FOKKER-PLANCK DESCRIPTION OF ELECTRON AND PHOTON TRANSPORT IN HOMOGENEOUS MEDIA

Starting from a Fokker-Planck description of particle transport, which is valid when the scattering is forwardly peaked and the energy chang e in scattering is small, we systematically obtain an approximate diff usionlike equation for the particle density by eliminating the directi on variable <(Omega)over cap> with an elimination scheme based on Zwan zig's projection operator formalism in the interaction representation. The elimination procedure closely follows one described by Grigolini and Marchesoni [in Memory Function Approaches to Stochastic Problems i n Condensed Matter, edited by Myron W. Evans, Paolo Grigolini, and Gui seppe P. Parravicini, Advances in Physical Chemistry, Vol. 62 (Wiley-I nterscience, New York, 1985), Chap. II, p. 29], but with a different p rojection operator. The resulting diffusion equation is correct up to the second order in the coupling operator between the particle directi on and position variable. The diffusion coefficients and mobility in t he resulting diffusion equation depend on the initial distribution of the particles in direction and on the path length traveled by the part icles. The full solution is obtained for a monoenergetic and monodirec tional pulsed point source of particles in an infinite homogeneous med ium. This solution is used to study the penetration and the transverse and longitudinal spread of the particles as they are transported thro ugh the medium. Application to diffusive wave spectroscopy in calculat ing the path-length distribution of photons, as well as application to dose calculations in tissue due to an electron beam are mentioned.