  Isoscalar (T=0,J=1) and isovector (T=1,J=0) pairing correlations in the
ground state of self-conjugate nuclei are treated in terms of alpha-like
quartets built by two protons and two neutrons coupled to total isospin T=0 and
total angular momentum J=0. Quartets are constructed dynamically via an
iterative variational procedure and the ground state is represented as a
product of such quartets. It is shown that the quartet formalism describes
accurately the ground state energies of realistic isovector plus isoscalar
pairing Hamiltonians in nuclei with valence particles outside the 16O, 40Ca and
100Sn cores. Within the quartet formalism we analyse the competition between
isovector and isoscalar pairing correlations and find that for nuclei with the
valence nucleons above the cores 40Ca and 100Sn the isovector correlations
account for the largest fraction of the total pairing correlations. This is not
the case for sd-shell nuclei for which isoscalar correlations prevail. Contrary
to many mean-field studies, isovector and isoscalar pairing correlations mix
significantly in the quartet approach.
