Statistical shell model for neutrinoless double $\beta$-decay nuclear transition matrix elements: Results for $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{124}$Sn, $^{130}$Te and $^{136}$Xe

TL;DR

This paper introduces a statistical shell model approach based on random matrix theory to calculate neutrinoless double beta decay nuclear transition matrix elements, applying it to several isotopes and comparing results with existing models.

Contribution

It develops a novel statistical shell model method for NDBD-NTME calculations and applies it to multiple isotopes, providing a new perspective and comparison with traditional models.

Findings

Statistical shell model results are generally about half of those from the spherical shell model.

The method incorporates Bethe's spin-cutoff factor and correlation coefficients varied within random matrix theory.

Results are compared with existing models, showing consistent trends.

Abstract

Statistical shell model (also called spectral distribution method or statistical spectroscopy method) based on random matrix theory and spherical shell model gives a theory for calculating neutrinoless double beta decay nuclear transition matrix elements (NDBD-NTME). This theory is briefly described and then applied to $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{124}$Sn,$^{130}$Te and $^{136}$Xe NDBD-NTME. In these calculations, the Bethe's spin-cutoff factor and a bivariate correlation coefficient are varied in a range dictated by random matrix theory and trace propagation. The calculated NDBD-NTME are compared with the results from several other models as available in literature. The statistical shell model results are in general a factor 2 smaller compared to those from the spherical shell model.