Covariant multiple scattering series for elastic projectile-target scattering

A covariant formulation of the multiple scattering series for the optical potential is presented. We consider the case of a scalar ``nucleon'' interacting with a spin zero isospin zero A-body target through meson exchange. We show that a covariant equation for the projectile-target t matrix can be obtained that sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and we show that in the impulse approximation, the two-body t matrix associated with the first-order optical potential is the one in which one particle is kept on mass shell. The meaning of various terms in the multiple scattering series is given and we describe how to construct the first-order optical potential for elastic scattering calculations.