  We analyze the role of maximally aligned isoscalar pairs in heavy $N=Z$ nuclei by employing a formalism of quartets. Quartets are superpositions of two neutrons and two protons coupled to total isospin $T=0$ and given $J$. The study is focused on the contribution of spin-aligned pairs carrying the angular momentum $J=9$ to the structure of $^{96}$Cd and $^{92}$Pd. We show that the role played by the $J=9$ pairs is quite sensitive to the model space and, in particular, it decreases considerably by passing from the simple $0g_{9/2}$ space to the more complete $1p_{1/2}$,$1p_{3/2}$,$0f_{5/2}$,$0g_{9/2}$ space. In the latter case the description of these nuclei in terms of only spin-aligned $J=9$ pairs turns out to be unsatisfactory while an important contribution, particularly in the ground state, is seen to arise from isovector $J=0$ and isoscalar $J=1$ pairs. Thus, contrary to previous studies, we find no compelling evidence of a spin-aligned pairing phase in $^{92}$Pd. 
Quarteting and spin-aligned proton-neutron pairs in heavy N=Z nuclei