Analyticity of Amplitudes and Separable Potentials

Abstract

Expressions for the partial scattering amplitudes from nonlocal separable potentials are written down in the form of dispersion relations. These relations are automatically expressible in the $\frac{N}{D}$ form discussed by Chew and Mandelstam. Criteria for "acceptable" separable potential shapes are discussed. The relation between "local" and separable potentials is clarified with the help of a concrete potential shape which conforms to the above criteria. With such a potential shape the physical meaning of the "range of the interaction" in terms of separable potentials becomes clearer.