1 - Angular momentum and transition dipole moment

Summary

Anisotropy of angular momenta: ideas and methods

The fundamental idea forming the basis of early quantum theory was the quantization of the angular momentum of the atom, which, at a later stage, assumed the form of the Bohr–Sommerfeld quantization rule [360], namely ∲ pdq = nℏ where p and q are the generalized momentum and coordinate. This concept has retained its physical meaning in modern-day quantum mechanics [371, 372]. In the course of the further development of quantum mechanical concepts it became increasingly clear that in the theory of atoms and molecules the angular momentum is a ‘dominant’ notion, the fundamental significance of which is in no small degree connected with its dimension of action, which coincides with that of Planck's constant ℏ.

In the interaction between particles and a directed beam of photons the angular momentum of the system is conserved, thus forming the basis for the optical method of producing spatial anisotropy of the distribution of the angular momenta of the ensemble of particles, i.e. its optical polarization. In terms of quantum concepts, spatial anisotropy means that in an ensemble of particles a non-equilibrium population of magnetic sublevels m_j of angular momenta is created. We make a distinction between the alignment of momenta, for instance in the absorption of linear polarized light, when there is no difference between the population of ±m_j-sublevels, and orientation, when such a difference exists. Anisotropic distribution of angular momenta in an excited state, as produced in absorption, manifests itself directly in the polarization of fluorescence.

It is rather likely that understanding of the anisotropic distribution of the angular momenta of atoms was enhanced by Hanle's [184] discovery in 1924.