Atomic form factor information

In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray, electron or neutron. The common feature of all form factors is that they involve a Fourier transform of a spatial density distribution of the scattering object from real space to momentum space (also known as reciprocal space). For an object with spatial density distribution, $\rho (\mathbf {r} )$ , the form factor, $f(\mathbf {Q} )$ , is defined as

f(\mathbf {Q} )=\int \rho (\mathbf {r} )e^{i\mathbf {Q} \cdot \mathbf {r} }\mathrm {d} ^{3}\mathbf {r}

,

where $\rho (\mathbf {r} )$ is the spatial density of the scatterer about its center of mass ( $\mathbf {r} =0$ ), and $\mathbf {Q}$ is the momentum transfer. As a result of the nature of the Fourier transform, the broader the distribution of the scatterer $\rho$ in real space $\mathbf {r}$ , the narrower the distribution of $f$ in $\mathbf {Q}$ ; i.e., the faster the decay of the form factor.

For crystals, atomic form factors are used to calculate the structure factor for a given Bragg peak of a crystal.

Atomic form factor information

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