Coulomb-scattering states and partial-wave decompositions

Abstract

It is customary to split the physical Coulomb-scattering wave function ψ o (+) into an incoming part φ i and a scattered part φ g : We derive analytic formulae for the partial-wave projections of φ i and φ g and discuss the asymptotic convergence of the corresponding partial-wave series. It is found that the above splitting is unsatisfactory. We propose a different splitting of ψ o (+) into an incoming part and a scattered part which is in close analogy with the standard separation of the scattering wave function for a short-range potential.