Approximation to the Relativistic Scattering Problem

We extend the calculation of the relativistic phase-shift problem, as given before, to second order in $\hslash$ by means of Miller and Good's modified WKB method. The scheme of Bertocchi, Fubini, and Furlan is used to avoid the divergences introduced in the second-order terms. The example indicates that the phase shifts are greatly improved at lower angular quantum numbers.