Velocity collisional

The ab initio points were selected with the dynamics applications in mind. Since high-velocity collisional excitation of the... 

Collisional ionization can play an important role in plasmas, flames and atmospheric and interstellar physics and chemistry. Models of these phenomena depend critically on the accurate detennination of absolute cross sections and rate coefficients. The rate coefficient is the quantity closest to what an experiment actually measures and can be regarded as the cross section averaged over the collision velocity distribution. 

Back reflection of translational and rotational velocity is rather reasonable, but the extremum in the free-path time distribution was never found when collisional statistics were checked by computer simulation. Even in the hard-sphere solid the statistics only deviate slightly from Pois-sonian at the highest free-paths [74] in contrast to the prediction of free volume theories. The collisional statistics have recently been investigated by MD simulation of 108 hard spheres at reduced density n/ o = 0.65 (where no is the density of closest packing) [75], The obtained ratio t2/l2 = 2.07 was very close to 2, which is indirect evidence for uniform... 

With t = 0 the present expression reduces to the result obtained in Eq. (3.28). If, e.g., t = 2, then spectral exchange takes place both within the branches of an isotropic scattering spectrum (Fig. 6.1) and between them. The latter type of exchange is conditioned by collisional reorientation of the rotational plane, whose position is determined by angle a. As a result, the intensity of adsorbed or scattered light is redistributed between branches. In other words, exchange between the branches causes amplitude modulation of the individual spectral component, which accompanies the frequency modulation due to change of rotational velocity. 

The time constant r, appearing in the simplest frequency equation for the velocity and absorption of sound, is related to the transition probabilities for vibrational exchanges by 1/r = Pe — Pd, where Pe is the probability of collisional excitation, and Pd is the probability of collisional de-excitation per molecule per second. Dividing Pd by the number of collisions which one molecule undergoes per second gives the transition probability per collision P, given by Equation 4 or 5. The reciprocal of this quantity is the number of collisions Z required to de-excite a quantum of vibrational energy e = hv. This number can be explicitly calculated from Equation 4 since Z = 1/P, and it can be experimentally derived from the measured relaxation times. 

This is, beyond all doubt, the most important process and the only one which has been already tackled with theoretically. Nevertheless, the prediction given by the classical overbarrier transition model is not correct for this collision [9] and the modified multichaimel Landau-Zener model developed by Boudjema et al. [34] caimot explain the experimental results for collision velocities higher than 0.2 a.u.. With regard to the collision energy range, we have thus performed a semi-classical [35] collisional treatment... 

For rough estimates, the collisional cross section may be assumed to be velocity-independent, Qn(vn) = Qo = constant (hard-sphere approximation), so that the mean time between collisions becomes... 

Since the velocities and angular distributions of products from collisional dissociations at low incident-ion energies have generally not been determined, the precise mechanism by which the products are formed is unknown. Thus in the collisional dissociation of H2+ with helium as the target gas, H+ may result from dissociation of H2+ that has been directly excited to the vibrational continuum... 

Fig. 14.7 Experimental apparatus configured with the electric field perpendicular to the collisional velocity (from ref. 14).

Fig. 14.11 Experimental apparatus configured so that the electric field and collisional velocity are parallel (from ref. 14).

The observed cross sections for the 18s (0,0) collisional resonance with v E and v 1 E are shown in Fig. 14.12. The approximately Lorentzian shape for v 1 E and the double peaked shape for v E are quite evident. Given the existence of two experimental effects, field inhomogeneties and collision velocities not parallel to the field, both of which obscure the predicted zero in the v E cross section, the observation of a clear dip in the center of the observed v E cross section supports the theoretical description of intracollisional interference given earlier. It is also interesting to note that the observed v E cross section of Fig. 14.12(a) is clearly asymmetric, in agreement with the transition probability calculated with the permanent electric dipole moments taken into account, as shown by Fig. 14.6. 

One of the potentially most interesting aspects of the resonant collisions is that, in theory, the collision time increases and the linewidth narrows as the collision velocity is decreased. According to Eqs. (14.6) and (14.8) the collision time is proportional to l/v3/2. Collisions between thermal atoms with temperatures of 500 K lead to linewidths of the collisional resonances that are a few hundred MHz at n = 20. In principle, substantially smaller linewidths can be observed if the collision velocity is reduced. 

The first and most obvious question is whether or not a narrower velocity distribution leads to narrower collisional resonances. In Fig. 14.14 we show the Na 26s + Na 26s — Na 26p + Na 25p resonances obtained under three different experimental conditions.20 In Fig. 14.14(a) the atoms are in a thermal 670 K beam. In Figs. 14.14(b) and (c) the beam is velocity selected using the approach shown in Fig. 14.13 to collision velocities of 7.5 X 103 and 3.8 X 103 cm/s, respectively. The dramatic reduction in the linewidths of the collisional resonances is evident. The calculated linewidths are 400, 28, and 10 MHz, and the widths of the collisional resonances shown in Figs. 14.14(a)-(c) are 350,40, and 23 MHz respectively. The widths decrease approximately as l/v3/2 until Fig. 14.14(c), at which point the inhomogeneities of the electric field mask the intrinsic linewidth of the collisional resonance. 

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