Diffusion heating and cooling of positrons in constrained media

Thermalized positrons in media with spatial constraints can be trapped by sinks, and annihilate with electrons into $\gamma$ quanta with characteristics that are discernibly different from those of positrons annihilating in the bulk. The dependence of the cross sections for scattering in the medium on positron velocity determines whether the fastest or the slowest particles in the velocity distribution disappear preferentially from the volume. This causes the cooling or heating of the positrons remaining in the medium. The diffusion equation is solved to derive the annihilation characteristics of positrons, with the result that diffusion heating and cooling always reduce the effective diffusion coefficient pertinent for trapping relative to that in the infinite medium. The effects on the annihilation characteristics are those of a reduced trapping rate and of an apparent initial positron population in sinks, as it is recorded by an instrument with finite time resolution. The results pertain to positronium diffusion in small gas cells, to the escape of positrons or positronium from small solids, and to the trapping of positrons by vacancies or voids in solids. They are compared with experimental results.