A new approach to two-level model calculation of isospin mixing in nuclei

TL;DR

This paper introduces a novel method for calculating isospin mixing probabilities in nuclei using a two-level model, overcoming limitations of traditional shell model approaches, and demonstrates its effectiveness with experimental data.

Contribution

The paper presents a new approach based on locating unperturbed levels to calculate isospin mixing, applicable to nuclei and potentially other multi-level mixing problems.

Findings

Large isospin mixing observed in $^{24}Mg$, up to 48.76%.

Method successfully applied to seven self-conjugate nuclei.

Largest isospin mixing ever found in a nucleus.

Abstract

A new method has been proposed for isolated two-level model to calculate isospin mixing probability in nuclei overcoming common limitations of usual shell model results with isoscalar nuclear Hamiltonian. The method is based on locating the unperturbed levels of the mixed doublet before mixing. Experimental and shell model level energies, electromagnetic/Gamow-Teller transition matrix elements associated with a doublet or two doublet pairs in a nucleus are used to calculate isospin mixing probability in seven self-conjugate nuclei. The four self-conjugate nuclei (P, S, Cl, Ar) considered here show large isospin mixing matrix elements and large unperturbed energy-gaps of the observed isospin-mixed doublet pairs. Large isospin mixing (31.40-48.76 %) is found in the observed doublet ($1^{+},1^{+}$) at 9828.11 and 9967.19 keV, respectively, in $^{24}Mg$. This is probably the largest isospin mixing ever found in a nucleus. This is much larger than that $({20}_{-9.904}^{+9.142}$%) has been found recently in $^{26}$Si. The method is general enough to be applicable to other two-level/multi-level mixing problems and in particular, might be useful for consideration of isospin mixing in the context of Fermi beta decay also.