  The Quasiparticle Random Phase Approximation equations are solved taking into
account the Pauli Principle at the expectation value level, and allowing
changes in the mean field occupation numbers to minimize the energy while
having the correct number of particles in the correlated vacuum. The study of
Fermi pn excitations in $^{76}$Ge using a realistic Hilbert space shows that
the pairing energy gaps in the modified mean field are diminished up to one
half of the experimental value when strong proton-neutron correlations are
present. Additionally, the Ikeda sum rule for Fermi transitions is violated due
to the lack of scattering terms in the phonon operators. These results call for
a critical revision of the double beta decay half-lives estimated using the
QRPA extensions when standard QRPA calculations collapse.
