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.

Comments: 17 pages, 5 figures