Knowledge Bank

The correct quantum mechanical operator for spin-forbidden electric-dipole transition probabilities is shown to be II, the sum of the linear momentum P and a spin-dependent term. The dipole length R is also valid unless both initial and final states are unbound. Selection rules for the operator II with respect to eigenstates without spin-orbit coupling differ from those for R. showing the artificial nature of the frequent question, ``from what spin-allowed transition is the intensity borrowed?'' Since R is correct, it is proper to include contributions from diagonal dipole moments in low symmetry molecules. Even if spin-other orbit coupling is considered, R is a valid operator, although to II there is added a two-electron spin-dependent term. Multipole processes higher than electric dipole include a new term that may be significant for very weak spin and parity forbidden transitions. This term transforms like the spin magnetic octupole operator, but has the magnitude of spin-forbidden, orbital magnetic dipole matrix elements. Examples from the spectra of atoms, aromatic molecules, and complexes of transition metal and rare-earth ions are used to illustrate all results.