Nonrelativistic Scattering Theory

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Abstract
A method of treating nonrelativistic scattering problems is presented. This gives the converging wave function and phase shift for potentials of usual use. The asymptotic form of the wave function is taken as the zero order function in the iteration. The scattering amplitude is determined self-consistently. When the partial wave is not coupled, this method is equivalent to the Jost's method. The discussion in the present paper covers over not only non-coupled partial waves but also coupled partial waves. Explicit formulas ready for calculation are given. The converging nature of this method enables us to discuss the scattering length, the effective range, the resonance and bound states. The general pattern showing the distribution of resonances and bound states follows directly. We can derive the resonance formula without introducing the channel radius. The phase shift formulas of all previous theories, whenever they converge, reduce to the formula derived in the present paper. Bearing on the dispersion relation is also discussed. Criticism as to convergence of other methods are given.

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