The occupancies of individual orbits and the nuclear matrix element of the $^{76}$Ge neutrinoless $\beta\beta$ decay

TL;DR

This paper investigates how constraining nuclear wave functions to match experimental occupancies affects the nuclear matrix element calculations for neutrinoless double beta decay of Ge-76, revealing approach-dependent variations and reducing discrepancies.

Contribution

It demonstrates that constraining wave functions to experimental occupancies alters NME values, reducing differences between the Interacting Shell Model and QRPA methods.

Findings

Interacting Shell Model NME increases by ~15%.

QRPA NME decreases by 20-30%.

Short-range correlations impact NME calculations.

Abstract

We discuss the variation of the nuclear matrix element (NME) for the neutrinoless double beta ($0\nu\beta\beta$) decay of $^{76}$Ge when the wave functions are constrained to reproduce the experimental occupancies of the two nuclei involved in the transition. In the Interacting Shell Model description the value of the NME is enhanced about 15% compared to previous calculations, whereas in the QRPA the NME's are reduced by 20%-30%. This diminishes the discrepancies between both approaches. In addition, we discuss effect of the short range correlations on the NME in the light of the recently proposed parametrizations based on a consistent renormalization of the $0\nu\beta\beta$ transition operator.