New Formulation of Dispersion Relations for Potential Scattering

Abstract

The amplitude for Yukawa potential scattering is represented by a Watson- Sommerfeld integral over Legendre functions P/sub ip-1/2/ p real. A dispersion relation and unitarity condition are given for the amplitudes appearing in this integral and it is shown that the resulting system for iterative calculation of the amplitude from the Born approximation is considerably simpler than in other formulations. lt is also shown that these amplitudes behave similarly to thc partial waves on the second energy sheet. (auth)