A general formalism to include inelastic scatterings in the differential absorption method for hard x-ray spectroscopy

Abstract

A complete formulation of the differential absorption method that includes inelastic scatterings inside the filters, is presented. Such scatterings produce secondary photons that can reach the detector system modifying the registered spectrum as compared with that emitted by the source under study. Erroneous results can be obtained as a consequence. It is shown that, for instance, as much as 22% of photons belonging to the 200 keV region that incide on 3 mm thick Cu filters can reach the detector with an energy that differs from that they had when emitted from the source. A total of 12 materials of different thicknesses commonly used as filters together with incident photon energies covering the 20–600 keV range is reported. The formalism is detailed, discussed and applied to a real case.