Alternative partial wave representations for ultrarelativistic Dirac potential scattering

Abstract

After reviewing briefly the point Coulomb scattering problem in the nonrelativistic, Klein-Gordon, and Dirac cases, the form of the ultrarelativistic vector (Coulomb-like) potential scattering amplitude f/sub 0/ is developed in partial wave form for the ''spinor'' representation. The latter is one of a variety of different Dirac scattering amplitudes, and arises naturally in perturbation theory as the coefficient of a spinor matrix element. Unlike the traditional amplitudes, f/sub 0/ is not required to vanish at theta = ..pi.., which makes it the natural choice for eikonal treatments. This representation is also the one closest to the usual nonrelativistic and Klein-Gordon amplitudes. Summation by parts, a potentially powerful rearrangement technique, is used to verify several previously known relationships among the various amplitudes, and illustrates the problems associated with summing poorly convergent series.