The transport equation for electron scattering through plane parallel targets has been solved by expanding the electron distribution function into spherical harmonics. The electron energy is assumed to be constant. No simplifying assumptions have been made concerning the scattering cross sections. In fact, a simple technique has been found for accurately determining the screening angle which plays an important role in multiple scattering. For small angles (≤ 10°) and thin targets, the emerging electron distribution agrees well with earlier theories. However, for larger angles the present theory predicts a greater probability of scattering than earlier theories. For thin targets it is well known that the earlier theories merge with the single-scattering distribution function at large angles. This difference at large angles between the present and earlier theories implies that the electron distribution predicted by the present calculations will not merge with the single-scattering distribution. For thick targets, as one would expect, the earlier theories are poor approximations of the emergent electron distribution function for all angles.

• Received 7 December 1972

DOI:https://doi.org/10.1103/PhysRevA.8.226