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Time-dependent perturbation theory and a model form of the core-hole-photoelectron potential are used to obtain results for the secondary electron shake-off probabilities as a function of photon energy above the X-ray absorption edge. The shake-off probabilities and the resulting EXAFS amplitude reduction factor agree reasonably well with experiment close to an absorption edge and in the region of energy appropriate to EXAFS data analysis. The model form for the potential gives excitation probabilities which are too large at high photon energies.

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