Simplified model of low energy x-ray backscattering

The reflection of x-rays from a half space is studied within the framework of a model that assumes multiple isotropic scattering of photons without energy loss. An exactly solvable analytical expression for the angular distribution of reflected photons is derived. The range of validity of the model was determined by the Monte Carlo simulation thereby incorporating energy loss and angular dependences. For water as a scatterer, in the energy range from 10 to 60 keV, which is often used in x-ray diagnostics, the two approaches differ by at most 5%. The analytic results, confirmed by the Monte Carlo simulation, show that the angular distribution of reflected photons for energies greater than 30 keV-where multiple scattering events dominate-may be represented by a cosine law, within a few per cent of accuracy.