Spin-tensor decomposition of nuclear transition matrix elements for neutrinoless double-${\hat{I}}^2$ decay of ${}^{76}$Ge and ${}^{82}$Se nuclei within PHFB approach

Abstract

Employing the PHFB model, nuclear transition matrix elements $M^{\left(K\right)}$ for the neutrinoless double-$β^{-} $ decay of ${}^{76}$Ge and ${}^{82}$Se isotopes are calculated within mechanisms involving light as well as heavy Majorana neutrinos, and classical Majorons by considering the spin-tensor decomposition of realistic KUO and empirical JUN45 effective two-body interaction. It is noticed that the effects due to the SRC on NTMEs $M^{\left(0\hat{I}½\right)}$ and $M^{\left(0N\right)}$ due to the exchange of light and heavy Majorana neutrinos, respectively, is maximally incorporated by the central part of the effective two-body interaction, which varies by a small amount with the inclusion of spin-orbit and tensor components. The maximum uncertainty in the average NTMEs ${\overline{M}}^{(0\hat{I}½)}$ and ${\overline{M}}^{(0N)}$ turns out to be about 10\% and 37\%, respectively.