Systematic Law for Half-lives of Double $β$-decay with Two Neutrinos
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ID: 283535
2014
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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.
| Reference Key |
ren2014systematic
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| Authors | Yuejiao Ren; Zhongzhou Ren |
| Journal | arXiv |
| Year | 2014 |
| DOI |
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