Analytic expressions for high-energy full three-dimensional continuum wave functions and phase shifts in screened-Coulomb potentials

Analytic expressions are obtained for nonrelativistic high-energy three-dimensional continuum wave functions (at small distances) and phase shifts in smoothed screened-Coulomb potentials of the form V(r) = -ag(lambdar)/r, where a = Zα, with α the fine structure constant, and lambda is a small parameter characterizing atomic screening (lambdaapprox. =αZ/sup 1/3/). For this purpose we combine information from an interation of an eikonal equation with an analytic perturbation theory (APT) for screened-Coulomb potentials, based on an expansion of the function g in the interior of the atom. Using the general three-dimensional APT solutions found previously, the particular solution which satisfies the correct scattering boundary condition at large distances is constructed. The iterated eikonal wave function is used as a bridge between small- and large-distance regions. It is shown that the iterated eikonal expansion of the wave function is valid for large complex momenta. By expanding the iterated eikonal at small distances the desired three-dimensional wave function for large real momenta in the entire small-distance region can be identified. The screened-Coulomb phase shifts may then be read out as the phases of the radial functions in the partial wave series expansion of the three-dimensional scattering wave function solution. In this way a high-momentum expansion of the non-relativistic screened-Coulomb phase shifts up to and including terms of the third order in p-1 has been obtained