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

TL;DR

This study investigates the uncertainties in nuclear matrix elements for neutrinoless double beta decay using a self-consistent QRPA approach with various Skyrme interactions, highlighting the importance of pairing interactions.

Contribution

It provides a systematic analysis of how different pairing interactions affect NME calculations in the QRPA framework for multiple isotopes.

Findings

NMEs are less sensitive to particle-hole interactions.

Strong dependence of NMEs on isovector pairing interactions.

Precise isovector pairing is crucial to reduce uncertainties.

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.