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

TL;DR

This study calculates nuclear matrix elements for neutrinoless double-beta decay in several isotopes using a triaxial projected shell model, highlighting the effects of deformation and configuration mixing on decay rates.

Contribution

It introduces a comprehensive method incorporating triaxial deformation and quasiparticle mixing to improve nuclear matrix element calculations for double-beta decay.

Findings

Quasiparticle configuration mixing reduces matrix elements by 2-7%.

Odd-odd intermediate states increase matrix elements by 4-20%.

Triaxial deformation significantly affects matrix elements, especially in $^{150}$Nd.

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 $B(E2:0^+\rightarrow2^+)$ 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.