Yuejiao Ren | Searcharxiv

arXiv2015

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.

nucl-th↗

arXiv2014

Systematic Law for Half-lives of Double $β$-decay with Two Neutrinos

Nuclear double $β$-decay with two neutrinos is a rare and important process for natural radioactivity of unstable nuclei. The experimental data of nuclear double $β^{-}$-decay with two neutrinos are analyzed and a systematic law to calculate the half-lives of this rare process is proposed. It is the first analytical and simple formula for double $β$-decay half-lives where the leading effect from both the Coulomb potential and nuclear structure is included. The systematic law shows that the logarithms of the half-lives are inversely proportional to the decay energies for the ground state transitions between parent nuclei and daughter nuclei. The calculated half-lives are in agreement with the experimental data of all known eleven nuclei with an average factor of 3.06. The half-lives of other possible double $β$-decay candidates with two neutrinos are predicted and these can be useful for future experiments. The law, without introducing any extra adjustment, is also generalized to the calculations of double $β$-decay half-lives from the ground states of parent nuclei to the first $0^+$ excited states of daughter nuclei and the calculated half-lives agree very well with the available data. Some calculated half-lives are the first theoretical results of double $β$-decay half-lives from the ground states of parent nuclei to the first $0^+$ excited states of daughter nuclei. The similarity and difference between the law of $α$-decay and that of double $β^{-}$-decay are also analyzed and discussed.

nucl-th↗