The validity of form-factor, modified-form-factor and anomalous-scattering-factor approximations in predictions of elastic photon-atom scattering is assessed with the aid of the state-of-the-art numerical calculation of Rayleigh scattering obtained using the second-order Smatrix theory, in the photon energy range from 100 eV to 1 MeV. A comparison is made with predictions from Smatrix theory in the same atomic model for representative low-Z (carbon, Z = 6) and high-Z (lead, Z = 82) elements to get a general idea of the validity of these simpler more approximate methods. The importance of bound-bound contributions and the angle dependence of the anomalous scattering factors is discussed. A prescription is suggested, with the assumption of angle independence, that uses simpler approaches to obtain the elastic scattering cross sections in the soft-X-ray regime at the level of accuracy of the S-matrix calculation, failing at large momentum transfers for high-Z elements. Predictions from this prescription are compared with experiment. With starting point the many-body elastic scattering amplitude, a detailed discussion is presented of the partition of the elastic scattering amplitude into Rayleigh and Delbrtick scattering components. This partition of the optical theorem reveals contributions from bound-bound atomic transitions, bound pair annihilation and bound pair production that are not usually associated with elastic scattering. In the parti-* Present address: 395 Henry Street, Apartment IN, Brooklyn, New York 11201, USA. tioned optical theorem for Rayleigh scattering, as in the many-body optical theorem for scattering from excited states, subtracted cross sections naturally appear. These terms are needed, in addition to the familiar terms for photoionization, to relate the real and imaginary parts of the scattering amplitude.

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Elastic photon scattering from the ground state and various excited states of carbon atoms and ions has been investigated, using the S-matrix formalism, for incident photon energies ranging from 100 eV to 10 keV, contrasting the results obtained for different configurations. The excited states considered include hollow-atom states, where one or more inner shells are completely vacated. Ionic cases are considered as a limit of excitation. Results demonstrate how cross sections for different excited states group together according to shared properties of the configurations, such as the number of K electrons. Cross sections may exhibit deep dips below the K edge, depending on the occupation of the subshells corresponding to the strongest transitions. Scattering from excited states can have significantly larger cross sections than scattering from the ground state, particularly just below the K resonance region, and therefore it needs to be considered in situations where there is a large population of these excited states. Results are interpreted in terms of form-factor arguments and the qualitative behavior of individual subshell amplitudes. The angular dependence of cross sections can be understood in terms of angle-dependent form factors and anomalous scattering factors, taken to be angle independent. Cases are identified for which excited-state total integrated cross sections are much larger than the corresponding cross sections for scattering from the ground state. Our main results use an averaging over magnetic substates at the level of the amplitude, exact only for fully filled subshells, but generally appropriate for the carbon case considered, which simplifies the discussion and explains most of the general features. We also present results for a hollow lithium atom with and without this approximation to illustrate the differences that can arise in certain circumstances.

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