Slowing-down and penetration of positrons in condensed matter

Quantitative treatment of the penetration of positrons into a sample and of their slowing-down is often the key to the reliable interpretation of positron keV-beam experiments. The close relationship to problems arising in neutron physics and in X-ray and gamma-ray penetration is pointed out, and the correspondence between the physical quantities appearing in the different fields is established. Mathematical techniques for solving or simplifying Boltzmann's transport equation originally developed for neutrons are shown to be applicable to positrons as well. The present paper derives in detail the positron version of Fermi's age theory, which, in its simplest form, enables us to reduce the solution of the steady-state Boltzmann equation to that of the equation of heat conduction. In age theory, the time-like variable is a mechanism-dependent quantity that is proportional to the mean square displacement of the positrons during the slowing-down from their original momentum to a given momentum. Time-dependent problems are handled by the Laplace-transformation technique. This approach and its generalisations permit analytical or semi-analytical solutions to problems that had hitherto been thought to be accessible by simulation techniques only. Additional mathematical techniques allowing us to tackle problems beyond the applicability of age theory an outlined. (C) 1999 Elsevier Science B.V. All rights reserved.