In this article we present an updated spectrum-shape analysis of the ¹¹³Cd fourfold forbidden non-unique β-decay transition in order to address the quenching of the weak axial-vector coupling $g_{\mathrm{A}}$ in low-momentum exchange nuclear processes. The experimental data were collected in a dedicated low-threshold run with the COBRA demonstrator at the LNGS and resulted in 44 individual ¹¹³Cd spectra. These data are evaluated in the context of three nuclear model frameworks based on a revised version of the spectrum-shape method and the conserved vector current hypothesis. The novel idea devised in the present work is to fit the value of the small relativistic nuclear matrix element (s-NME) driving the nuclear model calculations, which remained essentially as a free parameter in previous studies. This is done by tuning the nuclear structure calculations and making use of the interplay of $g_{\mathrm{A}}$ and the s-NME such that the experimentally known ¹¹³Cd half-life gets reproducible by the different frameworks. In this way, a best fit s-NME value can be derived for each of the considered nuclear models, which finally enters the template calculations used to perform the spectrum-shape analysis for each of the obtained ¹¹³Cd spectra. The primary analysis strategy results in significantly quenched values of the axial-vector coupling for all three nuclear models: ${\bar{g}}_{\mathrm{A}}(\text{ISM})=0.907\pm 0.064$, ${\bar{g}}_{\mathrm{A}}(\text{MQPM})=0.993\pm 0.063$ and ${\bar{g}}_{\mathrm{A}}(\text{IBFM-2})=0.828\pm 0.140$. Moreover, with our data-driven approach one of the main shortcomings of the spectrum-shape method has been resolved. This achievement is a milestone in the description of strongly forbidden β-decays and adds to the indications for the existence of a quenching of $g_{\mathrm{A}}$ in low-momentum exchange nuclear processes.

在本文中，我们提出了¹¹³ Cd 四重禁止非唯一β衰变跃迁的更新谱形分析，以解决弱轴矢量耦合的淬火问题$G_{\mathrm{一种}}$在低动量交换核过程中。实验数据是在 LNGS 的 COBRA 演示器的专用低阈值运行中收集的，并产生了 44 个单独的¹¹³ Cd 光谱。这些数据是在基于频谱形状方法的修订版和守恒矢量电流假设的三个核模型框架的背景下进行评估的。在目前的工作中设计的新想法是拟合驱动核模型计算的小相对论核矩阵元素 (s-NME) 的值，这在以前的研究中基本上仍然是一个自由参数。这是通过调整核结构计算并利用$G_{\mathrm{一种}}$和 s-NME，使得实验上已知的¹¹³ Cd 半衰期可以通过不同的框架重现。通过这种方式，可以为每个考虑的核模型推导出最佳拟合 s-NME 值，最终进入模板计算，用于对每个获得的¹¹³ Cd 光谱进行光谱形状分析。主要分析策略导致所有三个核模型的轴向矢量耦合值显着降低：${\bar{G}}_{\mathrm{一种}}(\text{主义})=0.907\pm 0.064$, ${\bar{G}}_{\mathrm{一种}}(\text{MQPM})=0.993\pm 0.063$ 和 ${\bar{G}}_{\mathrm{一种}}(\text{IBFM-2})=0.828\pm 0.140$. 此外，通过我们的数据驱动方法，频谱形状方法的主要缺点之一已得到解决。这一成就是描述强烈禁止的β-衰变的里程碑，并增加了存在淬灭的迹象。$G_{\mathrm{一种}}$ 在低动量交换核过程中。