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In this article we present an updated spectrum-shape analysis of the$^{113}$Cd fourfold forbidden non-unique $\beta$-decay transition in order toaddress the quenching of the weak axial-vector coupling $g_{\rm A}$ inlow-momentum exchange nuclear processes. The experimental data were collectedin a dedicated low-threshold run with the COBRA demonstrator at the LNGS andresulted in 44 individual $^{113}$Cd spectra. These data are evaluated in thecontext of three nuclear model frameworks based on a revised version of thespectrum-shape method and the conserved vector current hypothesis. The novelidea devised in the present work is to fit the value of the small relativisticnuclear matrix element (s-NME) driving the nuclear model calculations, whichremained essentially as a free parameter in previous studies. This is done bytuning the nuclear structure calculations and making use of the interplay of$g_{\rm A}$ and the s-NME such that the experimentally known $^{113}$Cdhalf-life gets reproducible by the different frameworks. In this way, a bestfit s-NME value can be derived for each of the considered nuclear models, whichfinally enters the template calculations used to perform the spectrum-shapeanalysis for each of the obtained $^{113}$Cd spectra. The primary analysisstrategy results in significantly quenched values of the axial-vector couplingfor all three nuclear models: $\overline{g}_{\rm A}(\text{ISM}) = 0.907 \pm0.064$, $\overline{g}_{\rm A}(\text{MQPM}) = 0.993 \pm 0.063$ and$\overline{g}_{\rm A}(\text{IBFM-2}) = 0.828 \pm 0.140$. Moreover, with ourdata-driven approach one of the main shortcomings of the spectrum-shape methodhas been resolved. This achievement is a milestone in the description ofstrongly forbidden $\beta$-decays and adds to the indications for the existenceof a quenching of $g_{\rm A}$ in low-momentum exchange nuclear processes.

physics letters b

Confirmation of $g_{\rm A}$ quenching using the revised spectrum-shape  method for the analysis of the $^{113}$Cd $\beta$-decay as measured with the  COBRA demonstrator