Slow Neutrons

neutrons having kinetic energies of up to 100 kiloelectron volts (keV). A distinction is made among ultracold neutrons (0-10^-7 eV), cold neutrons (10^-7-5 × 10^-3 eV), thermal neutrons (5 × 10^-3-0.5 eV), resonance neutrons (0.5 eV-10 keV), and intermediate neutrons (10-100 keV). Resonance and intermediate neutrons are often combined under the general term “intermediate neutrons” (0.5 eV to 100 keV). Neutrons with energies greater than 100 keV are called fast neutrons. “Slow neutrons” and “fast neutrons” are distinguished because of the different character of their interaction with matter, the different methods of producing and detecting them, and the differences in their uses. The values given above for the limiting energies are arbitrary. In fact, these limits are not rigid and depend on the type of phenomenon and on the specific substance.

Interaction of slow neutrons with nuclei. Neutron scattering is a universal process that takes place in all nuclei at all neutron energies. A unique feature of the scattering of slow neutrons is that the process is not accompanied by the transmutation of the nucleus to an excited state (elastic scattering). Inelastic scattering becomes possible at an energy equal to (1 + 1/A)ε_ex, where A is the mass number of the scattering nucleus and ε_ex is the energy of the nucleus’ first excited level. This energy generally is at least a few tens of kiloelectron volts and reaches several megaelectron volts for even-even spherical nuclei.

Since an energy of 100 keV is a small quantity on the nuclear scale of energies, slow neutrons can produce only nuclear reactions that are accompanied by a release of energy (exothermic reactions). The chief example of an exothermic reaction is the capture of a neutron by a nucleus accompanied by electromagnetic radiation (radiative capture). Radiative capture is energetically favorable and is observed, with a higher or lower probability (with a larger or smaller effective cross section), for all nuclei with the exception of ⁴He. Three other types of nuclear reactions that are energetically favorable for many nuclei are the (n,p), (n,a), and fission reactions. The ³He(n,p)³H, ¹⁰B(n,a)⁷Li, ⁶Li(n,a)³H, and ¹⁴N(n,p)¹⁴C reactions are widely used to detect slow neutrons (see below) and (with the exception of the first reaction) to provide shielding against slow neutrons. The last two reactions are also used to produce tritium and the carbon isotope ¹⁴C. A fission reaction is induced by slow neutrons only in certain very heavy nuclei, for example, ²³³U, ²³⁵U, and ²³⁹Pu.

The existence of resonance maxima (resonances) in the energy dependence of the effective cross sections is the most characteristic feature of the interaction of slow neutrons with nuclei. Each resonance corresponds to an excited state of a compound nucleus with mass number (A + 1) and an excitation energy equal to the binding energy of the neutron with the nucleus plus the quantity [A/(A + 1)]ǀε_o, where ε_o is the kinetic energy of the neutron for which a resonance is observed. The energy dependence of the effective cross section near a resonance is described by the BreitWigner formula.

As the neutron energy increases, the resonance lines broaden and begin to overlap, and there is a transition to a smooth dependence of cross section on energy that is characteristic of fast neutrons.

The cross section of any nuclear reaction produced by a sufficiently slow neutron is inversely proportional to the neutron velocity v. This relation is called the 1/v law. A correction to the 1/v law—which is as general as the law itself—is also known, but this correction is important only for certain reactions that have a very large effective cross section [for example, ⁷Be(n,p) and ³He(n,p)]. Deviations from the 1/v law usually begin to appear when the energy of the neutron becomes comparable to the energy of the resonance level closest to 0. For thermal neutrons, the 1/v law is valid for most nuclei.

Scattering of slow neutrons in atomic systems. The nature of the scattering of slow neutrons in molecules and in crystals depends on the relation between the energy of the neutron ε_n and the energy difference △ε between energy levels of the system and also depends on the relation between the wavelength of the neutron λ and the interatomic distances a. When ε_n > △ε and λ « a (<< α (ε_n ≥ 1 eV), a neutron does not “sense” the atomic bonding and order in the atomic array. Scattering usually takes place in the same way as for isolated fixed nuclei,’ with the neutron losing an energy of the order of 2Aε_n/(A + 1)² (A is the mass number of the nucleus).

When ε_n is of the order of △ε and λ is of the order of a (thermal neutrons), elastic scattering is possible (without a change in the neutron energy); however, in inelastic scattering, a neutron can not only lose energy but also gain energy such that the change in the neutron energy is dependent not only on the mass of the nucleus but also on the energy spectrum of the system. In this case, the nucleus remains unexcited. When X is of the order of a, neutron diffraction and magnetic scattering by atomic electrons take place.

For thermal neutrons, total reflection is observed for grazing incidence upon the surface of many solids, with the range of angles in which reflection takes place increasing with decreasing neutron energy. Ultracold neutrons (velocity ≤ 5 m/sec) can undergo mirror reflection at any angle of incidence on the smooth surface of many solids. Therefore, such neutrons can be stored for a long time (hundreds of seconds) within closed vessels with polished walls.

Sources and detectors. Slow neutrons with ε_n ≳ 10 KeV can be produced by electrostatic generators in nuclear reactions of the type (p,n). The reactions ⁷Li(p,n) and ³H(p,n) are most often used. The neutron energy is regulated by changing the voltage that accelerates the protons. The moderation of fast neutrons is used to produce slow neutrons. Upon moderation, a continuous spectrum of neutrons is formed, and for good moderators (such as water and graphite) of sufficiently large bulk, a large fraction of the neutrons reach thermal velocities. This result leads to the formation of thermal neutrons that are in thermal equilibrium with the medium and whose velocity distribution is Maxwellian. At room temperature, the most probable energy in a flux of thermal neutrons is equal to 0.025 eV.

In order to obtain slower neutrons, the moderators are cooled to the temperature of liquid nitrogen or below. A beam of thermal neutrons can be filtered through certain substances such as Be, Pb, and graphite in order to isolate cold neutrons. Such substances are transparent to neutrons having a wavelength of λ > 2d, where d is the maximum distance between the atomic planes. Beryllium and graphite filters transmit neutrons having energy less than 5.2 ç 10^-3 eVand 1.5 × 10^-3 eV, respectively.

Slow neutrons are recorded by detecting the products of the nuclear reactions that they induce. The method of detecting the recoil nuclei that arise during neutron scattering, which is used to record fast neutrons, is unsuitable for slow neutrons, since slow recoil nuclei do not produce ionization.

Uses. Slow neutrons and, in particular, thermal neutrons are of great importance in the operation of nuclear reactors. High thermal-neutron fluxes in nuclear reactors are widely used to produce radioactive isotopes. Neutron resonances allow the excitation properties of the levels of nuclei to be studied in a narrow band of excitation energies for binding energies of the neutron in the nucleus of the order of 5-8 MeV. Structural studies of crystals by means of thermal-neutron diffraction are of great importance in solid-state physics. Studies of the inelastic scattering of thermal and cold neutrons provide important information on the dynamics of atoms in solids and liquids and on the properties of molecules.