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.

This scattering length varies by isotope (and by element as the weighted arithmetic mean over the constituent isotopes) in a way that appears random, whereas the X-ray scattering length is just the product of atomic number and Thomson scattering length, thus monotonically increasing with atomic number.

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, while for vanadium already the opposite signs of the only naturally occurring isotope's two spin configurations give a near cancellation.

However, neutrons will still undergo strong incoherent scattering in these materials.

By using heavy water as solvent and/or selective deuteration of the probed molecule (exchanging the naturally occurring protium by deuterium) this difference can be leveraged in order to image the hydrogen configuration in organic matter, which is nearly impossible with X-rays due to their small sensitivity to hydrogen's single electron.