Precise 113Cd \(\beta \) decay spectral shape measurement and interpretation in terms of possible \(g_A\) quenching

Highly forbidden \(\beta \) decays provide a sensitive test to nuclear models in a regime in which the decay goes through high spin-multipole states, similar to the neutrinoless double-\(\beta \) decay process. There are only 3 nuclei (⁵⁰V, ¹¹³Cd, ¹¹⁵In) which undergo a \(4^\textrm{th}\) forbidden non-unique \(\beta \) decay. In this work, we compare the experimental ¹¹³Cd spectrum to theoretical spectral shapes in the framework of the spectrum-shape method. We measured with high precision, with the lowest energy threshold and the best energy resolution ever, the \(\beta \) spectrum of ¹¹³Cd embedded in a 0.43 kg \(\hbox {CdWO}_4\) crystal, operated over 26 days as a bolometer at low temperature in the Canfranc underground laboratory (Spain). We performed a Bayesian fit of the experimental data to three nuclear models (IBFM-2, MQPM and NSM) allowing the reconstruction of the spectral shape as well as the half-life. The fit has two free parameters, one of which is the effective weak axial-vector coupling constant, \(g_A^{\text {eff}}\), which resulted in \(g_A^{\text {eff}}\) between 1.0 and 1.2, compatible with a possible quenching. Based on the fit, we measured the half-life of the ¹¹³Cd \(\beta \) decay including systematic uncertainties as \(7.73^{+0.60}_{-0.57} \times 10^{15}\) yr, in agreement with the previous experiments. These results represent a significant step towards a better understanding of low-energy nuclear processes.