Accurate shell-model nuclear matrix elements for neutrinoless double-beta decay

Abstract

We investigate a novel method of accurate calculation of the neutrinoless double-$\beta$ decay shell-model nuclear matrix elements for the experimentally relevant case of ${}^{76}$Ge. We demonstrate that with the new method the nuclear matrix elements have perfect convergence properties and, using only the first 100 intermediate states of each spin, the matrix elements can be calculated with better than 1% accuracy. Based on the analysis of neutrinoless double-beta decays of ${}^{48}$Ca, ${}^{82}$Se, and ${}^{76}$Ge isotopes, we propose a new method to estimate the optimal values of the average closure energies at which the closure approximation gives the most accurate nuclear matrix elements. We also analyze the nuclear matrix elements for the heavy-neutrino-exchange mechanism, and we show that our method can be used to quench contributions from different intermediate spin states.

5 pages, 3 figures, 1 table

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Cited by in corpus (6)

• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Shell model studies of the ${}^{130}Te$ neutrinoless double-beta decay
• Nuclear matrix element of neutrinoless double-$\beta$ decay: Relativity and short-range correlations
• Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method
• Deformed shell model results for neutrinoless double beta decay of nuclei in A=60-90 region
• Imperfect World of $\beta \beta$-decay Nuclear Data Sets?