We develop a manifestly microscopic method to deal with strongly interacting nuclear systems that have different interactions in spin-singlet and spin-triplet states. In a first step we analyze variational wave functions that have been suggested to describe such systems, and demonstrate that the so-called commutator contributions can have important effects whenever the interactions in the spin-singlet and the spin-triplet states are very different. We then identify these contributions as terms that correspond, in the language of perturbation theory, to non-parquet diagrams. We include these diagrams in a way that is suggested by the Jastrow-Feenberg approach and show that the corrections from non-parquet contributions are, at short distances, larger than all other many-body effects.
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