径向重叠校正到超允许的$0^+ \to 0^+$ $β$ -重新审视衰减
Radial Overlap Correction to Superallowed $0^+ \to 0^+$ $β$-decay revisited
摘要：
在核壳层模型中，我们研究了由于质子和中子单粒子径向波函数之间的不匹配引起的费米矩阵元的修正$δ_{RO}$。重新研究了$sd$ -壳层中的8个超允许$0^+ \to 0^+$ $β$衰变，包括$^{22}$ Mg，$^{26m}$ Al，$^{26}$ Si，$^{30}$ S，$^{34}$ Cl，$^{34}$ Ar，$^{38m}$ K和$^{38}$ Ca.径向波函数是从一个球形的伍兹-撒克逊潜在的参数化得到的深度和长度参数，如核子分离能量和电荷半径，分别在一个一致的调整进行优化。所选择的拟合策略消除了径向失配校正对特定参数化的强烈依赖性，除了具有附加表面峰值项的计算。作为一种改进，我们的模型提出了一种新的方法来计算电荷半径的基础上，亲子扩展，占超越极端独立粒子模型的相关性。除了使用表面峰项的计算和我们使用不同模型空间的情况外，新的$δ_{RO}$集与Towner和Hardy [1]的早期结果基本一致。观察到校正平均$\overline{\mathcal{F}t}$值的微小差异。
英文摘要：
Within the nuclear shell model, we investigate the correction $δ_{RO}$ to the Fermi matrix element due to a mismatch between proton and neutron single-particle radial wave functions. Eight superallowed $0^+ \to 0^+$ $β$ decays in the $sd$-shell, comprised of $^{22}$Mg, $^{26m}$Al, $^{26}$Si, $^{30}$S, $^{34}$Cl, $^{34}$Ar, $^{38m}$K and $^{38}$Ca are re-examined. The radial wave functions are obtained from a spherical Woods-Saxon potential whose parametrizations are optimized in a consistent adjustment of the depth and the length parameter to relevant experimental observables, such as nucleon separation energies and charge radii, respectively. The chosen fit strategy eliminates the strong dependence of the radial mismatch correction to a specific parametrization, except for calculations with an additional surface-peaked term. As an improvement, our model proposes a new way to calculate the charge radii, based on a parentage expansion which accounts for correlations beyond the extreme independent-particle model. Apart from the calculations with a surface-peak term and the cases where we used a different model space, the new sets of $δ_{RO}$ are in general agreement with the earlier result of Towner and Hardy [1]. Small differences of the corrected average $\overline{\mathcal{F}t}$ value are observed.
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