Non-linear collisions

For the more general case of a non-linear collision of an H-atom with an H2-molecule, classical trajectory calculations were first made by WALL et al./53/ and KARPLUS et al /54/ Similar calculations have been performed more recently for a number of atom-diatomic molecule reactions /55-57/. 

In the more general case, in which the masses of A,X,and B are comparable, the methods described in Sec.4 2.II are necessary for an accurate or approximate evaluation of the transition probabilities nn valid especially in treating non-linear collisions in... 

The adiabatic assumption involved in equations (52-55.IV) may not be a good approximation nevertheless, it provides the possibility of simulating the non-linear collisions between the H-atoms and the H2-molecules. The importance of such a treatment will become clear in a comparison between the results of the theoretical calculations and the experimental data to be made in the next section. 

Alignment behaviour similar to that of the "unfavourable" case is also uncommon. Simons and co-workers [23] have observed an increasing P2 with E. in the Ar + N2 excitation transfer system. They ascribe this trend to a preference for non-linear collision geometries at low collision energies. De Vries et al [24] have reported isotropic, and even positive values 11 at the lowest... 

In both of the examples (8), the chemiluminescence is associated with a "parallel transition the positive polarisation ratios found experimentally reflect the expected negative alignment, i.e, a tendency for J j. k However, the ultimate spectator stripping limit was only attained at superthermal collision energies, see Fig. 1 [28]. Despite the low mass of the H atom there is a significant release of orbital motion in the separating products and a clear indication of a preferred non-linear collision geometry. 

Together with Eq. (66), this equation describes exactly the linear response of the system to an external field, with arbitrary initial conditions. Its physical meaning is very simple and may be explained precisely as for Eq. (66) 32 the evolution of the velocity distribution results in two effects (1) the dissipative collisions between the particles which are described by the same non-Markoffian collision operator G0o(T) 35 1 the field-free case and (2) the acceleration of the particles due to the external field. As we are interested in a linear theory, this acceleration only affects the zeroth-order distribution function It is... 

Of a special astronomical interest is the absorption due to pairs of H2 molecules which is an important opacity source in the atmospheres of various types of cool stars, such as late stars, low-mass stars, brown dwarfs, certain white dwarfs, population III stars, etc., and in the atmospheres of the outer planets. In short absorption of infrared or visible radiation by molecular complexes is important in dense, essentially neutral atmospheres composed of non-polar gases such as hydrogen. For a treatment of such atmospheres, the absorption of pairs like H-He, H2-He, H2-H2, etc., must be known. Furthermore, it has been pointed out that for technical applications, for example in gas-core nuclear rockets, a knowledge of induced spectra is required for estimates of heat transfer [307, 308]. The transport properties of gases at high temperatures depend on collisional induction. Collision-induced absorption may be an important loss mechanism in gas lasers. Non-linear interactions of a supermolecular nature become important at high laser powers, especially at high gas densities. 

Most of these theoretical investigations have been carried out using methyl compounds as the substrate. For example, the Sn2 reaction between OFT and methyl chloride has been investigated for non-linear and linear collisions using ab initio molecular dynamics calculations.105 The potential energy surface was calculated at the MP2/6-311-I— -G(2df,2pd) level of theory and the collision energy was set at 25 kcal mor1. The results for 495 trajectories indicated that the reactants pass from the initial encounter complex to the transition state in 0.02 ps and to the product encounter... 

The ion achieves an internal equilibrium condition where the energy is distributed with an equal probability among all of the internal modes. Considering that an ion with N non-linear atoms has 3N - 6 vibration modes, it is easy to understand how the collision yield decreases in a manner inversely proportional to the ion mass. 

The bi-linear collision term resulting from neutral neutral interaction Cnm is simplified in present edge models to non-linear BGK-like model collision expressions [15]. 

We shall then account for the observed phenomena by the orientation of transient aggregates (postulated few years ago (24), recently observed in attractive systems by neutron scattering O) ) formed during sticky collisions between droplets. Such an explanation agrees with the first experimental fact (non linear behavior of B versus ) and with the measured characteristic times at low volume fraction (1 to 10 ps). The characteristic rotation time for a single droplet with R=50 A would be 70ns which is much shorter than the measured times. 

The spectroscopic methods are based on time-resolved pump-probe schemes where the collision-free regime is usually attained by using low pressure conditions. Application of various linear and non-linear laser techniques, such as LIF (laser-induced fluorescence), REMPI (resonant-enhanced multiphoton ionization) and CARS (coherent antistokes Raman spectroscopy) have provided detailed information on the internal states of nascent reaction products [58]. Obviously, an essential prerequisite for the application of these techniques is the knowledge of the spectroscopic properties of the products. 

MCT is a popular liquid viscosity theory (Gee, 1970 Gotze et al., 1981 Leutheuser, 1984, Jackie, 1989). It is based on the description of the dynamical properties of density fluctuations in terms of a dynamical structure factor. There are inherent density fluctuations in liquids, which decay with characteristic relaxation times. The decay becomes slower as the temperature is lowered due to increase of viscosity. It is controlled by dynamically correlated collisions. The equations governing the decay are non-linear. Analysis of the non-linear equation of motion of the density fluctuations gives a density correlation function of the type... 

In equation (17) 5 is defined as the overlap of two electronic determinantal wave functions S = z,R, P z,R,P ) and the energy is E = Pl[/2Mi + (z,7 ,Pl/7eiecl, ./ ,E)/(z,7 ,PIz,7 ,PX This level of theory can be characterized as fully non-linear time-dependent Hartree-Fock for quantum electrons and classical nuclei. It has been applied to a great variety of problems involving ion-atom [12,14,15,23-25], and ion-molecule reactive collisions... 

The rotational temperature of NO (A) in the HeJ/NO reaction was 1170 100 K, which was essentially independent of V. The similar rotational excitation for v = 0-5 levels was explained by the fact that the CT reaction occurs near resonantly because the RE of HeJ has a large latitude of 2 eV. Only 0.10 0.01 eV of the RE, which amounts to only 0.5% of the RE, is converted into the rotational energy of NO" (A). The rotational temperatures of NO (A) were slightly higher than those of Nf(B v = 0) and CO" (B v = 0). A higher rotational excitation is consistent with the fact that the HeJ/NO reaction proceeds through an intimate collision, where more conversion of the RE of HeJ into the rotational energy of the product NO" (A) ion becomes possible via decomposition of a non-linear complex. 

A non-linear detector response can be caused by direct transfer to the ground state (quenching) due to intermolecular collisions with co-eluting compounds or by phosphorescence. 

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