Nuclear matrix elements of neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay in the triaxial projected shell model
Y. K. Wang, P. W. Zhao, Jie Meng
Abstract
The nuclear matrix elements of neutrinoless double-$\ensuremath{\beta}$ decay for nuclei $^{76}\mathrm{Ge}$, $^{82}\mathrm{Se}$, $^{100}\mathrm{Mo}$, $^{130}\mathrm{Te}$, and $^{150}\mathrm{Nd}$ are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation and quasiparticle configuration mixing. The low-lying spectra, the $B(E2:{0}^{+}\ensuremath{\rightarrow}{2}^{+})$ values, and the occupancies of single-particle orbits 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 $^{76}\mathrm{Ge}$, $^{82}\mathrm{Se}$, $^{100}\mathrm{Mo}$, $^{130}\mathrm{Te}$, and $^{150}\mathrm{Nd}$, the nuclear matrix elements are respectively reduced by the quasiparticle configuration mixing by 6%, 7%, 2%, 3%, and 4%, and enhanced by calculating explicitly the transitions through odd-odd intermediate states by 7%, 4%, 11%, 20%, and 14%. Varying the triaxial deformation $\ensuremath{\gamma}$ from ${0}^{\ensuremath{\circ}}$ to ${60}^{\ensuremath{\circ}}$ for the mother and daughter nuclei, the nuclear matrix elements change by 41%, 17%, 68%, 14%, and 511%, respectively, for $^{76}\mathrm{Ge}$, $^{82}\mathrm{Se}$, $^{100}\mathrm{Mo}$, $^{130}\mathrm{Te}$, and $^{150}\mathrm{Nd}$, which indicates the importance of treating the triaxial deformation consistently in calculating the nuclear matrix elements.