Collision dynamics, angular momentum

Without resorting to the impact approximation, perturbation theory is able to describe in the lowest order in both the dynamics of free rotation and its distortion produced by collisions. An additional advantage of the integral version of the theory is the simplicity of the relation following from Eq. (2.24) for the Laplace transforms of orientational and angular momentum correlation functions [107] ... 

To simulate the particle-particle collision, the hard-sphere model, which is based on the conservation law for linear momentum and angular momentum, is used. Two empirical parameters, a restitution coefficient of 0.9 and a friction coefficient of 0.3, are utilized in the simulation. In this study, collisions between spherical particles are assumed to be binary and quasi-instantaneous. The equations, which follow those of molecular dynamic simulation, are used to locate the minimum flight time of particles before any collision. Compared with the soft-sphere particle-particle collision model, the hard-sphere model accounts for the rotational particle motion in the collision dynamics calculation thus, only the translational motion equation is required to describe the fluid induced particle motion. In addition, the hard-sphere model also permits larger time steps in the calculation therefore, the simulation of a sequence of collisions can be more computationally effective. The details of this approach can be found in the literature (Hoomans et al., 1996 Crowe et al., 1998). 

The desorption flux is so low under these conditions that no gas phase collisions occurred between molecular desorption and LIF probing. Phase space treatments " of final-state distributions for dissociation processes where exit channel barriers do not complicate the ensuing dynamics often result in nominally thermal distributions. In the phase space treatment a loose transition state is assumed (e.g. one resembling the products) and the conserved quantities are total energy and angular momentum the probability of forming a particular flnal state of ( , J) is obtained by analyzing the number of ways to statistically distribute the available (E, J). 

Each channel is defined by a unique set of quantum numbers for the target degrees of freedom. There are five such labels for each channel. They are (1) J — the total angular momentum and (2) M, its projection on an axis fixed in space. In addition there are labels (3) n for the vibrational motion of the molecule, (4) j for the molecular rotational degree of freedom, and (5) l for the atom-molecule orbital angular momentum. The equations for one set of (J,M) are uncoupled from equations for other values of (J,M). The equations for a function labeled by one value of (n,j,Z) are coupled to values of all the other functions labeled by (the same or) different values of (n,j, ). The number of coupled equations we have to solve therefore depends on the number of molecular vibration-rotation states we have to treat in the scattering dynamics at each collision energy. 

Since the scope of this article is purely theoretical, we just outline below the state of the experimental situation. The ideal experiment in Chemical Dynamics would be that in which starting with reactants in definite intramolecular quantum-states and running towards each other in a definite way (relative velocity and orbital angular momentum) the distribution of the products over the various intramolecular quantum-states and the state of the relative motion (direction and velocity) would be measured. Such an experiment would show whether there is a preferential molecular orientation at the heart of the collision, what the lifetime of the intermediate complex is, how the excess energy is distributed over the various degrees of freedom of... 

We denote by G the set of all the experimentally observable quantities (called physical observables) which must be reproduced. Such quantities are, for instance, the collision energy, the quantum numbers defining the intramolecular state (vibrations and the principal quantum number of rotation), the total angular momentum etc... However, there are other dynamical variables which have a clear meaning in Classical Mechanics but correspond to no physical observable because of the Uncertainty Principle. We call them phase variables and denote them globally by g. The phase variables must be given particular values to obtain, at given G, a particular trajectory. Such variables are, for instance, the various intramolecular normal vibrational phases, the intermolecular orientation, the secondary rotation quantum numbers, the impact parameter, etc... Thus we look for relationships of the type qo = qq (G, g) and either qo = qo (G, g) or po = Po (G, g)... 

Since atoms are strongly affected by the central potential of the nucleus, an important part in electron—atom collision theory is played by states that are invariant under rotations. From the general dynamical principle that invariance under change of a dynamical variable implies a conservation law for the canonically-conjugate variable we expect rotational invariance to imply conservation of angular momentum. Hence angular momentum... 

Chemical dynamics experiments in which OH product quantum state distributions and an absolute reaction cross section for reaction (1) could be measured were reported in 1984. Subsequent experiments revealed additional details about the reaction dynamics, including nascent OH( H) spin-orbit and A-doublet rotational fine structure state distributions, Oi P) product fine structure state distributions, and OH angular momentum polarization distributions,as well as differential cross sections. The experimental results indicate that depending on the reagent collision energy... 

---