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.

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