Electrichyphen;Quadrupole and Magnetichyphen;Dipole Radiation in Linear Molecules. Applications to1Pgr;mdash;3Pgr; Transitions

摘要

The electrichyphen;quadrupole and magnetichyphen;dipole operators of a rotating, linear molecule interacting with a radiation field are formulated, in the spacehyphen;fixed and in the molecularhyphen;coordinate systems, as contractions of irreducible spherical tensors. Radiative transition probabilities are obtained for the initial and final rotationhyphen;electronic states that are in Hund's Coupling Caseaorb, using the normalized rotation matrix as the separated rotational wavefunction in the Bornmdash;Oppenheimer approximation. Linehyphen;strength formulas are derived for (1) transitions between singlet Casebstates, in the case of an electric quadrupole, the1Sgr;mdash;1Sgr;,1Pgr;mdash;1Sgr;,1Dgr;mdash;1Sgr;,1Pgr;mdash;1Pgr;,1Dgr;mdash;1Pgr;,1PHgr;mdash;1Pgr;,1Dgr;mdash;1Dgr;,1PHgr;mdash;1Dgr;, and1Ggr;mdash;1Dgr; transitions; in the case of a magnetic dipole, the1Pgr;mdash;1Sgr;,1Pgr;mdash;1Pgr;,1Dgr;mdash;1Pgr;,1Dgr;mdash;1Dgr;, and1PHgr;mdash;1Dgr; transitions; (2) the1Pgr;mdash;3Pgr;(a) transitions; (3) the1Pgr;mdash;3Pgr;(b) transitions. The master linehyphen;strength formula as well as intensity distribution for different branches are given. In (2) and (3), some of the transitions are found to be dependent on theabsoluteKronig reflection symmetry, giving, for molecules of unequal nuclei, an intensity alternation for the two Lgr;hyphen;doubling components. A discussion of this reflection symmetry and the inversion symmetry is given and a consistent set of molecular wavefunctions of a given symmetry is constructed for (1) singlet Casebstates and triplet Caseastates (2) triplet Casebstates expressed as a linear combination of Caseastate wavefunctions through angular momentum coupling. The rotationmdash;vibration spectra due to these higher multipole radiations are briefly discussed. A new point of view for the possibility of Dgr;Lgr;equals;0 (for Lgr;ne;0) magnetichyphen;dipole pure rotation spectra is advanced.