In this paper the Galitskii–Migdal–Feynman (GMF) formalism is applied to dilute 3He-HeII mixtures. In particular, the effect of the hole-hole scattering on pairing in these systems is investigated. To this end, the relative phase shifts incorporating many-body effects based on both Brueckner–Bethe–Goldstone (BBG) and GMF formalisms are calculated. In the GMF formalism, the S-wave phase shift at zero relative momentum is –π and has a cusp at the Fermi momentum; while in the BBG formalism, this phase shift has zero values up to the Fermi momentum. From these results we conclude that hole-hole scattering plays a crucial role in any possible fermion-fermion pairing in these systems.

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The Galitskii Feynman T matrix, which sums the infinite ladder series in a many-fermion system .['or both particle~article and hole-hole scattering, is studied in detail for a family of realistic He-He interactions. The structure of the S-wave bound-state singularity, reported previously, and its dependence on the bare interaction are documented at length. Special attention is detoted to the T matrix in the scattering region, where the c.m. energy of the interacting pair is positive. In particular, the on-energy-shell T matrix in this region is parametrized in terms of real -effecti~,e" phase shifts incorporating many-body effects. The critical behavior discussed previously in the bound-state region manifests itself clearly in the zero-energy limit of these phase shifts for the S wave. Below (abot, e) a certain critical denszty, which is a fimction of both temperature and c.m. momentum, this limit approaches the t, alue O( -7r) radians. A generalized Let'inson's theorem relates this behavior to the existence of fermion-fermion pairing. An especially striking feature of these many-body phase shifts is the cusp behat, ior exhibited at the Fermi szoface in the lowtemperature limit, which turns out to arise essentially ft'om the structure of the particle and hole occupation probabilities. Throughout this stud)' the temperature dependence of the T matrix is particularly emphasized.

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