Understanding the mirror asymmetry in Gamow-Teller transition rates between ^28Al(β^-)^28mSi and ^28P(β^+)^28mSi

The long-standing discrepancy between shell-model and experimental values of the mirror asymmetry in Gamow-Teller transition rates for ^28Al(β^-)^28mSi and ^28P(β^+)^28mSi 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.