Quenching of $g_{\mathrm{A}}$ 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 $g_{\mathrm{A}}$ 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 $g_{\mathrm{A}}$. 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 ${\bar{g}}_{\mathrm{A}}(\text{ISM})=0.915\pm 0.007$, $\bar{g}{\rm A}($\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 $g_{\mathrm{A}}$. This can be seen as a first step towards answering the long-standing question regarding quenching effects related to $g_{\mathrm{A}}$ in low-energy nuclear processes.