Neutron scattering length


A neutron may pass by a nucleus with a probability determined by the nuclear interaction distance, or be absorbed, or undergo scattering that may be either coherent or incoherent. The scattering length of neutrons varies by element and isotope in a way that appears random, whereas the scattering of X-rays generally increases with the atomic number.
The scattering length may be either positive or negative. The scattering cross-section is equal to the square of the scattering length multiplied by 4π, i.e. the area of a circle with radius twice the scattering length. In some cases, as with titanium and nickel, it is possible to mix isotopes of an element whose lengths are of opposite signs to give a net scattering length of zero, in which case coherent scattering will not occur at all. However, neutrons will still undergo strong incoherent scattering in these materials.
There is a large difference in scattering length between protium and deuterium. This means that protium, the most common isotope of hydrogen, is poorly imaged due to its smaller absolute magnitude and because its scattering density tends to cancel that of adjacent carbon, nitrogen, or oxygen, which have positive scattering lengths. Because of these factors, as well as the much larger incoherent scattering cross section of protium, ordinary proteins cannot be imaged as well as those that are fully deuterated. Specific exchangeable hydrogens in a non-deuterated protein may be imaged if it is exposed to heavy water.
More comprehensive data is available from NIST and Atominstitut of Vienna.