Elastic Scattering of Positrons from Hydrogen: An Optical Potential Calculation

The optical potential of Bell and Squires is used to formulate the problem of the elastic scattering of positrons from atoms. An application is made to the scattering of $S$-wave positrons from hydrogen below the threshold for positronium formation. The single-particle states of the electron are chosen to be the hydrogenic solutions, while the positron states are obtained by using a single-particle potential which includes the Hartree potential plus a model polarization potential. Various models are investigated and a choice is made which effectively maximizes the calculated phase shifts through second order in the perturbation expansion of the optical potential. Phase shifts thus obtained yield approximately 67-80% of the difference between the static Hartree results and the variational results of Schwartz. Higher-order effects are evaluated using the techniques of Kelly. Intermediate states of multipole $l\le 3$ are included.