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

Abstract

Nuclear double $\beta$-decay with two neutrinos is a rare and important process for natural radioactivity of unstable nuclei. The experimental data of nuclear double ${\beta }^{-}$-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 $\beta$-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 $\beta$-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 $\beta$-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 $\beta$-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 $\alpha$-decay and that of double ${\beta }^{-}$-decay are also analyzed and discussed.

15 pages,1 figure. To appear in Physical Review C

References in corpus (4)

• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Precise half-life values for two neutrino double beta decay
• Measurement of the half-life of the two-neutrino double beta decay of Ge-76 with the Gerda experiment
• Double beta decay to the first $2^{+}$ state within a boson expansion formalism with a projected spherical single particle basis

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• Systematic Analysis of Double-Beta Decay Half Lives
• First direct search for $2\epsilon$ and $\epsilon {\beta }^{+}$ decay of ${}^{144}$Sm and $2{\beta }^{-}$ decay of ${}^{154}$Sm
• Radiative and exchange corrections for two-neutrino double-beta decay
• New limits on double-beta decay of ${}^{190}$Pt and ${}^{198}$Pt
• Half-lives of Double ${\beta }^{+}$-decay with Two Neutrinos
• ${\beta }^{-}$-decay half-lives of even-even nuclei using the recently introduced phase space recipe
• A Semi-Empirical Formula for Two-Neutrino Double-Beta Decay