Commutators and twisted chains: A variational approach to spin correlations

We formulate a variational theory that is capable of treating spin-dependent correlation functions and define a systematic hierarchy of hypernetted chain-like approximations. The square of the wave function is assumed to be a symmetrized operator product of central and spin-dependent correlations. A hypernetted chain procedure is introduced that treats the spin-structure of successively larger diagrammatic quantities exactly, and the first three steps in that procedure are carried out explicitly. We find a rather dramatic importance of "twisted chain" diagrams which lower the ground-state energy considerably whenever the interaction has a different core-size in the spin-singlet and the spin-triplet channels.