An analytical theory of the slowing down and the thermalization of positrons in condensed matter

The paper outlines an analytical treatment of the slowing down of positrons (ef) implanted into condensed matter based on the rather weak assumption t hat the loss of energy or momentum and the scattering angle are uniquely re lated. It goes beyond the mathematical techniques developed for the slowing down of neutrons by allowing for the annihilation rate of positrons and ma king use of the fact that for e(+), owing to its small mass, the energy los s per collision is usually very small compared with the kinetic energy. Exp licit expressions are given for the sample-averaged momentum distribution o f positrons as a function of the positron age and for the distribution func tion in space, momentum magnitude, and time of positronium that is slowed d own by the interaction with optical phonons.