Strong collision approximation

Kolomoitsev D. V., Nikitin S. Yu. Analysis of experimental data on nonstationary active spectroscopy of molecular nitrogen in the strong-collision approximation, Opt. Spectr. 66, 165-8 (1989) [Optika i Spectr. 66, 286-93 (1989)]. 

Then, making the strong collision approximation, one considers the mechanism... 

The most important practical consequence of the failure of the strong collision approximation is that the faU-off curve is shifted to higher pressures, and broadened a little. There are two main approaches to dealing with this situation. It is possible to find parametric corrections for the weak collision effect, which will be introduced below. Alternatively the energy transfer may be treated as a random process with transitions between states occurring on collision. This latter type of approach is called the Master Equation, and is the main subject of Part 3 of this work. 

The low pressure limit (activation) rate coefficient is given in the strong collision approximation by... 

The shape of the fall-off must then be corrected, both for the energy-dependence of the microcanonical rate coefficient in the strong collision approximation, and for the fact that the collisions are not, in fact, strong. 

Fig. 5.10. Comparison of fall-off curves for two of the four reaction products in the thermal isomerisation of monofluorocyclopropane, in the strong collision approximation. The upper theoretical curve corresponds to the rate of formation of (rans-1-fluoropropene, and the lower one to that of 2-fluoropropene. The points are the experimental results of Casas, Kerr Trotman-Dickenson [64.C] see Footnote 14 also the position of these curves is determined by an assumed internal relaxation rate constant r,= 3x 10 Torr s .

Fig. 3.2. Q-branch transformation with increase of density in strong collision (a) and weak collision (b) approximation at T = 0.1 (I) T = 0.3 (II) T = 10 (III). All spectra are normalized to 1 at their maxima.

Fig. 6.7. The first-order (curve 1), second-order (curve 2) and third-order (curve 3) approximations to the exact dependence x x ) in the strong collision model (curve 4).

Maxwellian distribution 129 infinite-order sudden (IOS) approximation 155-6 semi-classical calculation 136-7 Sack s model rotational relaxation 19 strong collision model 219 scattering see isotropic scattering spectra ... 

The strong collision assumption is often invoked to equate ks with the hard-sphere rate constant kns This approximation assumes that every collision of C (n) with another molecule M will completely stabilize (deactivate) the excited molecule. It fact different collision partners are more or less effective in such deactivation. A collision efficiency fi is introduced to account for this effect ... 

This means that the change of phase/amplitude of the wave [Eq. (2)] can be neglected on the space scale about a mean path passed by particles between strong collisions. This approximation holds for rather low frequencies, at which the wavelength of radiation in a medium is much larger than the above-mentioned microscopic distance. 

We consider collective motion of pairs of water molecules. Let the unit volume of the medium comprise Avlb/2 of such pairs, with Ny being the concentration of molecules suffering elastic vibration. Using the high-frequency approximation, we calculate the complex susceptibility /vib — Xvib + Yvib °f the medium pertinent to harmonic vibration of the HB particles (we omit the complex-conjugation symbol). We assume that for an instant just after a strong collision, the velocities and position coordinates of the particles have Boltzmann distributions. Then the elastic-vibration complex susceptibility /vib and permittivity Asvib in view of TGN are determined by the formulas... 

Let a unit volume of an isotropic medium comprise Vvib/2 of such pairs (nonrigid dipoles). We shall calculate the generated complex susceptibility x by using the high-frequency approximation for which it is assumed that at the instant just after a strong collision the velocities and position coordinates are given by the Boltzmann distribution (marked by the subscript B). Then, in view of Eq. (3.5) in GT1, the complex susceptibility x is proportional to the spectral function L ... 

T. P. Tsien and R. T Pack, Rotational excitation in molecular collisions A strong coupling approximation, Chem. Phys. Lett. 

For one-dimensional rotation (r = 1), orientational correlation functions were rigorously calculated in the impact theory for both strong and weak collisions [98, 99]. It turns out in the case of weak collisions that the exact solution, which holds for any happens to coincide with what is obtained in Eq. (2.50). Consequently, the accuracy of the perturbation theory is characterized by the difference between Eq. (2.49) and Eq. (2.50), at least in this particular case. The degree of agreement between approximate and exact solutions is readily determined by representing them as a time expansion... 

Fig. 3.9. (a) Dependence of the experimental half-width of the isotropic Q-branch of N2 and CO on the density ( ) CO, 295 K (+) CO in CF4, 273 K (A) CO in C02> 323 K (O) N2> 295 K (A) N2 in C02> 323 K. The error in the measurements of half-width is +0.2 cm-1, (b) The same data as in (a) but in relation to measured T = I/ojqXj. Theoretical curves for strong (curve 1) and weak (curve 2) collision limits are identical to curves A and B in Fig. 3.8. The upside-down triangles near the broken line present the difference between the actual half-width of CO in CO2 (A) and curve 1. The error in all cases is approximately the same as that indicated for CO.

For the parameters used to obtain the results in Fig. 3, X 0.6 so the mean free path is comparable to the cell length. If X -C 1, the correspondence between the analytical expression for D in Eq. (43) and the simulation results breaks down. Figure 4a plots the deviation of the simulated values of D from Do as a function of X. For small X values there is a strong discrepancy, which may be attributed to correlations that are not accounted for in Do, which assumes that collisions are uncorrelated in the time x. For very small mean free paths, there is a high probability that two or more particles will occupy the same collision volume at different time steps, an effect that is not accounted for in the geometric series approximation that leads to Do. The origins of such corrections have been studied [19-22]. 

Fig. 4. Accumulating evidence is starting to show that molecules which undergo large amplitude vibration can interact strongly with metallic electrons in collisions and reactions at metal surfaces. This suggests that the Born-Oppenheimer approximation may be suspect near transition states of reactions at metal surfaces.

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