Multiple Scattering, the Glauber Approximation, and the Off-Shell Eikonal Approximation

Abstract

It is pointed out that in potential theory the validity of the Glauber approximation for high-energy scattering from a composite system implies a high degree of cancellation in the multiple-scattering series for the same process: The off-shell contribution to double scattering must be precisely cancelled by the sum of all higher-order terms. This cancellation holds only if the same approximations used in obtaining the Glauber formula are made in the multiple scattering series. In particular, the eikonal approximation must be used for the off-shell two-body $t$ matrices. An explicit form is developed for these approximate off-shell $t$ matrices, and then used to verify the cancellation for some of the lower-order terms in the potentials. Possible applications of these potential-theory results to the actual relativistic scattering from composite systems are discussed.