# Renormalization of the GT operator within the realistic shell model

## TL;DR

This paper investigates the renormalization of the Gamow-Teller operator in the realistic shell model, demonstrating that effective operators can accurately reproduce nuclear transition data without empirical adjustments, thus enhancing predictive reliability.

## Contribution

It presents a method to derive effective shell-model operators from a realistic nucleon-nucleon potential using many-body perturbation theory, applied to Gamow-Teller transitions in nuclei.

## Key findings

- Effective operators reproduce experimental transition strengths.
- No empirical quenching of gA needed.
- Results applicable to neutrinoless double-beta decay studies.

## Abstract

In nuclear structure calculations, the choice of a limited model space, due to computational needs, leads to the necessity to renormalize the Hamiltonian as well as any transition operator. Here, we present a study of the renormalization procedure and effects of the Gamow-Teller operator within the framework of the realistic shell model. Our effective shell-model operators are obtained, starting from a realistic nucleon-nucleon potential, by way of the many-body perturbation theory in order to take into account the degrees of freedom that are not explicitly included in the chosen model space. The theoretical effective shell-model Hamiltonian and transition operators are then employed in shell-model calculations, whose results are compared with data of Gamow-Teller transition strengths and double-beta half-lives for nuclei which are currently of interest for the detection of the neutrinoless double-beta decay process, in a mass interval ranging from A=48 up to A=136. We show that effective operators are able to reproduce quantitatively the spectroscopic and decay properties without resorting to an empirical quenching neither of the axial coupling constant gA, nor of the spin and orbital gyromagnetic factors. This should assess the reliability of applying present theoretical tools to this problematic.