Polarization Potentials for Low-Energy Scattering:e+-H ande−-Li

Polarization-potential calculations are given for positron scattering by hydrogen and for electron scattering by lithium. The potentials are obtained in the adiabatic approximation by a simple variational calculation of the energy of the disturbed atom. This approach is more general than perturbation theory and is valid even for the large interactions typical of the alkali elements. The $l=0\mathrm{}$ phase shifts are calculated for positron-hydrogen scattering with differing numbers of excited states included in the coupling. First, only the $2p$ state is considered, next, all $p$ states, and finally all $p$ states plus the $2s$ state. Phase shifts and cross sections of five partial waves ($l=0\mathrm{}$ to $l=4\mathrm{}$) are calculated for the lithium problem when the interaction of the first excited state ($2p$) is considered. This accounts for all of the experimentally observed polarizability. Comparison with close-coupling results in both cases shows the present method to be of similar accuracy when coupling with the same excited states is included. The adiabatic approximation, inherent in the polarization potential, is therefore not a serious limitation and the method can be used with confidence for more complex atoms.