  We give for the first time, theoretical estimates of
ground-state-to-ground-state (GS-to-GS) electron-capture (EC) branch decay
rates of $^{44}$Ti, $^{57}$Co, and $^{139}$Ce. The nuclear-structure
calculations have been done exploiting the nuclear shell model (NSM) with
well-established Hamiltonians and an advanced theory of $\beta$ decay. In the
absence of experimental measurements of these GS-to-GS branches, these
estimates are of utmost importance for terrestrial searches of axion-like
particles (ALPs). Predictions are made for EC-decay rates of 2$^{nd}$-forbidden
unique (FU) and 2$^{nd}$-forbidden non-unique (FNU) EC transitions that can
potentially mimic nuclear axion production in experiments designed to detect
ALPs in nuclear environments.
