Electron gas with a strong pairing interaction:  Three-particle correlations and the Thouless instability

We derive simplified Faddeev-type equations for the three-particle T-matrix which are valid in the Hubbard model where only electrons with opposite spins interact. Using the approximation of dynamical mean-field theory these equations are partially solved numerically for the attractive Hubbard model. It is shown that the three-particle T matrix contains a term vanishing ∼T² at the Thouless (or BCS) instability where the two-particle T matrix diverges. Based on the three-particle term we further derive the low-density–strong-coupling extension for the two-particle vertex function. The resulting equations are discussed numerically and we understand our equations as a step towards a systematic low-density expansion from the weak-coupling BCS theory towards the stronger coupling limit.