Possible detection of the doubleβ+/electron-capture decay

The two-neutrino double β decay matrix elements of ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{96}{}_{}{}^{}\mathrm{Ru}$, ${}_{}{}^{106}{}_{}{}^{}\mathrm{Cd}$, and ${}_{}{}^{136}{}_{}{}^{}\mathrm{Ce}$ are calculated in the framework of the quasiparticle random phase approximation and the corresponding double ${\mathrm{\beta }}^{+}$/electron-capture (EC) decay (${\mathrm{\beta }}^{+}$ ${\mathrm{\beta }}^{+}$/${\mathrm{\beta }}^{+}$EC/ECEC) half-lives are estimated. The calculated ground-state-to-ground-state half-lives range from 3.9×${10}^{23}$ to 6.4×${10}^{19}$ yr indicating that the double ${\mathrm{\beta }}^{+}$/EC decay could, in principle, be detected using currently known experimental techniques.