Understanding the mirror asymmetry in Gamow-Teller transition rates between ${}^{28}$Al($β^-$)${}^{28m}$Si and ${}^{28}$P($β^+$)${}^{28m}$Si

Abstract

The long-standing discrepancy between shell-model and experimental values of the mirror asymmetry in Gamow-Teller transition rates for ${}^{28}$Al($β^-$)${}^{28m}$Si and ${}^{28}$P($β^+$)${}^{28m}$Si is partially resolved by integrating the $p$-orbital contribution into the radial mismatch correction term. This approach offers a potential estimate of the radial mismatch-induced core-orbital contribution based on the French-Macfarlane sum rules, avoiding the need for heavy calculations required by the first-principle shell model. Additionally, the isospin-mixing contribution undergoes considerable improvement through scaling the calculated isospin-mixing correction with the experimental energy separation between the lowest two admixed states, in accordance with the result from the two-level model.

6 pages, 1 figure, 1 table