In zero order dynamical theory of diffraction the refractive index is directly related to the scattering length density and is a measure of the strength of the interaction of a neutron wave with a given nucleus. The following table shows the scattering lengths for various elements (in 10-12 cm).
SANS usually uses collimation of the neutron beam to determine the scattering angle of a neutron, which results in an ever lower signal-to-noise ratio for data that contains information on the properties of a sample at relatively long length scales, beyond ~1 μm. The traditional solution is to increase the brightness of the source, as in Ultra Small Angle Neutron Scattering (USANS). As an alternative Spin-echo Small-angle Neutron Scattering (SESANS) was introduced, using neutron spin echo to track the scattering angle, and expanding the range of length scales which can be studied by neutron scattering to well beyond 10 μm.
A crucial feature of SANS that makes it particularly useful for the biological sciences is the special behavior of hydrogen, especially compared to deuterium. In biological systems hydrogen can be exchanged with deuterium which usually has minimal effect on the sample but has dramatic effects on the scattering.
The technique of contrast variation (or contrast matching) relies on the differential scatter of hydrogen vs. deuterium. Figure 1 shows the scattering length density for water and various biological macromolecules as a function of the deuterium concentration. (Adapted from .) Biological samples are usually dissolved in water, so their hydrogens are able to exchange with any deuteriums in the solvent. Since the overall scatter of a molecule depends on the scatter of all its components, this will depend on the ratio of hydrogen to deuterium in the molecule. At certain ratios of H2O to D2O, called match points, the scatter from the molecule will equal that of the solvent, and thus be eliminated when the scatter from the buffer is subtracted from the data. For instance the match point for proteins is typically around 40-45% D2O, and at that concentration the scatter from the protein will be indistinguishable from that of the buffer.
To use contrast variation, different components of a system must scatter differently. This can be based on inherent scattering differences, e.g. DNA vs. protein, or arise from differentially labeled components, e.g. having one protein in a complex deuterated while the rest are protonated. (For some examples of this method see .)