International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 229

Section 4.2.4.2.3. Theoretical Compton scattering data: σC

D. C. Creaghb and J. H. Hubbelld

4.2.4.2.3. Theoretical Compton scattering data: σC

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The bound-electron Compton scattering cross section is given by [\eqalignno{ \sigma _C = {}&\pi r \,^2_e \textstyle\int\limits^1_{-1} [1 + k (1 - \cos \varphi)] ^{-2}\cr &\times \{ + \cos ^2 \varphi + k ^2 (1 - \cos \varphi) ^2\cr &\times [1 + k (1 - \cos \varphi)] ^{-1} \} I (q,z)\, {\rm d} (\cos \varphi). &(4.2.4.10)}]Here [k = \hbar \omega /mc^2] and [I (q, z)] is the incoherent scattering intensity expressed in electron units. The other symbols have the meanings defined in §§4.2.4.2.1[link] and 4.2.4.2.2[link].

Values of [\sigma _C] incorporated into the tables of total cross section σ have been computed using the incoherent scattering intensities from the tabulation by Hubbell et al. (1975[link]) based on the calculations by Cromer & Mann (1967[link]) and Cromer (1969[link]).

References

First citation Cromer, D. T. (1969). Anomalous dispersion corrections computed from self consistent field relativistic Dirac–Slater wavefunctions. J. Chem. Phys. 50, 4857–4859.Google Scholar
 First citation Cromer, D. T. & Mann, J. B. (1967). Compton scattering factors for spherically symmetric free atoms. J. Chem. Phys. 47, 1892–1893.Google Scholar
 First citation Hubbell, J. H., Veigele, W. J., Briggs, E. A., Brown, R. T., Cromer, D. T. & Howerton, R. J. (1975). Atomic form factors, incoherent scattering functions and photon scattering cross sections. J. Phys. Chem. Ref. Data, 4, 471–538.Google Scholar








































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