Statistical shell model for neutrinoless double ${\hat{I}}^2$-decay nuclear transition matrix elements: Results for ${}^{76}$Ge, ${}^{82}$Se, ${}^{100}$Mo, ${}^{124}$Sn, ${}^{130}$Te and ${}^{136}$Xe

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.

25 pages, 7 figures, 1 table