Quantum Theory of Interference and Polarization of Stark—Zeeman Lines in Molecules

With special emphasis on the application to transitions between the rovibronic states of molecules, general formulas for the polarization and for the intensity inclusive of interference of multipole emission between Stark—Zeeman levels are derived. The derivation makes use of angular momentum method for molecules and irreducible spherical tensor operators for the interaction of radiation and matter. Results are made applicable to linearly polarized radiation with any arbitrary orientation (specified by three Euler angles) of the polarization and propagation vectors with respect to the space‐fixed axes. These higher multipole interference effects in a resolved molecular Stark—Zeeman line serve as an extension of the pioneer works on atomic Zeeman transitions of Van Vleck and others. The formulas are tabulated in terms of their dependence on reduced rovibronic matrix elements and their rotational and angular dependence. For the latter dependence that involve products of Clebsch—Gordon coefficients and products of rotational matrices we give explicit examples up to electric and magnetic octopole radiation. Rotation matrices of the third rank, some of which are needed in transitions involving octopole, are computed and tabulated. For the former dependence, general line strengths of linear molecules and rovibronic matrix elements are given with all dependence on rotational wavefunction evaluated, for any Hund's Case a states inclusive of the hypothetical ${}^{\text{2s+1}}{\Sigma }_{\Omega }^{\pm }\mathrm{(a)}$ states, singlet Case b states, and doublet Σ^±(b) states. For diatomic molecules of half‐integral spin (even multiplicity), general Case a and b state wavefunctions are constructed, their symmetry under inversion and selection rules are derived. Specific examples are given of the magnetic‐dipole—electric‐quadrupole radiation in ${}^{\text{2,4}}{\Pi }_{\frac{1}{2}}{\mathrm{(a)-}}^{\text{2,4}}{\Pi }_{\frac{1}{2}}\mathrm{(a)}$ and ${}^2{\Sigma }^{\pm }{-}^{\text{2.4}}{\Pi }_{\frac{3}{2}}\mathrm{(a)}$ transitions, and of the electric‐dipole—magnetic‐quadrupole—electric‐octopole radiation in ${}^{\text{2,4,6}}{\Pi }_{\frac{3}{2}}{\mathrm{(a)-}}^{\text{2,4,6}}{\Pi }_{\frac{3}{2}}\mathrm{(a)}$ transitions. Attention is called to the existence of cross terms which make the formulas dependent on different Λ‐doubling components and hence on the ``Kronig reflection'' symmetry specified by a (±) sign.