Absorption jump

In his treatment, Sherman makes use of emission coefficients t that perform the function of the empirical k in Equation 6-4. Both quantities are proportional to. the product of absorption coefficient, of fluorescence yield and of (1 — 1/r), where r is the absorption-jump ratio involved (4.4). 

Table 2. Fluorescence Yields, w, and Absorption-Jump Ratios, r...

Figure 5.3 K and L absorption edges of tungsten. The absorption of the solid decreases as the energy of the X-rays increases (i.e., as the wavelength decreases), but when the energy exceeds the threshold for a particular excitation process to occur (e.g., the eviction of an Lm electron at 10.2 KeV), the absorption jumps substantially.

When the unoccupied states are itinerant, a marked increase in the variation of photoabsorption coefficient forming a discontinuity appears at an energy just sufficient for the transfer of an electron to the first empty levels. The inflexion point of the discontinuity corresponds to the position of the Fermi level in a metal or the bottom of the conduction band in a semi-conductor or an insulator. The ratio between the photoabsorption coefficient on either side of the discontinuity is called the absorption jump. If the density of states is uniform, the shape of the discontinuity is that of the arctangent curve. When a high density of unoccupied states of the appropriate symmetry is situated near the Fermi level, an absorption maximum can be expected. 

In the case of localized empty states one or more absorption lines are observed in the variation of the photoabsorption coefficient. Beyond this an absorption jump is generally observed it corresponds to the transitions toward hybridized continuum states of positive energy and its inflexion point gives the ionisation energy. 

On the other hand, the degree of localization of the 5/electrons increases in the oxide, especially in UO2. Indeed, the localization increases with the internuclear distance because the overlap of neighbouring 5/ orbitals decreases. However, an absorption jump is always observed in the absorption spectra of oxides the 5/localization is therefore weaker in the light actinides than in the rare earths, except for 5-Pu. 

The absorption coefficient /x of an atom in a molecule or a solid has a fine structure amounting to about 15% of the absorption jump at the edge and extending up to several hundred electron volts above the absorption edge, whereas a free atom only shows a smooth absorption as seen in Fig. 5.95 [567]. 

Here / and are the relative fractions of the normalized absorption jumps in the 4f" and 4f" reference spectra and m is the number of outer valence electrons. This procedure was applied e.g. by Launois et al. (1980), Martin et al. (1980), Ravot et al. (1981) to extract the valence from the L, spectra of mixed valent lanthanide chalcogenides. Figure 14 reproduces the spectra of mixed valent TmSe together with its (isostructural) references TmS (nominally 3" ) and TmTe (nominally 2" ). Divalent Tm in TmTe exhibits a smaller and narrower line than trivalent Tm in... 

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