The validity of form-factor, modified-form-factor and anomalous-scattering-factor approximations in elastic scattering calculations

Abstract

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.

Structural study of conventional and bulk metallic glasses during annealing

“…[8,9] compiled in the DABAX data base [10]. The reduced radial distribution function was then obtained by Fourier transformation…”

Experimental and Theoretical Charge Density Analysis of Polymorphic Structures: The Case of Coumarin 314 Dye

“…The coefficients κ and κ 0 describe the contraction-expansion for the spherical and multipolar valence densities, respectively. For the structure factor computations, the form factor for the hydrogen atoms was taken from Stewart et al, 31 the form factors for nonhydrogen atoms were calculated from Clementi & Raimondi, 32 and wave functions and the real and imaginary dispersion corrections to the form factors were from Kissel et al 33 Atomic displacement parameters of hydrogen atoms are obtained using the recently described SHADE2 approach.…”

Nuclear Resonance Fluorescence for Safeguards Applications

“…As indicated in Table 3.1, the energy at which a nuclear Thomson cross section is equal to a Rayleigh scattering cross section increases with increasing Z. However, with larger scattering angles, the form-factor predictions of σ Ray (θ) become increasingly inaccurate [48]. Thus, the energies given in Table 3.1 may be inaccurate, but the general trends remain correct.…”