Remarks on the signs of g factors in atomic and molecular Zeeman spectroscopy

Various magnetic moments, associated with rotational, vibrational, nuclear spin, electron orbital and electron spin angular momenta, can contribute to the Zeeman effect in atoms and molecules. They are considered in this paper in the context of the effective Hamiltonian where relativistic and other corrections as well as the effects of mixing with other electronic states are absorbed in appropriate g factors. In spherically symmetric systems, the magnetic dipole moment arising from a specific angular momentum can be written as the product of three factors: the nuclear or Bohr magneton (which is positive), the g factor (which may be positive or negative), and the corresponding angular momentum (which is a vector). A convention is discussed, in which the sign of the g factor is positive when the dipole moment is parallel to its angular momentum and negative when it is antiparallel. This would have the advantage that it could be applied consistently in any situation. Such a choice would require the g factors for the electron orbital and electron spin angular momenta to be negative. This concept can easily be extended to the case of a general molecule where the relation between the dipole and angular momentum vectors has tensorial character.