In this work, we present a theoretical study of the electron spectral shapes for the second-forbidden nonunique \(\beta ^-\)-decay transitions \(^{59}\text {Fe}(3/2^-)\rightarrow \,^{59}\text {Co}(7/2^-)\) and \(^{60}\text {Fe}(0^+)\rightarrow \,^{60}\text {Co}(2^+)\) in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete \(0\hbar \omega \) calculation in the full fp model space using the KB3G and GXPF1A effective interactions. When compared with the available data, these interactions predict the low-energy spectra and electromagnetic properties of the involved nuclei quite successfully. This success paves the way for the computations of the \(\beta \)-decay properties, and comparison with the available data. We have computed the electron spectral shapes of the mentioned decay transitions as functions of the value of the weak axial coupling \(g_{\mathrm{A}}\). By comparing these computed shapes with the measured spectral shapes allows then to extract the effective value of \(g_{\mathrm{A}}\) for these decay transitions. This procedure, coined the spectrum-shape method (SSM) in several earlier studies, complements the method of determining the value of \(g_{\mathrm{A}}\) by reproducing the (partial) half-lives of decay transitions. Here we have enhanced the original SSM by constraining the value of the relativistic vector matrix element, \(^V{\mathcal {M}}^{(0)}_{KK-11}\), using the conserved vector-current hypothesis (CVC) as a starting point. We hope that this finding would be a strong incentive to measure the spectral shapes in the future.

在这项工作中，我们提出了第二个禁止非唯一性\(\beta ^-\) -衰变跃迁\(^{59}\text {Fe}(3/2^-)\ rightarrow \,^{59}\text {Co}(7/2^-)\)和\(^{60}\text {Fe}(0^+)\rightarrow \,^{60}\text {Co }(2^+)\)在核壳模型的框架中。我们通过使用 KB3G 和 GXPF1A 有效相互作用在完整fp模型空间中执行完整的\(0\hbar \omega \)计算来计算所涉及的波函数。与现有数据相比，这些相互作用非常成功地预测了相关原子核的低能谱和电磁特性。这一成功为计算\(\beta \) -衰减属性，并与可用数据进行比较。我们已经计算了上述衰变跃迁的电子光谱形状，作为弱轴向耦合\(g_{\mathrm{A}}\)值的函数。通过将这些计算的形状与测量的光谱形状进行比较，可以为这些衰减跃迁提取\(g_{\mathrm{A}}\)的有效值。该过程在早期的几项研究中创造了频谱形状方法 (SSM)，通过再现衰变跃迁的（部分）半衰期来补充确定\(g_{\mathrm{A}}\)值的方法。这里我们通过约束相对论向量矩阵元素的值来增强原始 SSM，\(^V{\mathcal {M}}^{(0)}_{KK-11}\)，使用守恒矢量电流假设 (CVC) 作为起点。我们希望这一发现将成为未来测量光谱形状的强大动力。