Neutron spectroscopy is a spectroscopic method of measuring atomic and magnetic motions by measuring the

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

of emitted

neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...

s. The measured neutrons may be emitted directly (for example, by

nuclear reactions In nuclear physics and nuclear chemistry, a nuclear reaction is a process in which two nuclei, or a nucleus and an external subatomic particle, collide to produce one or more new nuclides. Thus, a nuclear reaction must cause a transformation o ...

), or they may scatter off cold matter before reaching the detector. Inelastic neutron scattering observes the change in the energy and wavevector of the neutron as it scatters from a sample. This can be used to probe a wide variety of different physical phenomena such as the motions of atoms (diffusional or hopping), the rotational modes of molecules, sound modes and

molecular vibration A molecular vibration is a Periodic function, periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The infrared spectroscopy correlation table, typical vibrational fre ...

s, recoil in quantum fluids, magnetic and quantum excitations or even electronic transitions. Since its discovery, neutron spectroscopy has become useful in medicine as it has been applied to radiation protection and

radiation therapy Radiation therapy or radiotherapy (RT, RTx, or XRT) is a therapy, treatment using ionizing radiation, generally provided as part of treatment of cancer, cancer therapy to either kill or control the growth of malignancy, malignant cell (biology), ...

. It is also used in

nuclear fusion Nuclear fusion is a nuclear reaction, reaction in which two or more atomic nuclei combine to form a larger nuclei, nuclei/neutrons, neutron by-products. The difference in mass between the reactants and products is manifested as either the rele ...

experiments, where the neutron spectrum can be used to infer the plasma temperature, density, and composition, in addition to the total fusion power. Neutron spectroscopy is routinely conducted with a wide range of neutron energies, from as low as a few hundredths of an

electronvolt In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an Voltage, electric potential difference of one volt in vacuum ...

to as high as tens of megaelectronvolts. Much current research focuses on expanding these capabilities to higher energies. In 2001, US researchers were able to measure neutrons with energies up to 100

gigaelectronvolt In physics, an electronvolt (symbol eV), also written electron-volt and electron volt, is the measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum. When us ...

Scattering interactions involved in neutron spectroscopy

There are three different types of

scattering In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiat ...

interactions that allow for the probing of a variety of properties using neutrons: nuclear scattering (coherent scattering), spin-dependent nuclear scattering ( incoherent scattering), and magnetic dipole interactions between the neutron and dipolar field of unpaired

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

s. In most cases, coherent scattering and incoherent scattering are used to investigate molecular properties. With these scattering interactions, it is possible to probe diffusive motions in liquid water such as translational and rotational motions since the energies associated with this action are on the order of about 1 meV. Neutron spectroscopy can also be used to probe inter and intramolecular vibrational modes as the energies associated with such transfers are around 400-500 meV which is still within the range of energies possible for this method.

Coherent nuclear scattering

The first type of interaction is nuclear scattering occurs when neutrons interact with nuclei through the very short range nuclear force. The wavelength, λ, is on the order of a few angstroms (Å). Because a thermal neutron cannot “see” the internal structure of a nucleus, the scattering is considered to be

isotropic In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence '' anisotropy''. ''Anisotropy'' is also ...

. This interaction is thus characterized by a scattering length of b, which is on the same order of the size of a nucleus (10⁻¹⁵ m). Therefore, nuclear scattering allows for the probing of density correlations of nucleons in the nucleus.

Incoherent nuclear scattering

The second type of interaction is spin-dependent nuclear scattering, which is when the neutron and nucleus interaction depends on the total spin (spin of the neutron, ½, and spin of the nucleus, I) formed during the scattering event. The two possible states thus become I + ½ and I – ½. This spin dependence thus results in incoherent scattering, which allows for the probing of single-particle motion as well as the study of the ordering of nuclear spins at ultra-low temperatures.

Magnetic dipole interaction

The third type of interaction is between the

magnetic dipole moment In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude ...

of the neutron and the dipolar field from unpaired electrons. This allows the total spin of the unpaired electrons and neutron to be probed. The magnetic scattering length from one electron is b_m = 𝛾r₀ = 1.348 fm which is on the same order of magnitude as the nuclear scattering length. Because of the dipole-dipole character of the interaction, the scattering is considered to be anisotropic.

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