Effect of Virtual Excitations on the Elastic Scattering of Electrons and Positrons by Atomic Hydrogen

Total elastic cross sections for the scattering of electrons and positrons (neglecting positronium formation) from the $1s$ state of atomic hydrogen have been calculated allowing for virtual excitation to the $2s$ and $3s$ states. The S-, P-, and D-wave contributions to Q_1s-1s have been computed for incident energies below 10 ev. The results for positron scattering show that virtual excitation to the $2s$ and $3s$ states only slightly affects the phase shifts calculated in the static approximation. The influence of the $2s$ state appears to be much more important for electrons. The scattering lengths of these exploratory calculations are compared with the results of other calculations.