$0\nu \beta \beta$-decay nuclear matrix elements in self-consistent Skyrme quasiparticle random phase approximation: uncertainty from pairing interaction

Abstract

The uncertainty in the nuclear matrix elements (NMEs) of $0\nu \beta \beta$ decay for ${}^{76}$Ge, ${}^{82}$Se, ${}^{128}$Te, ${}^{130}$Te, and ${}^{136}$Xe in the self-consistent quasiparticle random phase approximation (QRPA) method is investigated by using eighteen Skyrme interactions supplemented with either a volume- or surface-type of pairing interactions. The NMEs for the isotopes concerned (except ${}^{136}$Xe) are less sensitive to the particle-hole ($ph$) interactions, while strongly dependent on the employed isovector particle-particle ($pp$) pairing interactions even though the pairing strengths are optimized to the same pairing gap. The results indicate that a precise determination of the isovector $pp$ pairing interaction in the Skyrme energy density functional is of importance to reduce the uncertainty in the NMEs within the QRPA framework.

7 pages, 5 figures