Coulomb Interference Corrections in Potential Scattering

Corrections to the usual formula which approximates the total phase shift by the sum of the nuclear plus Coulomb phases are considered. The first correction to the phase is of order $\alpha$ (the same order as the Coulomb phase itself) and has been shown to be important in a recent analysis of pion-helium scattering. A convergent expansion in $\alpha$ is derived for the correction terms, and is explicitly exhibited through order ${\alpha }^3$. The corrections are finite in each order; previously encountered logarithmic-type divergences are eliminated by a careful treatment of the asymptotic behavior of the Coulomb wave function.