$0\nu\beta\beta$ nuclear matrix elements and the occupancy of individual orbits

TL;DR

This paper refines calculations of neutrinoless double beta decay nuclear matrix elements by adjusting mean field energies based on experimental orbit occupancies, leading to reduced matrix element estimates closer to shell model results.

Contribution

It introduces a method to modify mean field energies using experimental occupancies within the SRQRPA framework, improving the accuracy of nuclear matrix element calculations for double beta decay.

Findings

Reduced $0 uetaeta$ matrix element for $^{76}$Ge by ~25%.

Matrix elements for $^{82}$Se also decreased, aligning better with shell model.

Enhanced agreement between QRPA and shell model predictions.

Abstract

The measured occupancies of valence orbits in $^{76}$Ge and $^{76}$Se are used as a guideline for modification of the effective mean field energies that results in better description of these quantities. With them, in combination with the selfconsitent renormalized quasiparticle random phase approximation (SRQRPA) method that ensures conservation of the mean particle number in the correlated ground state, we show that the resulting $0\nu\beta\beta$ nuclear matrix element for the $^{76}$Ge $\to$ $^{76}$Se transition is reduced by $\sim$25% compared to the previous QRPA value, and therefore the difference between the present approach and the interacting shell model predictions becomes correspondingly smaller. Analogous modification of the mean field energies for the A=82 system also results in a reduction of $0\nu\beta\beta$ matrix element for the $^{82}$Se $\to$ $^{82}$Kr transition, making it also closer to the shell model prediction.