Compton scattering revisited

Abstract

We review the standard theory of Compton scattering from bound electrons, and we describe recent findings that require modification of the usual understanding, noting the nature of consequences for experiment. The subject began with Compton and scattering from free electrons. Experiment actually involved bound electrons, and this was accommodated with the use of impulse approximation (IA), which described inelastic scattering from bound electrons in terms of scattering from free electrons. This was good for the Compton peak but failed for soft final photons. The standard theory was formalized by Eisenberger and Platzman (EP) [1970. Phys. Rev. A 2, 415], whose work also suggested why impulse approximation was better than one would expect, for doubly differential cross sections (DDCS), but not for triply differential cross sections (TDCS). A relativistic version of IA (RIA) was worked out by Ribberfors [1975. Phys. Rev. B 12, 2067]. And Surić et al. [1991. Phys. Rev. Lett. 67, 189] and Bergstrom et al. [1993. Phys. Rev. A 48, 1134] developed a full relativistic second order S-matrix treatment, not making impulse approximation, but within independent particle approximation (IPA). Newer developments in the theory of Compton scattering include: (1) Demonstration that the EP estimates of the validity of IA are incorrect, although the qualitative conclusion remains unchanged; IA is not to be understood as the first term in a standard series expansion. (2) The greater validity of IA for DDCS than for the TDCS, which when integrated give DDCS, is related to the existence of a sum rule, only valid for DDCS. (3) The so-called “asymmetry” of a Compton profile is primarily to be understood as simply the shift of the peak position in the profile; symmetric and anti-symmetric deviations from a shifted Compton profile are very small, except for high Z inner shells where further p ⇒ · A ⇒ effects come into play. (4) Most relativistic effects, except at low energies, are to be understood in terms of simple kinematic modifications of nonrelativistic IA, plus using a relativistic charge density for high Z inner shell states; these shift the peak and change its height. However, for high Z, corrections to RIA persist in the peak region, even at extreme relativistic energies (correction of about 15% for Z = 92 ).