Symmetry selection rules in rotationally inelastic collisions of open-shell diatomic molecules and polyatomic tops: Implications of an irreducible tensor expansion

An irreducible tensor formalism due to Grawert is applied to collisions of open-shell diatomics and polyatomic tops. Explicit examination of the reduced T-matrix elements within the infinite-order sudden and first-order Born limits allows the derivation of several general symmetry selection rules for a rotationally inelastic process. In particular, both differential and integral cross sections will vanish unless the symmetry indices of the initial and final states satisfy certain conditions, for the following types of transitions: J=0→J′M′; J,M=0→J′,M′=0; and JM→J,−M. The M=0→M′=0 selection rule represents the extension, to an arbitrary orientation of the quantization axis, of a selection rule we have derived earlier. A comparison with results of fully quantum studies of collisions of NH3 and H2CO with He confirms the predictive accuracy of these rules. We discuss how both the M=0→M′=0 and JM→J,−M selection rules could be directly verified, in experiments involving laser excitation of a particular symmetry level followed by resolution of the fluorescence polarization.