Angular momentum polarization in molecular collisions : Classical and quantum theory for measurements using resonance fluorescence

Abstract

Inelastic or reactive collisions typically produce an anisotropic distribution of rotational angular momentum. An explicit and general treatment is given for the intensity and polarization of resonance fluorescence from molecules produced in such processes. Both classical and quantum results are expressed in terms of bipolar harmonics and state multipoles formed from linear combinations of density matrix elements. The treatment provides an inversion procedure for determining moments of the rotational angular momentum distribution ; twelve independent moments can be obtained. The combinations of angular momentum operators involved are even in eight of these moments and odd in four, with respect to reflection in a plane containing the initial and final relative velocity vectors. Measurements of the even moments require linearly polarized excitation and fluorescence, whereas measurements of the odd moments require circularly polarized excitation. The requisite experimental geometry and other practical aspects are discussed. In the three appendices are discussed the classical limits of transition intensities, a density matrix treatment of atom-rigid-rotor collisions, including analysis of state multipole symmetries ; and the coupling coefficients for parallel angular momenta.