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I know that atomic form factors for x-ray scattering are obtained by Fourier transform of the electronic charge density.

I am looking for a citable elementary source (book, review, article) which covers the systematic and explicit derivation of the relationship between electronic charge density and the atomic form factor, to which people unfamiliar with the connection can be referred to for better context.

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Here is a possible source: Modern X-ray analysis on single crystals: a practical guide by Peter Luger, De Gruyter, Inc. 2014.

The relevant excerpt describing how to estimate the density of an atom j, and with that, the scattering factor (really scattering function) is below.

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So atomic scattering factors are derived by taking the Fourier transform of the computed electron density of a stationary atom (the density has spherical symmetry, so the scattering factor is a function that only depends on $s = \sin \theta / \lambda$).

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    $\begingroup$ Thanks for your time. But this is not what I am looking for. The atomic scattering factors are calculated by taking a Fourier transform of the charge density. But this relation itself has an analytical derivation which starts with differential scattering cross section. That is what I am interested in. $\endgroup$ – R.U. Apr 19 at 18:45

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