Polarized Neutrons

a collection of neutrons whose spins have a preferential orientation with respect to a particular direction in space, usually the direction of a magnetic field. Since a neutron has a spin of 1/2, in a magnetic field H two orientations of its spin are possible: parallel or antiparallel to H. A neutron beam is polarized if it contains a different number N of neutrons with spins oriented along (N₊) and against (N_–) the field. The degree of polarization is characterized by the quantity

p = (N₊ – N_–)/(N₊ + N_–)

Polarized neutrons were first produced by the transmission of a beam of neutrons through an iron plate magnetized to saturation; this method was proposed in 1936 by F. Bloch and investigated in 1947 by the American D. Hughes and coworkers. Neutrons whose spins are parallel to the direction of magnetization of a ferromagnet are scattered more strongly and leave the beam. As a result, a neutron beam that has passed through the plate is rich in neutrons with spins antiparallel to the magnetization. The method requires strong magnetizing fields. In fields of H ≈ 10,000 oersteds, the maximum degree of polarization is

More effective is the diffraction method, worked out by C. Shull, E. Wollan, and W. Coller of the USA in 1951. It is based on the diffraction of neutrons by certain planes of magnetized ferromagnetic single crystals, such as the alloy Co-Fe. By changing the magnitude of magnetization and the families of the reflecting planes of the crystal, the coherent magnetic scattering amplitude can be varied from zero to some maximum value. This means that for a ferromagnetic single crystal, a Bragg reflection and magnitude of magnetization can be selected such that the nuclear amplitude b and the magnetic amplitude f_m are equal. For neutrons with a spin antiparallel to the direction of magnetization, the net scattering amplitude is then equal to zero—that is, the beam of neutrons, reflected at the Bragg angle spins parallel to the magnetization. The diffraction method permits the obtaining of a monochromatic beam of polarized thermal and resonance neutrons with a degree of polarization of up to 0.99.

The method of neutron reflection from magnetized ferromagnetic mirrors, such as cobalt mirrors, is often used to produce polarized neutrons. Under certain conditions, neutrons with spins parallel to the magnetization of the ferromagnet undergo total reflection. This method permits the obtaining of intense reflected polarized beams of neutrons. An inhomogeneous magnetic field may also be used as a neutron polarizer. When a neutron beam passes through such a field, it is split into two beams, since oppositely directed forces act on the neutrons, which have two different spin orientations.

Another method of producing polarized neutrons is the scattering of neutrons by oriented nuclei. In this case, the neutrons are transmitted through a polarized nuclear target. The nuclear scattering amplitude depends on the orientation of the neutrons’ spin with respect to the spin of the nucleus. Maximum scattering corresponds to parallel spins of the neutron and nucleus, and minimum scattering to antiparallel spins. A target containing oriented protons is particularly effective. Since the cross section for the scattering of slow neutrons by protons is independent of the neutrons’ energy, polarized neutrons can be obtained in the range 10^-2 electron volts (eV) to 104–105 eV. This method was first used by F. L. Shapiro and coworkers in 1963. Polarized neutrons with an energy > 10⁶ eV are produced when neutrons are scattered by nuclei as a result of the spin-orbit interaction.

Polarized neutrons have numerous applications in nuclear physics. They are used both in the investigation of properties of the interaction of nucléons—the nonconservation of parity in nuclear forces, the time invariance of nuclear interactions, and the dynamics of neutron β-decay—and in the study of the structure of the nucleus. In solid-state physics, polarized neutrons make possible the investigation of the configuration of unpaired electrons in magnetic substances; precise measurements of the distribution of unpaired electrons of atoms and ions in the crystal lattice have, in many cases, resulted in the detection of deviations of the charge distribution from a spherically symmetric distribution. In addition, the use of polarized neutrons has permitted measurement of such quantities as the magnetic moments of the individual components of alloys and the magnitude and sign of magnetic scattering amplitudes. Other uses include the investigation of variations in the polarization of neutrons when scattered and the investigation of the rotation of the plane of polarization in some crystals—the study of this rotation facilitates the deciphering of complex magnetic structures. The inelastic scattering of polarized neutrons is of great importance for the investigation of the dynamic properties of the lattices of magnetic crystals. Polarized neutrons are also used, for example, in the study of ferromagnet-paramagnet phase transitions.