Knowledge Bank

Because the operators of magnetic dipole and electric quadrupole transitions are of the same parity, they may connect the same initial and final states. The intensity of the Zeeman lines for these transitions, which is proportional to the square of the sum of these transition matrix elements, has contributions from cross-terms known as interference terms, that may be non-vanishing when the states have good magnetic quantum numbers in the presence of a strong magnetic field and no summation over these quantum numbers need be effected. Using a standard approach of quantum electrodynamics, but expressing the orientation of the propagation and polarization vectors of radiation in terms of rotation matrices, expressions for the angular distribution of radiation are obtained for the different $\Delta M$ components. For a freely rotating linear molecule (or a symmetric top) with electronic angular momentum, detailed matrix elements are obtained that show not only the dependence on the space projection M of the total angular momentum but also all the dependence on the total angular momentum, J, and its projection, $\Omega$, on molecular symmetry axis. The non-interference in the total intensity due to transition among degenerate levels in the absence of a magnetic field is shown to be a consequence of the orthogonality of the Clebsch-Gordan Vector Coupling Coefficients. Specific examples, extension to non-linear molecules and higher multipole radiations will be discussed.