A new scheme for evaluating the stopping distance of a particle in a uniform medium is presented. The input is the bulk (inelastic) differential transition probability per unit time of the particle in the medium. The range is determined as the mean penetration depth associated with all possible paths available to the particle in the course of its slow down. The totality of possible paths is represented approximately by means of a tree-type construction which takes account of the role of angular deflections. The rms deviation in the penetration depth is also given. The procedure is applied to a positron entering a metal. We find that for medium energies the range is determined principally by positron-conduction-electron scattering while the spread in penetration depths is limited by positron-phonon scattering. Results also show that for incident energies ≲ 25 a.u. significant numbers of nonthermalized positrons reach the surface.

• Received 13 August 1979

DOI:https://doi.org/10.1103/PhysRevB.21.4918