decay detection, in a mass interval ranging from A=48 up to A=136, whose spin- and spin-isospin-dependent decay properties we have studied in previous works. Our results will be finally compared with shell-model calculations for the same set of nuclei.