  The long-standing discrepancy between shell-model and experimental values of
the mirror asymmetry in Gamow-Teller transition rates for
$^{28}$Al($\beta^-$)$^{28m}$Si and $^{28}$P($\beta^+$)$^{28m}$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.
