Abstract
The analytic properties of the potential scattering amplitude, considered as a function of the two complex variables energy and momentum transfer, are investigated for a nonlocal interaction assumed to be a superposition of a purely local Yukawa potential of the type extensively treated in the current literature and of a purely nonlocal, central, separable one. The exact partial-wave scattering amplitudes are constructed and the analytic properties of the total scattering amplitude are studied through the partial-wave expansion and the Sommerfeld-Watson transformation. If suitable restrictions are placed on the asymptotic form of the angular-momentum-dependence of the separable potential to allow a Sommerfeld-Watson transformation to be made, then the total scattering amplitude can be written as a double dispersion relation in the energy and momentum transfer, with possibly a finite number of pole terms and subtractions. The scattering amplitude for the class of nonlocal potentials considered has a cut along the negative real energy axis which would not be expected from the analogous results for a purely local potential.
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