The measurement of the ${}^{99}$Tc $\beta$-decay spectrum and its implications for the effective value of weak axial coupling

Measurements of $\beta$-spectral shapes is an important way to examine the effective value of the weak axial coupling $g_{\mathrm{A}}$. These stu\ dies focus specifically on forbidden non-unique ${\beta }^{-}$ transitions, as only in these cases is the spectral shape directly sensitive to th\ e ratio $g_{\mathrm{A}}\mathrm{/}{g}_{\mathrm{V}}$. Here, the value of the weak vector coupling constant, $g_{\mathrm{V}}$, is fixed at 1.0 according to the Conserve\ d Vector Current (CVC) hypothesis. In previous studies for the fourth-forbidden non-unique ${\beta }^{-}$ decays of ${}^{113}$Cd [J.~Kostensalo $\mathit{\text{et}}\mathit{\text{al.}}$, Phys. Lett. B 822, 136652 (2021)] and ${}^{115}$In [A.~F. Leder $\mathit{\text{et}}\mathit{\text{al.}}$, Phys. Rev. Lett. 129, 232502 \ (2022) and L. Pagnanini $\mathit{\text{et}}\mathit{\text{al.}}$, Phys. Rev. Lett. 133, 122501 (2024)] a quenched value was determined for the ratio $g_{\mathrm{A}}\mathrm{/}{g}_{\mathrm{V}}$ using $g_{\mathrm{V}}=1.0$. A notable exception is the recent measurement and analysis of the second-forbidden non-unique $\beta$-decay transition in ${}^{99}$Tc, performed by M. Paulsen $\mathit{\text{et}}\mathit{\text{al.}}$, Phys. Rev. C 110, 05503(2024). Where an enhanced ratio $g_{rmA}\mathrm{/}{g}_{\mathrm{V}}=1.526(92)$ was suggested. To resolve this apparently contradictory situation with the effective value of $g_{\mathrm{A}}$, we hav\ e performed calculations based on the nuclear shell model (NSM) Hamiltonians glekpn, jj45pnb, and the MQPM approach with a careful considera\ tion of the small relativistic vector nuclear matrix element (sNME). The theoretical spectra were compared to the ${}^{99}$Tc $\beta$-decay sp\ ectrum by using the 4$\pi$ gold absorber with a Metallic Magnetic Calorimeter (MMC). In all cases, we found that the data matches well with \ reduced $g_{\mathrm{A}}$/$g_{\mathrm{V}}$ values of 1.0–1.2. Our result contradicts the previously reported measurement for ${}^{99}$Tc and instead sup\ ports a quenched axial coupling as reported for other isotopes.