Electrostatic Corrections to Nucleon-Nucleon Dispersion Relations

Abstract

Assuming that a nonrelativistic wave-function description of the nucleon-nucleon scattering system is valid at low energy and large distances, we investigate the analytic properties of the nuclear (i.e., total minus Coulomb) partial wave scattering amplitudes as a function of the c.m. momentum $q$. For singlet states, we find that the essential singularity at $q^2=0\mathrm{}$ can be treated exactly in the partial wave dispersion relation. The remaining singularities are branch points located at the same position as for the non-Coulomb case. The discontinuity across the one-pion exchange cut is a simple multiplicative factor (which goes to unity as $e^2$ goes to zero) times the discontinuity in the absence of Coulomb scattering. From this structure we derive an integral equation for the partial wave scattering amplitude.