Partitioning of the total cross section

Some partial photoionization cross sections, derived in this way for neon, are shown in Fig. 2.11 as a function of photon energy. The uppermost curve is the total absorption cross section. At the onset of the ionization thresholds for the ejection of Is, 2s and 2p electrons this quantity shows the corresponding absorption edges (see the discussion related to equ. (2.11)). The partition of the total cross section into partial contributions cr(i) clearly demonstrates that the dominant features are due to main photoionization processes described by the partial cross sections satellite transitions from multiple photoionization processes are also present. If these are related to a K-shell ionization process, they are called in Fig. 2.11 multiple KL where the symbol KLX indicates that one electron from the K-shell and X electrons from the L-shell have been released by the photon interaction. Similarly, multiple I/ stands for processes where X electrons from the L-shell are ejected. Furthermore, these two groups of multiple processes are classified with respect to ionization accompanied by excitation, (e, n), or double ionization, ( ,e). If one compares in Fig. 2.11 the magnitude of the partial cross sections for 2p, 2s and Is photoionization at 1253.6 eV photon energy (Mg Ka radiation) and takes into account the different... 

Raith, W., Sinapius, G. and Stauffer, A.D. (1987). Partitioning of the positron-helium total scattering cross section. J. Phys. B At. Mol. Phys. 20 3557-3570. 

Note that in Table III local (Sza), (S ), and (Sa Sb) expectation values for the [Fe2] cluster 1 are listed. As shown in Section V the local expressions for the Mayer and the Clark and Davidson decomposition schemes differ. Hence, different values for the (S ), e.g., for partitioning schemes. The same argument holds for the cross terms (Sa Sb), here (Spei Sk< 2)- The total spin expectation value (S2) is shown to illustrate that spin contamination is fairly low for most spin states. The reader should not be confused by the fact that summation over the local spin values at the iron centers (Spel), (Spe2>, and (Spei SFe2) does not yield the same value for Mayer and for Clark and Davidson data and that they do not sum up to (S2). The total spin expectation value (S2) is only obtained when summing all local spin values of all atoms of the [Fe2] cluster 1. 

Suggestion Calculate the partition coefBcient of the solute between the pore solution and the external solution as the ratio of two cross-sectional areas, one in which the center of the solute molecule can move and the other as the total pore cross-sectional area. Rewrite the result in terms of a hydraulic radius of the pore. 

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