Theory of oriented symmetric-top molecule beams: Precession, degree of orientation, and photofragmentation of rotationally state-selected molecules

A theoretical study of the properties of rotationally state-selected symmetric top molecules has been carried out. Quantum mechanical and classical calculations are presented for the orientational probability density function PJKM( ρ), characterizing the molecular precessional motion for various rotational states ‖JKM〉 in terms of the degree of orientation ρ (≡μ̂⋅ℰ̂) of the dipole moment μ in a (weak) electric field ℰ. For all J>0, the breadths of the quantum mechanical distributions PJKM( ρ) are significantly greater than those of the classically calculated ones Pcl( ρ). Their first moments, i.e., 〈 ρ〉≡KM/(J2+J), are, of course, identical. P( ρ) is, in principle, directly observable through measurements of polarized laser-induced photofragmentation of oriented molecule beams. Expressions are derived to analyze experimentally observable angular distributions of photofragments. It is shown that IJKM/IJK=2PJKM( ρ), where IJKM and IJK are the photofragment intensities from oriented (JKM) and unoriented (JK) state-selected beams, respectively. From this result, one can determine the quantum number J purely from experimental photofragmentation data, i.e., I( f)JKM/IJK =(2J+1)δK,M. The f denotes that the molecules are oriented with their dipole moment parallel to the orienting field in the ‘‘favorable’’ direction. Expressions and calculations are presented appropriate to the description of the angular distribution of the photofragments of oriented symmetric-top molecules.