Half-lives of Double $β^+$-decay with Two Neutrinos

Nuclear double $β^-$-decays with two neutrinos were observed for many years and a systematic law describing the relation between their half-lives and decay energies was also proposed recently [Phys. Rev. C89, 064603 (2014)]. However, double $β^+$-decay ($β^+β^+)$ with emission of both two positrons and two neutrinos has not been observed up to date. In this article, we perform a systematic analysis on the candidates of double $β^+$-decay, based on the 2012 nuclear mass table. Eight nuclei are found to be the good candidates for double $β^+$-decay and their half-lives are predicted according to the generalization of the systematic law to double $β^+$-decay. As far as we know, there is no theoretical result on double $β^+$-decay of nucleus $^{154}Dy$ and our result is the first prediction on this nucleus. This is also the first complete research on eight double $β^+$-decay candidates based on the available data of nuclear masses. It is expected that the calculated half-lives of double $β^+$-decay in this article will be useful for future experimental search of double $β^+$-decay.

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