Constraints for rare electron-capture decays mimicking detection of dark-matter particles in nuclear transitions

We give for the first time, theoretical estimates of unknown rare electron-capture (EC) decay branchings of $^{44}$Ti, $^{57}$Co, and $^{139}$Ce, relevant for searches of (exotic) dark-matter particles. 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 rare branches, these estimates are of utmost importance for terrestrial searches of dark-matter particles, such as axionic dark matter in the form of axion-like particles (ALPs), anapole dark matter, and dark photons in nuclear transitions. 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 dark-matter-particle detection in dedicated underground experiments designed to observe the absence of the corresponding nuclear electromagnetic transitions.