Extended Two--Particle Green's Functions and Optical Potentials for   Two--Particle Scattering by Many--Body Targets
  An extension of the fermionic particle--particle propagator is presented, that possesses similar algebraic properties to the single--particle Green's function. In particular, this extended two--particle Green's function satisfies Dyson's equation and its self energy has the same analytic structure as the the self energy of the single--particle Green's function. For the case of a system interacting by one--particle potentials only, the two--particle self energy takes on a particularly simple form, just like the common self energy does. The new two--particle self energy also serves as a well behaved optical potential for the elastic scattering of a two--particle projectile by a many--body target. Due to its analytic structure, the two--particle self energy avoids divergences that appear with effective potentials derived by other means. 
Joachim Brand and Lorenz S. Cederbaum (Theoretical Chemistry,   Heidelberg,Germany)