  In the present work the sensitivity of the QRPA calculation results to a
realistic residual interaction is analyzed in the framework of the approach of
Refs. \cite{Rum98,Rodin05}. Both Gamow-Teller (GT) and Fermi (F) \bb-decay
amplitudes $M^{2\nu}$, along with the corresponding energy-weighted sum rules
$S$, are calculated. General expressions relating $S$ to a realistic residual
particle-particle interaction are derived, which show a pronounced sensitivity
of $S$ to the singlet-channel interaction in the case of F transitions, and to
the triplet-channel interaction in the case of GT transitions. Decompositions
of $M^{2\nu}$, as well as the monopole transition contributions to $M^{0\nu}$,
are obtained by the method of Refs. \cite{Rum98,Rodin05}. It is shown that in
most of the cases almost the whole dependence of $M^{2\nu}$ and $M^{0\nu}$ on
the particle-particle renormalization parameter $g_{pp}$ is accounted for by
the $g_{pp}$-dependence of the corresponding sum rules $S$. Thus, the
$g_{pp}$-sensitivity of calculated $M^{2\nu}$ and $M^{0\nu}$ is unavoidable
since it is dictated by the generic structure of the $\beta\beta$ amplitudes.
Finally, a better isospin-consistent way of a renormalization of the realistic
residual particle-particle interaction to use in QRPA calculations is
suggested.
