Singularities in the Galitskii-Feynman T matrix

The Galitskii-Feynman T matrix, which sums the ladder diagrams for both particle-particle and hole-hole scattering in a many-fermion system, is shown to have a singularity at negative values of the c.m. energy of the interacting pair. The singularity appears as a first-order pole in the T matrix, the position of which is a function of both the density of the system and the total c.m. momentum of the pair, and corresponds to the formation of bound pairs in the medium. The singularity structure exists in two distinct Fermi systems (liquid He³ and nuclear matter), and detailed numerical results are presented using a potential appropriate to liquid He³. The singularity in this case is shown to be present at all densities above a certain critical density which is lower than the physical density.