FUNDAMENTALS OF X-RAY FLUORESCENCE - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 50

Figure1.26. Compton-scatter of a photon with an initial energy E . On collision with a loosely
bound or free electron the photon is deflected by an angle ψ . It loses energy and keeps only the
fraction E / E . This fraction is represented by an ellipse in polar coordinates for a certain energy E

(50, 100, and 200 keV). It may be compared with the outer dashed circle, representing conservation
of the photon energy. Figure from Ref. [8], reproduced with permission. Copyright1996, John
Wiley and Sons.

´

polar coordinates. The fraction depends on the initial energy but is indepen-
dent of the substance of the scatterer. It shows maxima for ψ = 0 ° (forward
scatter), reaches minima for ψ = 180 ° (backward scatter), and decreases with
the initial energy.
In the wave picture, Compton scattering is controlled by a fixed wavelength
shift, d λ = λ

´

λ . It amounts to

d λ λ C ? 1 cos ψ (1.48)

where λ C is a small constant called Compton wavelength, which is defined by
λ C = hc 0 / E 0 = 0.002426 nm. The wavelength shift depends only on the deflec-
tion angle ψ and is independent of the wavelength λ itself. For ψ = 0 ° , the shift is
always zero, and for ψ = 180 ° , it is always 2 λ C , which is maximum.
The intensity of the scattered radiation shows a dependence on E and ψ ,as
shown in Figure 1.27 [72]. Minimum intensity or scattering is achieved for a
deflection around 90 ° -100 ° . For that reason, a rectangular geometric arrange-
ment of the X-ray tube, sample, and detector is generally chosen in X-ray
spectrometry in order to minimize the inelastic scatter into the detector.
Nevertheless, any primary radiation of an X-ray tube is scattered by the sample
and is reproduced as a blank spectrum. In particular, the characteristic peaks of