View source for Cromer–Mann coefficients

== Definition ==

The set of nine coefficients <math>a_i, b_i, c\, (i=1,\dots, 4)</math> in a parameterization of the non-dispersive part of the [[atomic scattering factor]] for neutral atoms as a function of <math>(\sin \theta)/\lambda</math>:

<math>f^0(\sin\theta/\lambda) = \sum_{i=1}^4 a_i \exp[-b_i(\sin\theta/\lambda)^2] + c</math>

for <math>0 < (\sin\theta)/\lambda < 2.0\,\mathrm{\AA}^{-1}</math>.

This expression is convenient for calculation in crystal structure software suites.

== History ==

Atomic scattering factors for non-hydrogen atoms were calculated from relativistic Hartree&ndash;Fock wavefunctions by Doyle, P. A. and Turner, P. S. [(1968). [https://doi.org/10.1107/S0567739468000756 ''Acta Cryst.'' A'''24''', 390–397]. ''Relativistic Hartree–Fock and electron scattering factors''] using the wavefunctions of Coulthard, M. A. [(1967). [https://doi.org/10.1088/0370-1328%2F91%2F1%2F309 ''Proc. Phys. Soc.'' '''91''', 44–49]. ''A relativistic Hartree–Fock atomic field calculation''], and in 1968 by Cromer, D. T. and Waber, J. T. using the unpublished wavefunctions of J. B. Mann [''International Tables for X-ray Crystallography'' (1974), Vol. IV, p. 71. Birmingham: Kynoch Press]. The latter are based on a more exact treatment of potential that allows for the finite size of the nucleus. Subsequent calculations [Fox, A. G., O'Keefe, M. A. and Tabbernor, M. A. (1989). [https://doi.org/10.1107/S0108767389007567 ''Acta Cryst.'' A'''45''', 786–793]. ''Relativistic Hartree–Fock X-ray and electron atomic scattering factors at high angles''] extended the useful range to 6 Å<sup>−1</sup> to accommodate the increasing numbers of applications for high-angle scattering factors.

== See also ==

*Intensity of diffracted intensities. P. J. Brown, A. G. Fox, E. N. Maslen, M. A. O'Keefe and B. T. M. Willis. ''International Tables for Crystallography'' (2006). [https://doi.org/10.1107/97809553602060000600 Vol. C, ch. 6.1, pp. 554-595], especially Table 6.1.1.4.


[[Category:Structure determination]]
[[Category:X-rays]]