Extended Two-Particle Green's Functions and Optical Potentials for Two-Particle Scattering by Many-Body Targets

Abstract

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 with 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.