$g_{\rm A}$-sensitive $\beta$ spectral shapes in the mass $A=86-99$ region assessed by the nuclear shell model

Recent years have witnessed an expanding interest in experimental studies of $\beta$ electrons (electrons emitted in $\beta^-$ decay transitions) and their energy distributions, the so-called $\beta$-electron spectra. These experiments are interested mainly in $\beta$ transitions with electron spectra sensitive to the effective value of the weak axial coupling $g_{\rm A}$. In the present paper we make an extensive search for $g_{\rm A}$ sensitive $\beta$ spectral shapes in the $A=86-99$ region using the nuclear shell model with the well established Hamiltonians $\textit{glekpn}$ and $\textit{jj45pnb}$, designed to render a good description of the spectroscopic properties of nuclei in this mass region. We have found eight $\beta^-$ decay transitions with various degrees of $g_{\rm A}$ sensitivity. Moreover, these transitions are also important in pinning down the value of the so-called small relativistic vector nuclear matrix element, sNME. In addition, some of the corresponding mother nuclei are important contributors to the antineutrino flux from nuclear reactors. All this means that the found $\beta$ transitions are potentially of great interest for future rare-events experiments.