InternationalReciprocal spaceTables for Crystallography Volume B Edited by U. Shmueli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B, ch. 1.2, p. 10
## Section 1.2.2. General scattering expression for X-rays |

The total scattering of X-rays contains both elastic and inelastic components. Within the first-order Born approximation (Born, 1926) it has been treated by several authors (*e.g.* Waller & Hartree, 1929; Feil, 1977) and is given by the expression where is the classical Thomson scattering of an X-ray beam by a free electron, which is equal to for an unpolarized beam of unit intensity, ψ is the *n*-electron space-wavefunction expressed in the 3*n* coordinates of the electrons located at and the integration is over the coordinates of all electrons. **S** is the scattering vector of length .

The coherent elastic component of the scattering, in units of the scattering of a free electron, is given by

If integration is performed over all coordinates but those of the *j*th electron, one obtains after summation over all electrons where is the electron distribution. The scattering amplitude is then given by or where is the Fourier transform operator.

### References

Born, M. (1926).*Quantenmechanik der Stoszvorgänge. Z. Phys.*

**38**, 803.

Feil, D. (1977).

*Diffraction physics. Isr. J. Chem.*

**16**, 103–110.

Waller, I. & Hartree, D. R. (1929).

*Intensity of total scattering X-rays. Proc. R. Soc. London Ser. A*,

**124**, 119–142.