Collision cross-section velocity dependence

This expression corresponds to the Arrhenius equation with an exponential dependence on the tlireshold energy and the temperature T. The factor in front of the exponential function contains the collision cross section and implicitly also the mean velocity of the electrons. 

Figure 10. Comparison of the velocity dependence of the disappearance cross-section of CHa+, formation cross-section of CH0 +, and Langevin orbiting collision cross-section, all as a function of reciprocal average kinetic energy of ions in the mass spectrometer source...

If the reverse of Reaction 1 is slow compared to 2 ( the colli sional stabilization step) then overall cluster growth will not depend strongly upon the total helium pressure. This is found to be the case using RRK estimates for k n and hard sphere collision cross sections for ksn for all clusters larger than the tetramer. The absence of a dependence on the total pressure implies that the product of [M] and residence time should govern cluster growth. Therefore, a lower pressure can be compensated for by increasing the residence time (slower flow velocities). 

Smith, N., Scott, T.P. and Pritchard, D.E. (1982). Substantial velocity dependence of rotationally inelastic collision cross section in Li -Xe, Chem. Phys. Lett., 90, 461-464. 

Utilization of both ion and neutral beams for such studies has been reported. Toennies [150] has performed measurements on the inelastic collision cross section for transitions between specified rotational states using a molecular beam apparatus. T1F molecules in the state (J, M) were separated out of a beam traversing an electrostatic four-pole field by virtue of the second-order Stark effect, and were directed into a noble-gas-filled scattering chamber. Molecules which were scattered by less than were then collected in a second four-pole field, and were analyzed for their final rotational state. The beam originated in an effusive oven source and was chopped to obtain a velocity resolution Avjv of about 7 %. The velocity change due to the inelastic encounters was about 0.3 %. Transition probabilities were calculated using time-dependent perturbation theory and the straight-line trajectory approximation. The interaction potential was taken to be purely attractive ... 

The velocity dependence of the total collision cross section is a restricted source of information regarding the intermolecular potential (IP), Bernstein (1973). Much more information is contained in differential cross section measurements which therefore form a great challenge for future scattering experiments with oriented molecules. 

Measurements on this system were done by Gengenbach et al. (1972) who determined the velocity dependence and the absolute value of the total collision cross section. From these measurements the isotropic part of the intermolecular potential (IIP) was obtained, see Fig. 1. Recently Riehl et al. 

Fig. 5. Isotropic and anisotropic glory structure. For a system resembling NO-Ar in the experimental set up of Stolte (1972), the total collision cross section a and its orientation dependent part Act /cr are calculated in d.w.a. as functions of the primary beam velocity vN0. Extremes of a coincide with zeros of Acrn/cr. The orientation dependent part oscillates around the average value (Aff /<7,0,) nB.

In Paper IV, the self-diffusion process in fluid neon was also studied with CMD using the pairwise pseudopotential method. In Fig. 17 the centroid velocity time correlation function is plotted for quantum neon using the pseudopotential method and for classical neon. When the quantum mechanical nature of the Ne atoms is taken into account, the diffusion constant is reduced by a small fraction. In the gas phase and to some degree in liquids, the diffusion process can be viewed as a sequence of two-body collisions, the frequency of which depends on the collision cross section. Because the quantum centroid cross section is larger than the corresponding classical value, the quantum diffusion constant is found... 

The level Ei of the molecule A can be depopulated not only by spontaneous emission but also by collision-induced radiationless transitions (Fig. 2.23). The probability dT f /dt of such a transition depends on the density of the collision partner B, on the mean relative velocity v between A and B, and on the collision cross section for an inelastic collision that induces the transition Ei Ek in the molecule A... 

Effective collision cross sections are related to the reduced matrix elements of the linearized collision operator It and incorporate all of the information about the binary molecular interactions, and therefore, about the intermolecular potential. Effective collision cross sections represent the collisional coupling between microscopic tensor polarizations which depend in general upon the reduced peculiar velocity C and the rotational angular momentum j. The meaning of the indices p, p q, q s, s and t, t is the same as already introduced for the basis tensors In the two-flux approach only cross sections of equal rank in velocity (p = p ) and zero rank in angular momentum (q = q = 0) enter die description of the traditional transport properties. Such cross sections are defined by... 

The temperature dependence of the reaction rate constant The translational energy dependence of the reaction cross-section translates into the temperature dependence of the reaction rate constant. The procedure is clear take k(v) = vo-R, Eq. (3.4), and average it over a thermal distribution of velocities, k(T) = (vctr(v)). We wrote ctr(v) as a reminder that the reaction cross-section can depend on the collision velocity. 

When the electrostatic field is sufficiently weak, the ion velocity in the gas will be the random motion of ions at the temperature of the gas, on which a small velocity component in the direction of the electrostatic field is imposed. Provided that these separation parameters are met, the IM is performed under so-called low-field conditions. At higher electrostatic fields, the ion velocity distribution depends less strongly on the temperature of the separation and the mean ion energy increases as it traverses the drift region. Consequently, K is no longer constant and depends on the specific ratio of the electrostatic field to the gas number density E/N). When the IM separations are performed in low-field conditions (i.e., constant K), the mobility is related to the collision cross section of the ion-neutral pair ... 

The sign minus reflects the fact that the flux density of the particles decreases with increasing x. The proportionality coefficient Go, which depends on the collision velocity v, is named the total collision cross section. Integrating (2.1.), we obtain... 

The collisional cross section, which is normally given the symbol cr, is a measure of the effective size of the colliding particles, expressed as an area The link between the rate coefficient and a is k = , where v refers to fiie relative velocity of the colliding molecules and the brackets r resent a Boltzmann-weighted average of the cross section (which depends on the collision energy) and the relative collision velocity. 

A bimoleciilar reaction can be regarded as a reactive collision with a reaction cross section a that depends on the relative translational energy of the reactant molecules A and B (masses and m ). The specific rate constant k(E ) can thus fonnally be written in tenns of an effective reaction cross section o, multiplied by the relative centre of mass velocity... 

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