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

Abstract Highly forbidden $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> 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- $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> decay process. There are only 3 nuclei ( 50 V, 113 Cd, 115 In) which undergo a $$4^\textrm{th}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>4</mml:mn> <mml:mtext>th</mml:mtext> </mml:msup> </mml:math> forbidden non-unique $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> decay. In this work, we compare the experimental 113 Cd 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 $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> spectrum of 113 Cd embedded in a 0.43 kg $$\hbox {CdWO}_4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mtext>CdWO</mml:mtext> <mml:mn>4</mml:mn> </mml:msub> </mml:math> 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, $$g_A^{\text {eff}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>A</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msubsup> </mml:math> , which resulted in $$g_A^{\text {eff}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>g</mml:mi> <mml:mi>A</mml:mi> <mml:mtext>eff</mml:mtext> </mml:msubsup> </mml:math> between 1.0 and 1.2, compatible with a possible quenching. Based on the fit, we measured the half-life of the 113 Cd $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> decay including systematic uncertainties as $$7.73^{+0.60}_{-0.57} \times 10^{15}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>7</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mn>73</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>0.57</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.60</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>15</mml:mn> </mml:msup> </mml:mrow> </mml:math> yr, in agreement with the previous experiments. These results represent a significant step towards a better understanding of low-energy nuclear processes.