Applied Physics and Mathematics Annotation << Back ANALYTICAL MODEL OF TRANSPORT OF PHOTONS AND ACCELERATED PARTICLES THROUGH LAYERS OF MATTER IN THE APPROXIMATION OF GENERALIZED DIFFUSION. AVERAGE RANGE, REFLECTION AND TRANSMISSION COEFFICIENTS, PARTICLE AND ENERGY DISTRIBUTIONS ALONG THE COORDINATE V.A. NIKEROV An analytical model of the transport of photons and accelerated particles through the layers of matter in the approximation of generalized diffusion is formulated consistently, based on the limiting cases of straightforward and diffusion transport, and also their cross-linking. The average range of the particles along the coordinate are calculated and analyzed. Analytical formulas are derived for the coeffi cient of volume refl ection of particles from the surface of the medium in the straightforward and diffusion approximations, and their dependence on the angle of incidence of the particle beam on the surface. Analytical formulas are derived for the average energy loss and average energy of the particles reflected from the layer of matter, as well as their dependence on the angle of incidence of the particle beam on the surface. An analytical formula is derived for the coeffi cient of refl ection of the beam energy from the surface of the medium in the diffusion approximation for a wide range of media, and also its dependence on the angle of incidence of the particle beam on the surface. Analytical formulas are derived for the coeffi cient of transmission of particles through a layer of matter in the straightforward and diffusion approximations, and their dependence on the angle of incidence of the particle beam on the surface. The distributions of particles and energy deposition over the depth of the layer are obtained. The possibility of a spatial maximum of the energy input of a particle beam is analytically justifi ed, the depth of this maximum location is calculated, as well as its dependence on the angle of incidence of the particle beam on the surface. The applicability and error origin the of the analytical model of the transport of photons and accelerated particles through the layers of matter in the approximation of generalized diffusion are estimated. Keywords: accelerated particles, photons, generalized diffusion, straightforward transport, diffusion transport, average range of the particles along the coordinate, the coeffi cient of volume refl ection of particles, the average energy of the particles refl ected from the layer of matter, the coeffi cient of refl ection of the beam energy from the surface of the matter, the coeffi cient of transmission of particles through the layer of matter, particle and energy deposition distributions over the depth of the layer. DOI: 10.25791/pfim.06.2018.028 Contacts: E-mail: n@wswr.ru Pp. 03-15.