The $0\nu\beta\beta$-decay nuclear matrix element for light and heavy neutrino mass mechanisms from deformed QRPA cacluations for $^{76}$Ge, $^{82}$Se, $^{130}$Te, $^{136}$Xe and $^{150}$Nd with isospin restoration

TL;DR

This study calculates neutrinoless double beta decay nuclear matrix elements for several isotopes using deformed QRPA with isospin restoration, revealing significant reductions and force-dependent variations in the results.

Contribution

It provides detailed deformed QRPA calculations of NMEs with isospin restoration for multiple isotopes, including decompositions and force comparisons, advancing understanding of decay mechanisms.

Findings

Reductions of 30-60% in NMEs compared to spherical models.

Force choice causes about 20% variation for light neutrino exchange.

Larger deviations observed for heavy neutrino exchange.

Abstract

In this work, with restored isospin symmetry, we evaluated the neutrinoless double beta decay nuclear matrix elements for $^{76}$Ge, $^{82}$Se, $^{130}$Te, $^{136}$Xe and $^{150}$Nd for both the light and heavy neutrino mass mechanisms using the deformed QRPA approach with realistic forces. We give detailed decompositions of the nuclear matrix elements over different intermediate states and nucleon pairs, and discuss how these decompositions are affected by the model space truncations. Compared to the spherical calculations, our results show reductions from $30\%$ to about $60\%$ of the nuclear matrix elements for the calculated isotopes mainly due to the presence of BCS overlap factor between the initial and final ground states. The comparison between different nucleon-nucleon forces with corresponding Short-Range-Correlations (src) shows, that the choice of the NN force gives roughly $20\%$ deviations for light exchange neutrino mechanism and much larger deviations for the heavy neutrino exchange mechanism.