Application of an Approximate Solution of Partial-Wave Dispersion Relations to Yukawa Potential Scattering

Abstract

The time-reversal symmetrization of the multichannel scattering amplitude proposed by Fulton and Shaw is used to construct the amplitude for nonrelativistic single-channel Yukawa potential scattering. It provides a modified determinantal method for the solution of the $\frac{N}{D}$ equations. This amplitude is compared to the exact solution of the Schrödinger equation. It is found that the scattering lengths predicted by this method are qualitatively the same as those predicted by the full $\frac{N}{D}$ equations and significantly better than the results of the determinantal method. The computational simplicity of the determinantal method has been retained and combined with the accuracy of the full $\frac{N}{D}$ solution, which, with first-order Born approximation, gives quite a reliable picture of the qualitative features of the scattering.