An intense monoenergetic, variable low energy beam of positrons has been constructed at the Brookhaven National Laboratory. This is more than 100 times greater than any existing beams from radioactive sources. They propose to increase further the low energy positron beam flux by two orders of magnitude, and to carry out two types of experiments with it. The first is to produce a beam of positronium atoms to determine the reflection coefficient of positronium as a function of its energy from solid surfaces to determine whether positronium diffraction would be a useful tool for analyzing the structure of solid surfaces. The second type of experiment consists of measuring the angular correlation of annihilation radiation resulting from positrons annihilating on the surface of solids, and thereby obtain the surface electrons momentum density distribution.