On the quantum and quasiclassical angular distributions of photofragments

Quantum and quasiclassical expressions for the angular distribution of photofragments from an initially polarized precursor molecule are compared under the conditions of a one-photon electric dipole transition to a repulsive state followed by prompt axial recoil into two separating fragments. The treatment is most readily applicable to diatomic molecules, but it is more general than that. It is shown that when the rotational and electronic angular momentum J(i) and its projection along the body-fixed z axis Omega(i) are well defined in the initial state, the quantum and quasiclassical expressions are identical for any initial polarization of the molecule prior to photolysis and for all values of J(i) and Omega(i). For the particular case of an mid R:J(i)Omega(i)M(i) selected state this is in agreement with a previous result [T. Seideman, Chem. Phys. Lett. 253, 279 (1996)]. Moreover, the quasiclassical expression is still a good approximation even when the initial state is a coherent superposition of mid R:J(i),Omega(i),M(i) levels for the same Omega(i). This near identity still pertains even when Omega(i) is not well defined for a parallel transition (DeltaOmega=0) but fails for a perpendicular transition (DeltaOmega=+/-1) if the initial state is in a coherent superposition of Omega(i) states differing by +/-2. These conclusions apply to preparation schemes employing optical excitation, static inhomogeneous and/or homogeneous electric and/or magnetic fields, as well as to molecules physisorbed on solids or clusters. We discuss the importance of these results in the interpretation of photofragment distributions when some other angular momenta are involved, such as electronic angular momentum, with and without nuclear spin, coupled to molecular rotation, asymmetric top rotational angular momentum, or internal vibrational angular momentum in polyatomics.