Dear Fellow Compatriots: A few pre-coffee random observations from the field offices of Dr. Cranky:
1. No mention of "Resonant Scattering in the index of JJ Sakurai Adv. Quantum Mechanics (1967, 1987 revision), which I used in (blush) 1989, although the phenomenon is discussed, with many exercises left to the reader. The index did, however, refer to the "retarded Green's function," which I find delightful in this context. 2. "Resonance scattering" does appear in JJ Sakurai, Modern Quantum Mechanics, which is a book he wrote a little bit later, and published in 1985 after he died. So I guess that dates the term as well as me. 3. "Anomalous scattering" in optics (i.e, the same phenomenon) describes the __inversion__ of the rainbow spectrum (dispersion) when white light propagates through a prism in which there are absorbers that absorb light near to the visible spectrum. This is accounted for with an imaginary component in the index of refraction. So violet is where you would normally expect to see red, and vice versa. 4. The QM analogue takes as its starting point the First Born approximation (I'm too tired to make a pun) in which a single photon scatters once elastically from a billiard ball point scattering center. You can then show that the diffraction pattern is the FT of the potential, and then get it into the form of electron density from there. Anomalous scattering dispersion and absorption effects are essentially grafted on as real and imaginary terms in the denominator of the scattering potential (see retarded Green's function, above). What comes out of that treatment is essentially identical to what you have in that equation in James that Blundell and Johnson use as a starting point for the derivation. The main point is it is phase shifting. The photon frequency is not changed. 5. Resonance scattering requires a different sort of potential in which you have what Sakurai calls a "quasi-bound state" with a soft barrier. The energy barrier has to be of the same order as the energy of the photon, so I think for X-rays this isn't a significant effect. Bill Scott
