Structure of the quartetting ground state of $$N=Z$$ N = Z nuclei

The formal equivalence between the quartetting picture and the symmetry restored BCS picture is established for the ground state correlations induced by the general isovector-isoscalar pairing interaction. Multiple ground state structures compatible with the particle number and isospin symmetries are evaluated. The competition of isovector and isoscalar correlations is discussed for the $$N=Z$$ nuclei above $$^{100}$$ Sn.