Investigations on compton scattering: New directions

Although inelastic (Compton) scattering of a photon off a free electron was well understood about 80 years ago, inelastic scattering off bound electrons remains an incompletely understood process. The availability of synchrotron light sources has led a great enhancement in the precision of experimental measurements involving this process. As a result, approximations made in obtaining numerical predictions of physical observables are being reexamined by theorists. In this article, we present a comparison of experimental measurements to theoretical predictions to assess the need for future advances in both experiment and theory

Asymmetry and the shift of the Compton profile

We show that the conventionally defined asymmetry of the Compton profile (CP) is, to a large extent, simply a shift of CP. Compton scattering is widely used in studying the electron momentum distribution (EMD) of complex systems. Extraction of information about the EMD is based on an impulse approximation (IA) description of the process. In IA the scattering from bound electrons is described as scattering from the EMD of free electrons. Most often the angular and energy distributions of scattered photons (doubly differential cross sections (DDCS)) is measured and presented in terms of CP, which is just the DDCS normalized by a kinematical factor. The deviations of measured CP from the IA results are conventionally described as an asymmetry of CP about the IA peak position. IA predicts CP to be symmetric. We have examined the discrepancy between IA predictions (and the corresponding relativistic version of IA, RIA) and more rigorous approaches ( A 2 and S-matrix), using independent particle approximations for the description of the bound state of electrons. In the nonrelativistic region (in which many measurements of CP are performed) we find that the conventional asymmetry can largely be understood as the shift of the peak position. The true asymmetry with respect to the shifted peak position is in fact much smaller. RIA has similar properties to IA, except that for atoms with high nuclear charge the p ⇒ · A ⇒ interaction may modify the shift and limit the utility of description as a shift

Limitations on the validity of impulse approximation in Compton scattering

The validity of impulse approximation (IA), which is commonly used in the description of Compton scattering of photons from atomic electrons, is discussed with particular attention to the kinematical region in which the photon momentum transfer k is not much larger than the average bound electron momentum a of a given shell. IA can be justified in the Compton peak region of the spectrum if a/k≪1. However, for the doubly differential cross-section of photon–atom scattering (ejected electrons not observed) IA is commonly used, and viewed as adequate, while only requiring that a/k<1. In addition to a general discussion of the validity of IA (and the relativistic version RIA) for doubly and triply differential cross-sections, in this paper, we are particularly concerned with (1) the asymmetry around the IA peak of the Compton profile and (2) the contribution of the p→·A→ interaction term (neglected in IA) in the peak region for a/k<1. We argue that the observed asymmetry of the Compton profile is to a large extent just a shift of the IA profile. We find that p→·A→ contribution to the peak region for a/k≈1 is important only for scattering from high Z K-shells

Compton scattering revisited

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 )