Doyle-Turner scattering factor

In this case we have a one dimensional potential and only one quantum number, n, and dipole selection rules dictate An odd. An example of the photon spectrum observed in the forward direction for the injection of 54 Mey electrons along the (110) planar direction in Si is shown in Fig. 16.xhe bound state An = 1 transitions are evident up to n = 5>4 and at higher energies the An = 3 transitions are also evident. One can now compare the observed spectrum with calculations based on e.g. Hartree-Fock descriptions of the Si atom. This can be done directly through the solution for the onedimensional Schrodinger equation or one may work in momentum space and use the many-beam formulation of the Schrodinger equation for the transverse motion. The results of the many-beam calculations which use Doyle-Turner scattering factors derived from Hartree-Fock wave functions are compared with experimental results in Table II. 

P. A. Doyle, P. S. Turner, Relativistic Hartree-Fock X-ray and Electron Scattering Factors, Acta Cryst, A24, 390-397,1968. 

For both structures atomic scattering factors for neutral F, Xe, and As given by Doyle and Turner and the values of the dispersion corrections, for Xe and As, of Cromer and Liberman were used. Calculations were performed on our CDC 6600 and CDC 7600 computers. ... 

Scattering factors for neutral F, Xe, and Pd were taken from Doyle and Turner" and Cromer and Waber." Cromer and Liberman s values" of Af and A/" were used for anomalous dispersion corrections. ... 

Three-dimensional Patterson functions showed the positions of the Xe and As atoms. Subsequent least-squares rerinements, Fourier calculations, and difference Fourier calculations revealed the fluorine atom positions. Least-squares refinements, in which the function EwdfJ -was minimized, converged rapidly to the final structures. Scattering factors of Doyle and Turner were used, and anomalous dispersion corrections were applied. The resulting R factors are given in Table I. 

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