Electron spectra in forbiddenβdecays and the quenching of the weak axial-vector coupling constantgA

Abstract

Evolution of the electron spectra with the effective value of the weak axial-vector coupling constant ${g}_{\mathrm{A}}$ was followed for 26 first-, second-, third-, fourth- and fifth-forbidden ${\ensuremath{\beta}}^{\ensuremath{-}}$ decays of odd-$A$ nuclei by calculating the involved nuclear matrix elements (NMEs) in the framework of the microscopic quasiparticle-phonon model (MQPM). The next-to-leading-order terms were included in the $\ensuremath{\beta}$-decay shape factor of the electron spectra. The spectrum shapes of third- and fourth-forbidden nonunique decays were found to depend strongly on the value of ${g}_{\mathrm{A}}$, while first- and second-forbidden decays were mostly unaffected by the tuning of ${g}_{\mathrm{A}}$. The ${g}_{\mathrm{A}}$-driven evolution of the normalized $\ensuremath{\beta}$ spectra was found to be quite universal, largely insensitive to the small changes in the nuclear mean field and the adopted residual many-body Hamiltonian producing the excitation spectra of the MQPM. This makes the comparison of experimental and theoretical electron spectra, coined ``the spectrum-shape method'' (SSM), a robust tool for extracting information on the effective values of the weak coupling constants. In this exploratory work two new experimentally interesting decays for the SSM treatment were discovered: the ground-state-to-ground-state decays of $^{99}\mathrm{Tc}$ and $^{87}\mathrm{Rb}$. Comparing the experimental and theoretical spectra of these decays could shed light on the effective values of ${g}_{\mathrm{A}}$ and ${g}_{\mathrm{V}}$ for second- and third-forbidden nonunique decays. The measurable decay transitions of $^{135}\mathrm{Cs}$ and $^{137}\mathrm{Cs}$, in turn, can be used to test the SSM in different many-body formalisms. The present work can also be considered as a (modest) step towards solving the ${g}_{\mathrm{A}}$ problem of the neutrinoless double beta decay.