Hard collision

Figure C3.3.9. A typical trajectory for a hard collision between a hot donor molecule and a CO2 bath molecule in which the CO 2 becomes translationally and rotationally excited.

It turns out that the CSP approximation dominates the full wavefunction, and is therefore almost exact till t 80 fs. This timescale is already very useful The first Rs 20 fs are sufficient to determine the photoadsorption lineshape and, as turns out, the first 80 fs are sufficient to determine the Resonance Raman spectrum of the system. Simple CSP is almost exact for these properties. As Fig. 3 shows, for later times the accuracy of the CSP decays quickly for t 500 fs in this system, the contribution of the CSP approximation to the full Cl wavefunction is almost negligible. In addition, this wavefunction is dominated not by a few specific terms of the Cl expansion, but by a whole host of configurations. The decay of the CSP approximation was found to be due to hard collisions between the iodine atoms and the surrounding wall of argons. Already the first hard collision brings a major deterioration of the CSP approximation, but also the role of the second collision can be clearly identified. As was mentioned, for t < 80 fs, the CSP... 

The first complication to be considered is the presence of an electrostatic field during the mass spectrometric study of the reaction. Only few quantitative studies have allowed for the possible contribution of hard collisions to cross-section (25), and the possibility that competitive reactions of the same ion may depend on ion energy is generally neglected in assigning ion-molecule reaction sequences. These effects, however, do not preclude qualitative application of mass spectrometric results to radiation chemistry. 

Collision widths considerably smaller than the doppler width have been observed by Szoke and Javan 344) when studying the effects of collisions on the saturation behaviour of the 1.15 ju Ne transition. The measurements showed that, in addition to pressure dependent broadening due to hard collisions, there exists an appreciable broadening due to soft collisions, and that the collisions cause an asymmetry in the average frequency response of individual atoms. 

Actually very small a we have very hard collisions. 

Finally, fast electrons also undergo infrequent hard collisions with molecule s, in which the latter are ionized and secondary electrons with appreciable kinetic energy of the order of hundreds of e.v. are ejected (8-electrons). These collisions thus contribute (6,17) by a small amount g — 0.1 to the yield of ionizations. A distinct specific role of them is apparent only in radiolysis of condensed media, where they constitute a pronounced structural track effect and may contribute to certain minor processes (see below). 

Figure 3 Possible collision conditions for two diatomic molecules (a) head on, hard collision, with diatom bonds almost parallel (b) glancing, soft collision, with bonds almost perpendicular.

Theoretical studies have approached relaxation in hquids from several points of view. Some have applied gaslike models, which involve hard collisions between pairs of molecules essentially unaffected by the surrounding medium, while others are solidlike in that they treat a central molecule surrounded by a fixed cage of neighbors. Still others have investigated the role of liquid-state collective modes in relaxation. In spite of much progress, a large number of imanswered questions remain. 

Shin and Keizer considered a simple model for a triple collision, in which a diatomic molecule undergoes collinear collisions with two atoms, one from each side. The initial velocities of the two atoms were assumed to be uncorrelated, and the time between the two collisions was taken to be random (a Poisson distribution). The interference effect was explicitly calculated and shown to change the relaxation rate for a low frequency mode of CSj in He by as much as 30% the effect was smaller for high frequency modes or heavier collision partners. The Keizer-Shin model probably underestimates the true interference effect for two reasons first, more than two collisions can interfere with each other, and second, hard collisions will tend to be grouped together. 

Chandler and co-workers successfully used stochastic dynamics in their studies of -alkanes and cyclohexane isomerization in solution. The method used is based on the BGK theory. The assumption is that the primary form of interaction between the solvent molecules and the isomerizing system is in the form of hard collisions. These collisions, when they occur, randomize the velocity of one of the isomerizing molecule s atoms. The computational implementation of this is quite simple at random times, based on the collision frequency (which is taken to be proportional to the solvent viscosity), instantaneously change one random atom s velocity to one selected from the Boltzmann distribution at the temperature of interest. Then continue running dynamics until the next collision occurs, at which time another... 

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