Quenching of $g_{\rm A}$ deduced from the $\beta$-spectrum shape of $^{113}$Cd measured with the COBRA experiment

A dedicated study of the quenching of the weak axial-vector coupling strength $g_{\rm A}$ in nuclear processes has been performed by the COBRA collaboration. This investigation is driven by nuclear model calculations which show that the $\beta$-spectrum shape of the fourfold forbidden non-unique decay of $^{113}$Cd strongly depends on the effective value of $g_{\rm A}$. Using an array of CdZnTe semiconductor detectors, 45 independent $^{113}$Cd spectra were obtained and interpreted in the context of three nuclear models. The resulting effective mean values are $\bar{g}_{\rm A}(\text{ISM}) = 0.915 \pm 0.007$, $\bar{g}_{\rm A}(\text{MQPM}) = 0.911 \pm 0.013$ and $\bar{g}_{\rm A}(\text{IBFM-2}) = 0.955 \pm 0.022$. These values agree well within the determined uncertainties and deviate significantly from the free value of $g_{\rm A}$. This can be seen as a first step towards answering the long-standing question regarding quenching effects related to $g_{\rm A}$ in low-energy nuclear processes.