Collisions partners, potential energy

The attractive energies 4D(cr/r)6 and ae2/2 r4 have two important effects on the vibrational energy transfer (a) they speed up the approaching collision partners so that the kinetic energy of the relative motion is increased, and (b) they modify the slope of the repulsive part of the interaction potential on which the transition probability depends. By letting m °°, we have completely ignored the second effect while we have over-emphasized the first. Note that Equation 12 is identical to an expression we could obtain when the interaction potential is assumed as U(r) = A [exp (— r/a)] — (ae2/2aA) — D. Similarly, if we assume a modified Morse potential of the form... 

The interactions between metastable noble-gas atoms and ground-state noble-gas atoms are relatively simple and have been investigated quite extensively. If the excitation energy is lower than the ionization potential of the collision partner, the only important inelastic process is the transfer of excitation energy.12 The excitation transfer is usually very efficient when the process is near resonant. The process that is responsible for the operation of the He-Ne laser,13... 

The noble-gas metastable atoms Ne through Xe are 3P2 0 atoms, so that more than one potential-energy curve governs the scattering, even with S-state collision partners. Because spin-orbit interactions are large whereas weak van der Waals interactions imply only weak coupling to the... 

The author and A. Robatino have pointed out that the sharp positron spectrum resembles electron spectra found in atomic collisions by Niehaus and coworkers. [21),25] The quantum mechanics in both cases is analogous. In our point of view, the sharpness of the spectra arises from interferences arising at avoided crossings of potential curves of the molecules formed by the collision partners. In particular, such a model is consistent in a natural way with the multiple summed energies found by the G. S. I. experimenters. [15,16,19] The molecular model predicts very different angular distributions than those of the particle model. [26] The more recent discovery of electron positron pairs is equally consistent with the molecular model, as with more exotic explanations. [26]... 

The moments and polarizabilities of molecules can be determined by indirect means. In collision experiments, the nature of the interaction is governed by the potential energy surface, itself a function of the molecular properties of the colliding partners. Usually the potential energy is written in a multipole expansion whereby the electrical properties are displayed in the long-range terms [38]. The potential that is generated must satisfy simultaneously... 

Figure 1. Schematic presentation of a short segment of a trajectory passing through an element dS of the potential energy surface near the critical dividing strriace element dC. Defined are the relevant components of the relative velocity v of the collision partners. R is the vector joining the centers of mass of the colliding species, n is the rmit vector in the direction of the potential gradient at dS.

Despite the clarity contained within the AM formalism, current collision theories such as the CC method, briefly outlined above, or the numerous modifications of reduced rigour, insight into the relationship between initial conditions and the outcomes is often very hard to obtain. Calculations are highly computer intensive, since many (j) channels must be summed over as the system traverses an intermolecular potential energy surface (PES). Furthermore, the PES must be accurately known for each collision pair. Scattering amplitudes are obtained but their relation to distinctive characteristics of the colliding species is rarely apparent and causal relationships are difficult to discern. Furthermore, any change in the collision partners, however small, requires a new PES appropriate to that pair, with... 

Obstacles to modelling the evolution of quantum state populations under multiple collisions primarily arise from the complexity of standard collision theory. An accurate PES is needed for all potential collision partners in a gas mixture and some species will be in highly excited states. State-to-state collision calculations are highly computer intensive for even the simplest of processes and, without a major increase in computational speed, are not suited to multiple, successive calculations. By contrast, the AM method is fast, accurate and calculations for atoms and/or diatomic molecules require only readily available data such as molecular bond length, atomic mass, spectroscopic constants and collision energy. 

A few computer simulations of classical trajectories in atom-polyatomic molecule systems have been reported. Leaving aside any questions related to the adequacy of the potential energy surfaces used, these studies have been directed toward understanding the overall vibrational relaxation of the polyatomic partner in the collision, with little attention focused on the nature of the accompanying intramolecular energy exchange. 

See, for example, R. N. Porter and L. M. Raff, Qassical trajectory methods in molecular collisions, in Dynamics of Molecular Collisions, Part B, p. 1, and P. J. Kuntz, Features of potential energy surfaces and their effect on collisions, in Dynamics of Molecular Collisions, Part B, p. 53, W. H. Miller, ed.. Plenum, New York 1976 S. A. Jayich, A. Study of the Collisional Energy Transfer of Methyl Isocyanide with Monatomic and Diatomic Collision Partners, Ph.D. Thesis, University of California, Irving, Calif., 1975. 

The total cross section (Ttot( o) will be sensitive to the intermolecular potential, which operates at the different collisional orientations. From the order of magnitude of experimentally determined dissociation rate constants, one can conclude that fftot( o) is of the order of the gas kinetic cross section. However, pronounced differences in collision efficiencies, e.g. of water or some atoms as collision partners, may be ascribed to long range forces which increase intermolecular forces obtained from vibrational relaxation studies can probably also be used for dissociation. However, the influence of these forces on vibrational relaxation times and on dissociation rates is completely different, owing to the difference between complex collisions on the one hand and simple transitions between levels separated by large energy intervals on the other. 

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