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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• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Shell model predictions for ${}^{124}$Sn double-beta decay
• Ab initio neutrinoless double-beta decay matrix elements for 48Ca, 76Ge, and 82Se
• Neutrinoless $\beta \beta$ decay mediated by the exchange of light and heavy neutrinos: The role of nuclear structure correlations
• Shell model studies of the ${}^{130}Te$ neutrinoless double-beta decay
• The $0\nu \beta \beta$-decay nuclear matrix element for light and heavy neutrino mass mechanisms from deformed QRPA cacluations for ${}^{76}$Ge, ${}^{82}$Se, ${}^{130}$Te, ${}^{136}$Xe and ${}^{150}$Nd with isospin restoration
• Nuclear matrix element of neutrinoless double-$\beta$ decay: Relativity and short-range correlations
• Precision Analysis of the ${}^{136}$Xe Two-Neutrino $\beta \beta$ Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements
• $0\nu \beta \beta$ nuclear matrix elements, neutrino potentials and $\mathrm{SU}(4)$ symmetry
• Neutrinoless double-beta decay matrix elements in large shell-model spaces with the generator-coordinate method
• Shell-model calculation of neutrinoless double-$\beta$ decay of ${}^{76}$Ge
• Analysis of mechanisms that could contribute to the neutrinoless double-beta decay
• Neutrinoless $\beta \beta$-decay nuclear matrix elements from two-neutrino $\beta \beta$-decay data
• QCD running in neutrinoless double beta decay: Short-range mechanisms
• Shell model study on the possibility of using an effective field theory for disentangling several contributions to the neutrinoless double-beta decay
• A Statistical Analysis for the Neutrinoless Double-Beta Decay Matrix element of 48Ca
• Probing flavor models with Ge-76-based experiments on neutrinoless double-beta decay
• Predicting the neutrinoless double-beta decay matrix element of ${}^{136}$Xe using a statistical approach
• Correlations Between Neutrinoless Double-Beta, Double Gamow-Teller and Double-Magnetic Decays in the pnQRPA Framework
• Neutrinoless $\beta \beta$ decay nuclear matrix elements complete up to N${}^2$LO in heavy nuclei
• Nuclear matrix elements for $\lambda$ mechanism of $0\nu \beta \beta$ of ${}^{48}$Ca in nuclear shell-model: Closure versus nonclosure approach
• 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?
• Nuclear matrix elements calculation for $0\nu \beta \beta$ decay of ${}^{124}$Sn using nonclosure approach in nuclear shell model
• Neutrinoless Double-Beta Decay and Realistic Shell Model
• The study of $0\nu \beta \beta$ decay of ${}^{136}$Xe using nonclosure approach in nuclear shell model
• Neutrinoless $\beta \beta$-Decay in DCEQTDA