# Cromerâ€“Mann coefficients

The set of nine coefficients in a parameterization of the non-dispersive part of the atomic scattering factor for neutral atoms as a function of (sinθ) / λ:

for .

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

### History

Atomic scattering factors for non-hydrogen atoms were calculated from relativistic Hartree–Fock wavefunctions by Doyle, P. A. & Turner, P. S. [(1968). *Acta Cryst.* A**24**, 390–397. *Relativistic Hartree–Fock and electron scattering factors*] using the wavefunctions of Coulthard, M. A. [(1967).*Proc. Phys. Soc.* **91**, 44–49. *A relativistic Hartree–Fock atomic field calculation*], and in 1968 by Cromer, D. T. & Waber, J. T. using the unpublished wavefunctions of J. B. Mann [*International Tables for X-ray Crystallography* (1974), Vol.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. & Tabbernor, M. A. (1989). *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^{−1} 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). Vol. C, ch. 6.1, pp. 554-595,especially Table 6.1.1.4.