Shell-model calculation of isospin-symmetry breaking correction to superallowed Fermi beta-decay

TL;DR

This paper uses shell-model calculations with realistic wave functions to evaluate isospin-symmetry breaking corrections in superallowed Fermi beta-decay, focusing on sd-shell nuclei and comparing Woods-Saxon and Hartree-Fock potentials.

Contribution

It introduces a refined shell-model approach with an adjustment procedure that reduces sensitivity to potential parametrizations, providing more consistent correction estimates.

Findings

Good agreement with previous studies.

Hartree-Fock wave functions yield systematically lower corrections.

Adjustment procedure minimizes model dependence.

Abstract

We investigate the radial-overlap part of the isospin-symmetry breaking correction to superallowed $0^+\to 0^+$-decay using the shell-model approach similar to that of Refs. [1, 2]. The 8 sd-shell emitters with masses between $A=22$ and $A=38$ have been re-examined. The Fermi matrix element is evaluated with realistic spherical single-particle wave functions, obtained from spherical Woods-Saxon (WS) or Hartree-Fock (HF) potentials, fine-tuned to reproduce the experimental data on charge radii and separation energies for nuclei of interest. The elaborated adjustment procedure removes any sensitivity of the correction to a specific parametrisation of the WS potential or to various versions of the Skyrme interaction. The present results are generally in good agreement with those reported in Refs. [3, 4]. At the same time, we find that the calculations with HF wave functions result in systematically lower values of the correction.