  We propose a particle number conserving formalism for the treatment of
isovector-isoscalar pairing in nuclei with $N>Z$. The ground state of the
pairing Hamiltonian is described by a quartet condensate to which is appended a
pair condensate formed by the neutrons in excess. The quartets are built by two
isovector pairs coupled to the total isospin $T=0$ and two collective isoscalar
proton-neutron pairs. To probe this ansatz for the ground state we performed
calculations for $N>Z$ nuclei with the valence nucleons moving above the cores
$^{16}$O, $^{40}$Ca and $^{100}$Sn. The calculations are done with two pairing
interactions, one state-independent and the other of zero range, which are
supposed to scatter pairs in time-revered orbits. It is proven that the ground
state correlation energies calculated within this approach are very close to
the exact results provided by the diagonalization of the pairing Hamiltonian.
Based on this formalism we have shown that moving away of N=Z line, both the
isoscalar and the isovector proton-neutron pairing correlations remain
significant and that they cannot be treated accurately by models based on a
proton-neutron pair condensate.
