标题： 理解 Gamow-Teller 跃迁率在 $^{28}$Al($β^-$)$^{28m}$Si 和 $^{28}$P($β^+$)$^{28m}$Si 之间的镜像不对称性 显示英文标题

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

摘要： Gamow-Teller跃迁速率中镜像不对称性的壳模型与实验值之间的长期差异，通过对$^{28}$Al($\beta^-$)$^{28m}$Si 和$^{28}$P($\beta^+$)$^{28m}$Si 的径向失配校正项引入$p$轨道贡献部分得到了解决。 这种方法基于French-Macfarlane求和规则，提供了径向失配引起的芯轨道贡献的潜在估算值，避免了第一性原理壳模型所需的繁重计算。 此外，通过按最低两个混合态的实验能量分离比例缩放计算得到的同位旋混合校正值，同位旋混合贡献得到了显著改善，这与双能级模型的结果一致。 显示英文摘要

摘要： 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.