Quantized momentum mechanics of inelastic and reactive collisions: the role of energy and angular momentum constraints

In addition to the quantized molecular structure that constrains the kinematics of atom-molecule collision, constraints arising from energy and angular momentum (AM) conservation strongly influence the magnitude and probability distribution of rotational transfer due to collisions. However, once the nature of these constraints is established, it is possible to predict quantitatively, using quantized momentum mechanics, the outcome of inelastic and reactive collisions. The existence of these constraints is most clearly portrayed in plots of relative velocity (upsilon(r)) versus final rotational AM (j'). These represent channel opening under the conditions: (i) energy conservation, (ii) simultaneous energy and angular momentum conservation, the latter via a specified maximum effective impact parameter b(n)(max) and (iii) angular momentum conservation via this same b(n)(max). b(n)(max) is generally set to be the half bond length (HBL) of the diatomic, as suggested by experimental and theoretical considerations. Each of these conditions may constrain the rotational transfer process. The upsilon(r)-j' plots also give indications of conditions under which backward or forward scattering will occur and when long-lived complexes will form. For sharply defined velocity distributions, scattering angle peaks are readily calculated and these agree well with experimental data. When energy constraints dominate, the value of b(n)(max) may be less than HBL and this reduced value may be obtained from the kinematic equations. This permits wider usage of the AM theory of rotational transfer. AM constraints effectively reduce the number of channels that appear to be accessible from energetic considerations. The upsilon(r)-j' plots may also be used to analyse reactive collisions and inelastic processes in polyatomic molecules for data in which the angular momentum change is directed principally along one of the molecule's inertial axes.