  Interpretation of x-ray absorption near-edge structure (XANES) experiments is
often done via analyzing the role of particular atoms in the formation of
specific peaks in the calculated spectrum. Typically, this is achieved by
calculating the spectrum for a series of trial structures where various atoms
are moved and/or removed. A more quantitative approach is presented here, based
on comparing the probabilities that a XANES photoelectron of a given energy can
be found near particular atoms. Such a photoelectron probability density can be
consistently defined as a sum over squares of wave functions which describe
participating photoelectron diffraction processes, weighted by their normalized
cross sections. A fine structure in the energy dependence of these
probabilities can be extracted and compared to XANES spectrum. As an
illustration of this novel technique, we analyze the photoelectron probability
density at the Ti K pre-edge of TiS2 and at the Ti K-edge of rutile TiO2.
