New relativistic S-matrix results for scattering -- beyond the usual anomalous factors/beyond impulse approximation

The relativistic second-order S-matrix elements for photon-atom scattering have been successfully calculated with numerical methods within the independent particle approximation (IPA). This permits an assessment of the validity of simpler approximate predictions which are commonly used and it offers the possibility of improved tabulations of theoretical predictions. A variety of unresolved issues remain, some associated with the relativistic theory, some with IPA. The systematic use of the second-order S-matrix in calculations of Rayleigh scattering from isolated atoms has led to significant progress in understanding this process and to a wide range of agreement with experiment. The energy and angular dependence of anomalous factors and the importance of relativistic, higher-multipole and bound-bound contributions in their calculation is better understood. However correlation effects must also be included to obtain predictions for the near-edge region, such extensions of the present S-matrix calculation have been discussed but few results are sofar available. Existing empirical approaches can be assessed in regard to their success in dealing with known IPA features. We have recently calculated the relativistic second-order S-matrix element for Compton scattering and have begun to try to understand this process in different regions. We can discuss when the more complete calculation confirms the standardmore » Compton peak. In the softer part of the spectrum impulse approximation fails. There can be resonant Raman peaks, and in the soft-photon region the spectrum is infrared divergent, proportional to the photoeffect angular distribution. This means the traditional incoherent scattering factor is undefined in the absence of a low-energy detector efficiency cutoff.« less