GA -driven shapes of electron spectra of forbidden β decays in the nuclear shell model

Abstract

The evolution of the shape of the electron spectra of 16 forbidden ${\ensuremath{\beta}}^{\ensuremath{-}}$ decays as a function of ${g}_{\mathrm{A}}$ was studied using the nuclear shell model in appropriate single-particle model spaces with established, well-tested nuclear Hamiltonians. The $\ensuremath{\beta}$ spectra of $^{94}\mathrm{Nb}({6}^{+})\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{94}\mathrm{Mo}({4}^{+})$ and $^{98}\mathrm{Tc}({6}^{+})\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{98}\mathrm{Ru}({4}^{+})$ were found to depend strongly on ${g}_{\mathrm{A}}$, which makes them excellent candidates for the determination of the effective value of ${g}_{\mathrm{A}}$ with the spectrum-shape method (SSM). A strong ${g}_{\mathrm{A}}$ dependence is also seen in the spectrum of $^{96}\mathrm{Zr}({0}^{+})\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}^{96}\mathrm{Nb}({6}^{+})$. This decay could be used for determining the quenching of ${g}_{\mathrm{A}}$ in sixth-forbidden decays in the future, when the measurement of the spectrum becomes experimentally feasible. The calculated shell-model electron spectra of the ground-state-to-ground-state decays of $^{87}\mathrm{Rb}$, $^{99}\mathrm{Tc}$, and $^{137}\mathrm{Cs}$ and the decay of $^{137}\mathrm{Cs}$ to the isomeric $11/{2}^{\ensuremath{-}}$ state in $^{137}\mathrm{Ba}$ were found to be in excellent agreement with the spectra previously calculated using the microscopic quasiparticle-phonon model. This is further evidence of the robust nature of the SSM observed in the previous studies.