Shell model studies of the ${}^{130}Te$ neutrinoless double-beta decay

Abstract

Most uncertainties regarding the theoretical study of the neutrinoless double-beta decay are related to the accuracy of the nuclear matrix elements that appear in the expressions of the lifetimes. We calculate the nuclear matrix elements for the $0\nu \beta \beta$ decay of ${}^{130}Te$ in a shell model approach, using a recently proposed effective Hamiltonian. To ensure the reliability of the results, we investigate this Hamiltonian by performing calculations of spectroscopic quantities and comparing them to the latest experimental data available, and we analyze the $2\nu \beta \beta$ and the $0\nu \beta \beta$ decay nuclear matrix elements of ${}^{136}$Xe. Finally, we report new nuclear matrix for the ${}^{130}$Te considering the light neutrino exchange and heavy neutrino exchange mechanisms, alongside with an overview of some recent values reported in the literature.

10 pages, 14 figures, 4 tables

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• Value of the axial-vector coupling strength in $\beta$ and $\beta \beta$ decays: A review
• 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
• Shell-model calculation of ${}^{100}$Mo double-$\beta$ decay
• Rearrangement of valence neutrons in the neutrinoless double-$\beta$ decay of ${}^{136}$Xe
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to 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
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• Neutrinoless Double-Beta Decay and Realistic Shell Model