X-ray absorption cross section

Regardless of the choice of the sample thickness, the total amount of sample particles in the x-ray probe beam under optimized conditions is directly proportional to the x-ray spot size and inversely proportional to the x-ray absorption cross section, whose photoinduced (small) changes we want to measure [12]. Typical x-ray foci at synchrotrons are in the 0.1 - 0.3 mm range. For the examples treated below, this means that we have between 1014 and 1016 molecules in the probed volume. In order to achieve a reasonable photoinduced signal we should excite as many solute molecules as possible. Neglecting the optical absorption cross sections for photoexcitation for the moment, this requires on the order of 1015 laser photons per pulse, or ca. 0.25 mJ of pulse energy (e.g., at 800 nm). In other words, one should aim to... 

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 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... 

Fig. 5. Schematic of X-ray absorption cross section as a function of the photon energy showing the threshold region (including pre-edge and edge regions), the EXAFS region, and relevant electron processes excitation of a core electron to a higher unoccupied atomic level, to the Fermi level (at absorption edge), and to the continuum (atom ionization).

Fig. 4.5. Si 2p continuum x-ray absorption cross sections (a in megabarns, Mb) calculated by the MS-SCF-Aa method for SiF at Si-F distances of 1.54 and 1.59 A electron energies ( ) in rydbergs (after Tossell, 1987).

Physical Principles. The physical origin of the n oscillations above the edge is the modification, due to the neighboring atoms, of the final state of the electron emitted by the atom that absorbs the incoming X-ray photon (hereafter called central or absorber atom) (Stem, 1988). The X-ray absorption cross-section, atom interacting with a photon described by a dipole transition operator D is given by ... 

The probability of exciting an electron from an initial state x r, to a final state can be described in terms of the X-ray absorption cross section, a, which is defined as the number of electrons excited per unit time divided by the number of incident photons per unit time per unit area [152]. By applying Fermi s golden rule and using the dipole approximation, can be written as... 

---