  A new model, based on the BCS approach, is specially designed to describe
nuclear phenomena $(A,Z)\rightarrow (A,Z\pm 2)$ of double-charge exchange
(DCE). After being proposed, and applied in the particle-hole limit, by one of
the authors (F. Krmpoti\'c [1]), so far it was never been applied within the
BCS mean-field framework, nor has its ability to describe DCE processes been
thoroughly explored. It is a natural extension of the pn-QRPA model, developed
by Halbleib and Sorensen [2] to describe the single $\beta$-decays
$(A,Z)\rightarrow (A,Z\pm 1)$, to the DCE processes. As such, it exhibits
several advantages over the pn-QRPA model when is used in the evaluation of the
double beta decay (DBD) rates. For instance, i) the extreme sensitivity of the
nuclear matrix elements (NMEs) on the model parametrization does not occur, ii)
it allows to study NMEs, not only for the fundamental state in daughter nuclei,
as the pn-QRPA model does, but also for all final $0^+$ and $2^+$ states,
accounting at the same time their excitation energies and the corresponding DBD
Q-values, iii) together with the DBD-NMEs it provides also the energy spectra
of Fermi and Gamow-Teller DCE transition strengths, as well as the locations of
the corresponding resonances and their sum rules, iv) the latter are relevant
for both the DBD and the DCE reactions, since the involved nuclear structure is
the same; this correlation does not exist within the pn-QRPA model. As an
example, detailed numerical calculations are presented for the
$(A,Z)\rightarrow (A,Z+ 2)$ process in $^{48}$Ca $\rightarrow ^{48}$Ti and the
$(A,Z)\rightarrow (A,Z- 2)$ process in $^{96}$Ru $\rightarrow ^{96}$Mo,
involving all final $0^+$ states and $2^+$ states.
