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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 asheavy Majorana neutrinos, and classical Majorons by considering the spin-tensordecomposition of realistic KUO and empirical JUN45 effective two-bodyinteraction. 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 andheavy Majorana neutrinos, respectively, is maximally incorporated by thecentral part of the effective two-body interaction, which varies by a smallamount with the inclusion of spin-orbit and tensor components. The maximumuncertainty in the average NTMEs $\overline{M}^{(0\nu)}$ and$\overline{M}^{(0N)}$ turns out to be about 10\% and 37\%, respectively.

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