Nuclear matrix elements of neutrinoless double-$\beta$ decay in the triaxial projected shell model

Abstract

The nuclear matrix elements of neutrinoless double-$\beta$ decay for nuclei ${}^{76}$Ge, ${}^{82}$Se, ${}^{100}$Mo, ${}^{130}$Te, and ${}^{150}$Nd are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation and quasiparticle configuration mixing. The low-lying spectra and the $B(E2:0^{+}\to 2^{+})$ values are reproduced well. The effects of the quasiparticles configuration mixing, the triaxial deformation, and the closure approximation on the nuclear matrix elements are studied in detail. For nuclei ${}^{76}$Ge, ${}^{82}$Se, ${}^{100}$Mo, ${}^{130}$Te, and ${}^{150}$Nd, the nuclear matrix elements are respectively reduced by the quasiparticle configuration mixing by 6%, 7%, 2%, 3%, and 4%, and enhanced by the odd-odd intermediate states by 7%, 4%, 11%, 20%, and 14%. Varying the triaxial deformation $\gamma$ from $0^{\circ }$ to $60^{\circ }$ for the mother and daughter nuclei, the nuclear matrix elements change by 41%, 17%, 68%, 14%, and 511% respectively for ${}^{76}$Ge, ${}^{82}$Se, ${}^{100}$Mo, ${}^{130}$Te, and ${}^{150}$Nd, which indicates the importance of treating the triaxial deformation consistently in calculating the nuclear matrix elements.

17 pages, 5 figures

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• Unraveling the $0\nu \beta \beta$ Decay Mechanisms
• Ab initio studies of double Gamow-Teller transition and its correlation with neutrinoless double beta decay
• Relativistic configuration-interaction density functional theory: Nonaxial effects on nuclear $\beta \beta$ decay
• Neutrinoless double-$\beta$ decay and double Gamow-Teller transitions
• Shape transition of Nd and Sm isotopes and neutrinoless double-beta decay nuclear matrix element of ${}^{150}$Nd
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Multireference covariant density-functional theory for the low-lying states of odd-mass nuclei
• Impact of isovector pairing fluctuation on neutrinoless double-beta decay in multi-reference covariant density functional theory
• Subspace-projected multireference covariant density functional theory