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Spin (quantum mechanics)
The intrinsic angular momentum of a particle. It is that part of the angular momentum of a particle which exists even when the particle is at rest, as distinguished from the orbital angular momentum. The total angular momentum of a particle is the sum of its spin and its orbital angular momentum resulting from its translational motion. The general properties of angular momentum in quantum mechanics imply that spin is quantized in half integral multiples of ħ (=h/2π, where h is Planck's constant); orbital angular momentum is restricted to half even integral multiples of ħ. A particle is said to have spin &frac32;, meaning that its spin angular momentum is &frac32;. See Angular Momentum
A nucleus, atom, or molecule in a particular energy level, or a particular elementary particle, has a definite spin. The spin is an intrinsic or internal characteristic of a particle, along with its mass, charge, and isotopic spin. See Quantum mechanics, Symmetry laws (physics)
the intrinsic angular momentum of an elementary particle. Spin is a quantized quantity. It is not connected with the motion of the particle as a whole. When the concept of spin was introduced, the electron was viewed as being like a rotating top. The electron’s spin was regarded as a quantity characterizing this rotation—hence the term “spin.”
The term “spin” is also applied to the intrinsic angular momentum of an atomic nucleus and, sometimes, of an atom. In this case, the spin is defined as the vector sum, calculated according to the rules of addition of momenta in quantum mechanics, of (1) the spins of the elementary particles forming the system and (2) the particles’ orbital angular momenta due to the particles’ motion inside the system.
Spin is measured in units of Planck’s constant ℏ and is equal to Jℏ, where J, called the spin quantum number or simply the spin, is a number characterizing each type of particle. The values of J can be 0, a positive integer, or a positive half integer. Accordingly, a particle is said to have integral or half-integral spin. For example, the electron, proton, neutron, neutrino, and the corresponding antiparticles have spin 1/2 in units of ℏ; the pions and kaons have spin 0; and the photon has spin 1. The intrinsic angular momentum of the photon, like that of the neutrino, cannot be measured, since there is no frame of reference in which the photon is at rest. Nevertheless, it is proven in quantum electrodynamics that the total angular momentum of a photon in an arbitrary frame of reference cannot be less than 1; this fact provides grounds for assigning a spin of 1 to the photon. That the neutrino has spin 1/2 follows, for example, from the law of conservation of angular momentum in the process of beta decay.
The projection of a spin on any fixed direction z in space can assume the values J, J – 1, . . ., –J. Thus, a particle of spin J has 2J + 1 spin states (for example, two states when J = 1/2). These spin states represent an additional, internal degree of freedom of the particle. According to quantum mechanics, the square of the spin vector is equal to ℏ2J(J + 1). Owing to its spin, a particle of nonzero rest mass has a spin magnetic moment µ = Ƴjℏ, where the factor 7 is the magnetomechanical ratio.
The concept of spin was introduced into physics in 1925 by G. Uhlenbeck and S. Goudsmit. On the basis of an analysis of spectroscopic data, the two scientists postulated that the electron has a spin angular momentum of ℏ/2 and an associated spin magnetic moment of one Bohr magneton ℏe/2mc, where e is the electron charge, m is the mass of the electron, and c is the speed of light. Thus, for the spin of the electron the ratio of the magnetic moment to the angular momentum is equal to Ƴ = elmc. From the standpoint of classical electrodynamics, this ratio is anomalous: for the orbital motion of the electron and for any motion of a classical system of charged particles with a given ratio elm, y is half as large, being equal to e/2mc.
By taking into account the spin of the electron, W. Pauli was able to formulate the exclusion principle, which asserts that an arbitrary physical system cannot contain two electrons in the same quantum state (seePAULI EXCLUSION PRINCIPLE). A number of effects can be explained by assuming that the electron has spin 1/2. Examples are the multiplet structure of atomic spectra (fine structure), the characteristics of the splitting of spectral lines in magnetic fields (the anomalous Zeeman effect), the order in which the electron shells are filled in multielectron atoms (and, consequently, the regularities of the periodic table), and the phenomenon of ferromagnetism.
On the basis of experimental data, the American physicist D. M. Dennison postulated that the proton has spin 1/2. The experimental verification of this hypothesis led to the discovery in 1929 of ortho-hydrogen and para-hydrogen. Somewhat earlier, Pauli had proposed that the hyperfine structure of atomic energy levels is determined by the interaction of the electrons with the nuclear spin. Pauli’s assumption was soon proved by E. Back and Goudsmit as a result of an analysis of the Zeeman effect in bismuth.
The spin of particles is connected with the nature of the statistics that the particles obey. As Pauli showed in 1940, it follows from quantum field theory that particles with integral spin are bosons (that is, they obey Bose-Einstein statistics) and particles with half-integral spin are fermions (that is, they obey Fermi-Dirac statistics). The Pauli exclusion principle holds for fermions, such as electrons, but not for bosons.
Spin was consistently incorporated into the mathematical apparatus of nonrelativistic quantum mechanics by Pauli. His description of spin was phenomenological in character. It follows directly from the relativistic Dirac equation that the electron has a spin and a spin magnetic moment. For an electron in an electromagnetic field, the Dirac equation in the limit of small velocities reduces to the Pauli equation for a nonrelativistic particle with spin 1/2.
The values of the spins of elementary particles determine the transformation properties of the fields that describe the particles. Under Lorentz transformations, the field corresponding to a particle with spin 0 is transformed as a scalar (or pseudoscalar), the field describing a particle with spin 1/2 is transformed as a spinor, the field for a particle with spin 1 is transformed as a vector (or pseudovector), and so on.
O. I. ZAV’IALOV
in aviation, a special, critical flight regime of an airplane or glider. In a spin, the aircraft descends in a steep spiral of small radius, simultaneously turning relative to all three of its axes, and enters autorotation.
Spins are classified as tailspins and inverted (outside) spins, depending on the pattern; as steep (50°–90°), banked (30°–50°), and flat (< 30°) spins, depending on the inclination of the longitudinal axis of the aircraft to the horizon; and as stable and oscillating spins, depending on the nature of the occurrence. The descent and entry of an aircraft into a spin occurs when the aircraft achieves a supercritical angle of attack (above the stalling angle). Antispin parachutes and rockets are used in flight testing to provide for escape from a stable spin that has already developed.
The first deliberate entry of an airplane into a spin was achieved by the Russian military aviator K. K. Artseulov in 1916. The problem of spins was studied in 1918 and 1919 by the British scientist H. Glauert. The theoretical basis of spins was elaborated by the Soviet scientist V. S. Pyshnov, and subsequent experimental studies were carried out by A. N. Zhuravchenko.
S. IA. MAKAROV