Eikonal Approximation for Inelastic Processes

Abstract

The eikonal approximation for the contributions to inelastic scattering from arbitrarily crossed ladder graphs is considered. The particle represented by one of the "sidepieces" of the ladders is allowed to change its state and mass at each rung; the other sidepiece particle is restricted to have at most one change of state, and that only if its elastic interactions are the same in the two states. When the denominators of the latter sidepiece can be linearized, the amplitudes reduce to forms essentially identical to those found in nonrelativistic coupled-channel potential theory. This result is independent of the ratio of the energy to the sidepiece mass and connects smoothly the nonrelativistic and extreme relativistic regimes. Its implications for absorptive models are discussed briefly.