Pairing Fluctuations in The Attractive Hubbard Model in the Atomic Limit
  BCS theory accounts for the pairing instability in the weak coupling limit, but fails to describe pairing fluctuations above $T_c$. One possibility for describing these fluctuations in the dilute limit is the T-matrix approximation. We critically examine various degrees of self-consistency in the T-matrix formalism, along with a non-diagrammatic two-particle self-consistent (TPSC) formulation, in the strong coupling regime, where an exact solution is readily available. We find that one particular degree of self-consistency is quite accurate, particularly at low temperature as evidenced by examining both static and dynamic properties. 
S. Verga, R.J. Gooding, and F. Marsiglio