Dispersion Relations for Scattering in the Presence of a Coulomb Field

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Abstract
A dispersion relation is derived for short-range potential scattering in the presence of a Coulomb field, and on the basis of this result a conjecture is made as to the Coulomb modifications of the Goldberger relations for pion-nucleon scattering. The new relations contain in addition to Coulomb phase shifts only amplitudes that are directly measurable experimentally, the assumption of charge independence not being required. Estimates are made to show that the Coulomb phases that appear explicitly are of no practical importance.