Positron-Hydrogen Scattering at Low Energies

Abstract

The complete Dalgarno-Lynn second-order adiabatic potential is used to compute the $s$-wave elastic scattering of positrons by atomic hydrogen below the threshold for positronium formation. Comparison with the definitive results of Schwartz indicates that the potential is too attractive, as expected. A simple, one-parameter modification of the potential, related to the monopole distortion term, can yield exact agreement with Schwartz's value for the scattering length. Without further adjustment of the parameter, excellent agreement is also obtained for all energies up to the positronium threshold, and fairly good results are found for higher partial waves. The results encourage one to attempt similar work with more complex atoms, for which detailed variational calculations are impractical.