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The ratio of angular momentum to magnetic moment for atomic systems. This ratio is usually expressed in terms of the magnetomechanical factor g′, as in Eq. (1).
The magnetomechanical ratio is the inverse of the gyromagnetic ratio. It is usually denoted by γ and is equal to g′e/2mc. The magnetomechanical ratio of a substance identifies the origin of the magnetic moment. For example, for electron spin the angular momentum is ½ℏ, where ℏ is Planck's constant divided by 2π. The magnetic moment is the Bohr magneton eℏ/2mc. Thus, the magnetomechanical ratio
the ratio of the magnetic moment of elementary particles and systems of elementary particles, such as atoms, molecules, and atomic nuclei, to their angular momentum (mechanical moment). The gyromagnetic ratio has a definite value for each elementary particle with nonzero mechanical momentum, or spin. The values may be determined for various states of an atomic system from the equation γ = gγo, where γo is the unit of the gyromagnetic ratio and is the Lande factor. In this case, the unit of the gyromagnetic ratio is its value for the orbital motion of the electron in an atom, —e/2meC, where e is the magnitude of the elementary electric charge, me is the mass of an electron, and c is the speed of light. The gyromagnetic ratio for nuclei is the analogous quantity for the proton in a nucleus: e/mpC, where mp is the mass of a proton.
The value of the gyromagnetic ratio determines the effect of magnetic fields on a system that has a magnetic moment. According to classical theory, the magnetic moment in an external magnetic field of intensity H undergoes precession, which is uniform rotation about the direction of H, with the preservation of the angle of inclination, at an angular velocity ω = — γH. In a special case, in which the magnetic moment is due to the orbital motion of the electrons, Larmor precession results. The characteristic value of magnetic splitting of the energy levels in a magnetic field is determined by the gyromagnetic ratio according to quantum theory. In this case the value is γhH = gγohH, where h is Planck’s constant.
M. A. EL’IASHEVICH