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Study applies the nonequilibrium collision theory of reaction rates to the estimation of rate constants for simple reactions. The complications in the quantum mechanical description of chemical reactions and the care needed in approximating the exact wave function for the collision are shown.
An adiabatic quantal theory of spectral line shapes in collision-induced absorption and emission is presented which incorporates the induced translation-rotation and translation-vibration spectra. The generalization to account for the anisotropy of the scattering potential is given. Calculations are carried out of the collision-induced absorption spectra of He in collisions with H2 with ab initio electric dipole functions and realistic potentials. The anisotropy of the interaction potential is small and is not included in the calculations. The predicted spectra are in satisfactory agreement with experimental data though some deviations occur which may be significant. The rotational line shapes have exponential wings and are not Lorentzian. The connection between the quantal and classical theories is written out explicitly for the isotropic overlap induction.
Summaries and reviews of conference papers on electron-atom collision theory
Atomic collision theory, discussing cross section calculations by Gryzinski classical method, variational methods and Fadeev equations for three particles
A classical model for laser action is discussed, in which an active medium consisting of anharmonic oscillators interacts with an electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. A theoretical model is presented for the pressure dependence of the intensity of a gas laser, in which only velocity-changing collisions with foreign gas atoms are included. A collision model for hard sphere, repulsive interactions was derived. Collision theory was applied to a third-order expansion of the polarization in powers of the cavity electric field (weak signal theory).
Various aspects were studied of past or present chemistry in the atmospheres of the outer planets and their satellites using lab simulations. Three areas were studied: (1) organic chemistry induced by kinetically hot hydrogen atoms in the region of Jupiter's atmosphere containing the ammonia cirrus clouds; (2) the conversion of NH3 into N2 by plasmas associated with entry of meteors and other objects into the atmosphere of early Titan; and (3) the synthesis of simple hydrocarbons and HCN by lightning in mixtures containing N2, CH4, and NH3 representing the atmospheres of Titan and the outer planets. The results showed that: (1) hot H2 atoms formed from the photodissociation of NH3 in Jupiter's atmosphere could account for some of the atmospheric chemistry in the ammonia cirrus cloud region; (2) the thermalization of hot H2 atoms in atmospheres predominated by molecular H is not as rapid as predicted by elastic collision theory; (3) the net quantum loss of NH3 in the presence of a 200 fold excess of H2 is 0.02, much higher than was expected from the amount of H2 present; (4) the conversion of NH3 into N2 in plasmas associated with infalling meteors is very efficient and rapid, and could account for most of the N2 present on Titan; (5) the yields of C2H2 and HCN from lightning induced chemistry in mixtures of CH4 and N2 is consistent with quenched thermodynamic models of the discharge core; and (6) photolysis induced by the UV light emitted by the gases in the hot plasmas may account for some, if not most, of the excess production of C2H6 and the more complex hydrocarbons.
The experimental ion-beam behavior obtained without neutralizers is compared with both simple collision theory and plasma-wave theory. This comparison indicates that plasma waves play an important part in beam behavior, although the present state of plasma-wave theory does not permit more than a qualitative comparison. The theories of immersed-emitter and electron-trap neutralizer operation are discussed; and, to the extent permitted by experimental data, the theory is compared with experimental results. Experimental data are lacking completely at the present time for operation in space. The results that might be expected in space and the means of simulating such operation in Earth-bound facilities, however, are discussed.
The time-dependent equations of the classical picture of inelastic collisions (classical-trajectory equations) are derived using the momentum-space semiclassical approximation. Thereby it is shown that the classical-trajectory equations remain valid in the vicinity of classical turning points provided that (a) the momentum-space semiclassical approximation is valid, (b) the trajectories for elastic scattering in the various internal states differ only slightly, and (c) the slopes of the elastic scattering potentials have the same sign. A brief review of the existing derivations of the classical-trajectory equations is given, and the general conditions for their validity are discussed.
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Spin exchange theory for collisions between atoms extended to include target polarization
A modified Bhatnagar-Gross-Krook (BGK) collision method is used for the derivation of reactive collision terms to allow for complete higher-moment approximations in fluid transport theory. The general reactive collision terms for the 8-, 10- and 13-moment approximation for binary reactions are derived. Then, reactive collision terms for specific chemistry are derived with the assumptions: (1) all reactants and products have 13-moment distribution functions; (2) simple, classical assumptions provide sufficient models for reaction dynamics; and (3) the reaction rate is energy-independent. The derived specific formulas reflect two extremes in reactive collision dynamics: direct and indirect reaction mechanisms. Finally, considerations for correct use of the reactive collision terms are discussed in the context of space plasma environments.
We derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom-diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H2-D2 and D2-D2 collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations.
Diatomic molecules inelastic collision cross sections for specific rotational transitions, discussing S matrix energy requirements for statistical analysis
The collision operator that appears in the equation of motion for a particle distribution function that was averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. An expansion is derived for the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasilinear expansion.
The collision operator that appears in the equation of motion for a particle distribution function that has been averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. In this note we derive an expansion of the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest non-trivial order. The validity of this expansion is seen to be the same as that of the standard quasi-linear expansion.
The experimental determination of absorption line profiles for OCS nu3 vibrational transitions broadened by collisions with Ar, He, and H3 buffer gases is reported. The experimental method using diode laser spectroscopy in the five micron region is described. The data are compared with theoretical values obtained using intermolecular potentials previously suggested for these systems and infinite order sudden approximation molecular scattering calculations.
Binary collision-induced rotational far IR spectrum of tetrahedral molecular gas, using induced absorption theory