Observation of the Darwin top hat and the precise determination of the positron band gap in rare gas crystals.

We have measured the energy dependence of the elastic specular reflection of positrons from the (111) surfaces of solid rare gas crystals. For each sample we observe an intense first- order Bragg peak with a profile closely resembling the ideal "top hat" shape first derived by Darwin. The well-defined width and center of the peak enables us to determine the positron energy gap and inner potential as a sensitive test of the positron- gas atom interaction in the solid.