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 interference effects in coherent scattering can be computed via the coherent
scattering length The scattering length in quantum mechanics describes low-energy scattering. For potentials that decay faster than 1/r^3 as r\to \infty, it is defined as the following low-energy limit:
:
\lim_ k\cot\delta(k) =- \frac\;,
where a is the scatterin ...
of neutrons, being proportional to the amplitude of the spherical scattered waves according to
Huygens–Fresnel theory. 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
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
and
Thomson scattering length
The classical electron radius is a combination of fundamental physical quantities that define a length scale for problems involving an electron interacting with electromagnetic radiation. It links the classical electrostatic self-interaction energ ...
, thus monotonically increasing with 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
In geometry, the area enclosed by a circle of radius is . Here the Greek letter represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
One method of deriving this formula, which origi ...
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, 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.
There is a large difference in scattering length between
protium (-0.374) and
deuterium
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
(0.667). 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. On the other hand, neutron scattering studies of hydrogen-containing samples often suffer from the strong incoherent scattering of natural hydrogen.
More comprehensive data is available from
NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
and Atominstitut of Vienna.
[{{cite web, url=https://www.tuwien.at/en/phy/ati/neutron-and-quantum-physics/research/techniques-of-neutron-physics/table-of-neutron-scattering-lengths, title=Neutron Scattering Lengths]
References
Neutron scattering