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Neutron Spectroscopy

Volume 25, Issue 12, pp. 12-14

David W. Ball
Most of us are at least nominally aware that light (rather, electromagnetic radiation) is not the only possible probe of matter and its behavior. One type of analysis uses neutrons as the probe of matter. As such, this is a form of neutron spectroscopy, or as it is more commonly called, neutron scattering. Neutron scattering is separated into two types: elastic neutron scattering and inelastic neutron scattering. In elastic neutron scattering, the neutrons have the same energy coming out of a sample as they did going in, while in inelastic neutron scattering the energy of the neutrons changes because of their interaction with matter. Here I will briefly introduce both types of scattering.

Sources of Neutrons

Neutrons are a kind of subatomic particle normally found in the nucleus of atoms. Hence, production of neutrons invariably requires nuclear processes. A common source of neutrons for research (as opposed to power generation) purposes is a small nuclear reactor that uses low-enriched uranium, or LEU. LEU is defined as uranium enriched in 235 U at concentrations less than 20% (natural uranium consists of 0.7% 235 U). According to the International Atomic Energy Agency's web site (1), at this writing there are currently 235 reactors around the world that are supplying neutrons for research purposes.

The other way of generating neutrons is by spallation, which is the name given to the process by which a target is hit with a projectile and pieces of the target are ejected as a result. In nuclear spallation, hydride ions (H ) are accelerated by a particle accelerator, then stripped of their electrons down to the bare proton, which is accelerated further and directed to a heavy metal (like tantalum or mercury) target. As many as 20–30 neutrons are given off by the metal nucleus for each proton that impacts the nuclei. The neutrons are then directed toward various experiments. The person who first envisioned nuclear spallation? Glenn Seaborg.

In many circumstances, neutrons that are produced by either method are too high in energy, so their energies must be decreased before they are used; we say that the neutrons must be moderated. Materials that moderate neutrons include light and heavy water, beryllium, and graphite.

Neutrons are classified by their energies (expressed in electron-volts, eV), which are directly related to their velocities (in meters or kilometers per second) and temperatures (in kelvins). For a particle the size of a neutron (1.675 10–27 kg), 1 eV of energy corresponds to a velocity of 13.8 km/s; keep in mind that the energy of a neutron depends on the square of the velocity (remember, K = mv 2 ). As such, classification can imply a neutron's velocity or its temperature. Fast neutrons have an energy of 0.1–1 MeV (megaelectron-volt), or a velocity of 4000–14,000 km/s. Slow neutrons have an energy of 100 eV or less, corresponding to a velocity of 138 km/s. (Take these numbers with a grain of salt; references can differ greatly about the energy and velocity cutoffs. It should be clear, however, that fast neutrons are, well, faster and more energetic than slow neutrons.)

Thermal neutrons have an average temperature of room temperature, or about 295 K. This corresponds to an energy of 0.025 eV and a velocity of 2.2 km/s. Neutrons with an energy/velocity/temperature higher than this are called hot neutrons, and neutrons with an energy/velocity/temperature lower than this are called cold neutrons. Even within cold neutrons, there are other classifications, going down to ultracold neutrons, which have energies in the range of nanoelectron-volts and velocities on the order of meters per second.

One other thing to remember is that neutrons have an equivalent wavelength given by the de Broglie relation:

λ = h/p = h/mv

where λ is the de Broglie wavelength in meters, h is Planck's constant in units of joule-seconds, m is the mass of a particle in kilograms, and v is the velocity of the particle in meters per second. For a neutron, h and m are constants (we're assuming that most velocities are nonrelativistic, or that relativistic corrections — which for these neutrons are on the order of 1.5% at most — can be ignored), so the de Broglie relation reduces to

λ = (3.956 10–7)/v

Thus, neutron wavelengths range from 2.8 10–14 m (0.00028 ) or smaller for fast neutrons to 1.8 10–10 m (1.8 ) for thermal neutrons to 4.95 10–8 m (495 , which is the same wavelength as extreme ultraviolet [EUV] light) for ultracold neutrons. Some forms of neutron scattering take advantage of the wave nature of neutrons.

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