What is Anomalous Scattering?

Interaction of incident photon with scattering electron

The classical derivation of the physical basis for anomalous scattering is developed by treating the scattering interaction as a pair of coupled oscillators. One oscillator is the e component incident x-ray wave; the other is an electron of the scattering atom treated as a dipole oscillator with frequency equal to the observed value of an absorption edge. This treatment is expounded at length by James (1948). A more compact presentation is given by this IUCr teaching pamphlet.

Unfortunately, the classical approach does not lend itself to an intuitive summary. I will therefore instead try to give a basic description in terms of the scattering cross section of an atom as seen by an incident x-ray photon.

When the incident photon has relatively low energy:

• The photon is either scattered or not, but is not absorbed as it has insufficient energy to excite any of the available electronic transitions.
• The scattering cross-section of the atom (or if you like, the probability that the photon is scattered) may be adequately described in using the normal atomic scattering coefficient f⁰ only.
• The photon scatters with no phase delay (imaginary, or f", component is 0).

When the incident photon has high enough energy:

• Some photons are scattered normally.
• Some photons are absorbed and re-emitted at lower energy (fluorescence).
• Some photons are absorbed and immediately re-emitted at the same energy (strong coupling to absoption edge energy).
• The scattered photon gains an imaginary component to its phase (f" scattering coefficient becomes non-zero); i.e. it is retarded compared to a normally scattered photon.

This effect is most easily measured as a function of x-ray energy by noting either the sharp increase in absorption or in fluorescence (see figure below). The imaginary scattering component f" is proportional to these directly measurable quantities. The real scattering component f' is related to f" via the Kramers-Kronig relationship.

Breaking Friedel's Law