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Recent years have witnessed an expanding interest in experimental studies of$\beta$ electrons (electrons emitted in $\beta^-$ decay transitions) and theirenergy distributions, the so-called $\beta$-electron spectra. These experimentsare interested mainly in $\beta$ transitions with electron spectra sensitive tothe effective value of the weak axial coupling $g_{\rm A}$. In the presentpaper we make an extensive search for $g_{\rm A}$ sensitive $\beta$ spectralshapes in the $A=86-99$ region using the nuclear shell model with the wellestablished Hamiltonians $\textit{glekpn}$ and $\textit{jj45pnb}$, designed torender a good description of the spectroscopic properties of nuclei in thismass region. We have found eight $\beta^-$ decay transitions with variousdegrees of $g_{\rm A}$ sensitivity. Moreover, these transitions are alsoimportant in pinning down the value of the so-called small relativistic vectornuclear matrix element, sNME. In addition, some of the corresponding mothernuclei are important contributors to the antineutrino flux from nuclearreactors. All this means that the found $\beta$ transitions are potentially ofgreat interest for future rare-events experiments.

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