Oriented Nuclei

(or polarized nuclei), an assembly of atomic nuclei with ordering in the spatial orientation of their spins (spin ordering). The projection m of the spin I of a nucleus on a given axis in space can assume 2I + 1 discrete values, from m = –I to m= +I, at intervals of 1. Spin ordering with respect to this axis is characterized by the set of probabilities W_m for all possible values of m. For a disordered assembly of nuclei, all W_m = 1/(2I + 1). Violation of this condition signifies the presence of spin ordering.

Instead of W_m an equivalent set of orientation parameters f_k, where k = 1, …, 2I, is often used in describing spin ordering. The parameters are polynomials in the average values of powers of m:

for example,

The quantity f₁ is called the polarization of the nuclei, and f₂ the nuclear alignment. These quantities have a comparatively simple meaning: the polarization f₁ characterizes the preferential orientation of the nuclear spins parallel to a given direction on some axis, and the alignment f₂ characterizes the orientation parallel and antiparallel to the axis—that is, the symmetry of the orientation with respect to a plane perpendicular to the axis. In particular, the orientation parameters f_k are introduced because it is precisely these parameters that enter directly into the expression for the energy of interaction of the nuclei with an electromagnetic field (this interaction is used to produce oriented nuclei; see below). Thus,f₁ determines the interaction energy of the magnetic moment of the nucleus with a magnetic field, and f₂ the interaction energy of the nuclear quadrupole moment with a nonuniform electric field.

In naturally occurring substances, the atomic nuclei are not oriented. Special methods based on the presence in nuclei of magnetic dipole and electric quadrupole moments directed along the nuclear spins have been developed to produce oriented nuclei. The methods may be static or dynamic. The static method uses the orienting interaction of a magnetic field with the magnetic dipole moments of the nuclei (the greater the field and the magnetic moment of the nucleus, the stronger the orientation) and the interaction of the nuclear quadrupole moment with an inhomogeneous electric field. Polarization appears in the case of the magnetic field, and alignment (quadrupolarization) in the case of the electric field.

The thermal motion of atomic nuclei suppresses the orienting action of fields. The magnetic and electric moments of nuclei are so small that even in the maximum attainable fields the spin ordering of nuclei in thermal equilibrium with matter is found to be negligibly small at room temperatures (300°K). Therefore, in addition to sufficiently strong fields, cooling of the substance containing the nuclei to cryogenic temperatures (10^–2°K and lower) is necessary to produce oriented nuclei by static methods. For example, the polarization of nuclei with a magnetic moment equal to 1 nuclear magneton and with a spin of ½ in a magnetic field H = 10⁵ oersteds at a temperature of 10^–2°K is 0.35. This means that about 70 percent of the nuclei have their spins oriented in a given direction.

Because of the difficulties associated with achieving such temperatures and fields, “internal” (or local) fields created at nuclei by the intra-atomic electrons are widely used to produce oriented nuclei. The intensity of such fields greatly exceeds the intensity currently attainable by the experimental techniques for generating “external” fields. If the internal fields are oriented identically in space, then the assembly of the nuclei will be found in a very strong field. Internal magnetic fields are created at the nuclei of paramagnetic atoms and reach 10⁶—10⁷ oersteds. Internal fields of the order of 10⁵-10⁶ oersteds also arise at the nuclei of diamagnetic atoms when small quantities of a diamagnetic substance (about 1 percent) are dissolved in ferromagnets. Since the magnetic moments of electrons are greater than nuclear magnetic moments by a factor in excess of 10³, they, and consequently the internal fields they generate, can be oriented with much smaller external fields and at higher temperatures.

Inhomogeneous electric fields capable of aligning nuclei can be generated by using the internal electric fields in certain substances with covalent chemical bonds when the electron cloud surrounding the nucleus is markedly asymmetric. In this case the substance that contains the aligned nuclei and that must be cooled is used in the form of a single crystal.

In dynamic methods, the thermal equilibrium of the system of nuclear spins is artificially disrupted in such a way that spin orderingarises. In most dynamic methods the electron spins are (statically) oriented in the external magnetic field. The orientation of the electron spins is subsequently transmitted to the system of nuclear spins using methods of electron paramagnetic resonance (EPR) and nuclear magnetic resonance (NMR). An advantage of the dynamic methods is that very strong fields and superlow temperatures are not required; a shortcoming is that such methods can be used to orient only a comparatively narrow range of nuclei.

Oriented nuclei are used in nuclear physics for the study of the spin dependence of nuclear forces and for determination of the spins, magnetic moments, and parities of excited states of atomic nuclei. Experiments with β-radioactive oriented nuclei made possible the establishment of one of the fundamental properties of elementary particles, parity nonconservation in weak interactions. In the physics of rigid bodies, oriented nuclei are used to study the intracrystalline field.