Editing Small-angle neutron scattering (section)

==Technique==
During a SANS experiment a beam of neutrons is directed at a sample, which can be an [[aqueous]] solution, a solid, a [[Powder diffraction|powder]], or a [[Neutron crystallography|crystal]]. The neutrons are elastically scattered by nuclear interaction with the nuclei or interaction with magnetic momentum of unpaired electrons. In X-ray scattering, photons interact with the electronic cloud so the bigger the element, the bigger the effect is. In neutron scattering, neutrons interact with nuclei and the interaction depends on the isotope; some light elements like deuterium show similar scattering cross section as heavy elements like Pb.

In zero order [[dynamical theory|dynamical theory of diffraction]] the [[refractive index]] is directly related to the '''[[scattering length|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 [[neutron scattering length]] for a few chemical elements (in 10<sup>−12</sup> cm).<ref name="Jacrot">{{cite journal
 | last = Jacrot
 | first = B
 | title = The study of biological structures by neutron scattering from solution
 | journal = Reports on Progress in Physics
 | volume = 39
 | issue = 10
 | pages = 911–53
 | date = 1976
 | url = http://www.iop.org/EJ/abstract/0034-4885/39/10/001
 | doi = 10.1088/0034-4885/39/10/001
|bibcode = 1976RPPh...39..911J | s2cid = 250751286
 }}</ref>
{| class="wikitable"
|-
! H !! D !! C !! N !! O !! P !! S
|-
| −0.3742 || 0.6671 || 0.6651 || 0.940 || 0.5804 || 0.517 || 0.2847
|}
Note that the relative scale of the scattering lengths is the same. Another important point is that the scattering from hydrogen is distinct from that of [[deuterium]]. Also, hydrogen is one of the few elements that has a negative scattering length, which means that neutrons deflected from hydrogen are 180° out of phase relative to those deflected by the other elements. These features are important for the technique of contrast variation (see below).

=== Related techniques ===

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.

[[Grazing-incidence small-angle scattering]] (GISANS) combines ideas of SANS and of [[neutron reflectometry]].