On the Analytic Properties of Partial Wave Amplitudes in Yukawa Potential Scattering

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Abstract
A new proof is given of the dispersion relation for the lth partial wave amplitude when the potential is of the Yukawa form or (by obvious extension) a suitable linear combination of such forms. The requisite analyticity properties are obtained by rewriting the integral equation for the quantity fl(k,r), which is related to the l‐wave amplitude, as a Volterra equation on a finite interval in which the contribution from the asymptotic part of the integral is absorbed into the inhomogeneous term. The Born series for the inhomogeneous term is analytically continued termwise into the cut complex‐wave‐number plane and the uniform convergence of the series is then established utilizing approximations which apply in the asymptotic region. The properties of fl(k,r) then follow from a well‐known theorem on Volterra equations.