Fundamentals of Near-Edge X-Ray Absorption Spectroscopy

The contribution to the X-ray absorption coefficient due to the excitation of a deep core level may be expressed as /rc = nco-c, where nc is the density of atoms with the core level of concern and rc is the absorption cross section for this level on a single atom. Assuming the X-ray field to be a small perturbation, the latter can be evaluated from the golden rule transition rate per unit photon flux. The general X-ray absorption cross section is given by 

Interpretation of X-ray absorption spectra (and most other types of coreelectron spectra) is complicated by the creation of a core hole in one of the atoms in the solid. In many cases (e.g., for transition and rare-earth metals) the magnitude of this effect is not known as yet. Further, these spectra depend on the excited states of the electronic system, which are less well understood than the corresponding ground-state properties (202). 

Absorption-edge spectroscopy deals with electronic transitions from a core atomic level to unoccupied conduction states above the Fermi level. In this process X-ray photons promote a bound electron from an inner level to the 

Dipole selection rules (Al = +1) apply in the absorption process (see however refs. 135, 138). The fine structures of the K edge (s-to-p transition) and LiH edge (p absorption) of an element are not identical. The structure of Lj (s absorption) is also quite different from the Lii iU structures, which are alike, and correspond to processes in which an X-ray photon is absorbed by promoting an electron from 2p core states to d states (with a small and calculable p-to-s contribution). The Ln X-ray absorption edge arises from 2pi/2 core states, while the LiU X-ray absorption edge arises from the 2p3/2 core states and is at a lower energy. The d states are usually by far the most strongly peaked and most favored in the transition (88). 

For X-rays well above the absorption edge (AE 30 eV), the final electron is unbound, that is, has a continuous distribution of allowed energies, and the density of allowed states p(E ) at the final-state energy Ef is then a smooth function which may be approximated by the density of states of a free electron of energy 

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