International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by E. Arnold, D. M. Himmel and M. G. Rossmann © International Union of Crystallography 2012 
International Tables for Crystallography (2012). Vol. F, ch. 2.1, p. 54
Section 2.1.4.3.1. Scattering by one atom^{a}Laboratory of Biophysical Chemistry, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands 
Electrons in an atom are bound by the nucleus and are – in principle – not free electrons.
However, to a good approximation, they can be regarded as such if the frequency of the incident radiation ν is greater than the natural absorption frequencies, , at the absorption edges of the scattering atom, or the wavelength of the incident radiation is shorter than the absorptionedge wavelength (Section 2.1.4.4). This is normally true for light atoms but not for heavy ones (Table 2.1.4.1).

If the electrons in an atom can be regarded as free electrons, the scattering amplitude of the atom is a real quantity, because the electron cloud has a centrosymmetric distribution, i.e. .
A small volume, , at r contains electrons, and at −r there are electrons. The combined scattering of the two volume elements, in units of the scattering of a free electron, isthis is a real quantity.
The scattering amplitude of an atom is called the atomic scattering factor f. It expresses the scattering of an atom in terms of the scattering of a single electron. f values are calculated for spherically averaged electrondensity distributions and, therefore, do not depend on the scattering direction. They are tabulated in IT C (2004) as a function of . The f values decrease appreciably as a function of (Fig. 2.1.4.5). This is due to interference effects between the scattering from the electrons in the cloud. In the direction , all electrons scatter in phase and the atomic scattering factor is equal to the number of electrons in the atom.
References
International Tables for Crystallography (2004). Vol. C. Mathematical, Physical and Chemical Tables, edited by E. Prince. Dordrecht: Kluwer Academic Publishers.