Spin-tensor decomposition of nuclear transition matrix elements for neutrinoless double-$β$ 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-$\beta^{-} $ 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 $M^{\left( 0\nu \right) }$ 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 $\overline{M}^{(0\nu)}$ and $\overline{M}^{(0N)}$ turns out to be about 10\% and 37\%, respectively.