Collisions phase perturbing

These experiments give information on the polarizability of excited molecules (from the amplitude of the oscillation), on the transverse phase relaxation times T2 (which depend on the cross sections of phase-perturbing collisions, Vol.l, Sect. 3.3), and on the population decay time T. For more details see [911, 913]. 

The elastic collisions do not change the amplitude, but the phase of the damped oscillator is changed due to the frequency shift As(jo R) during the collisions. They are often termed phase-perturbing collisions (Fig. 3.11). 

The elastic collisions could be described as phase-perturbing collisions. 

As has been discussed above, molecular clusters produced in a supersonic expansion are preferred model systems to study solvation-mediated photoreactions from a molecular point of view. Under such conditions, intramolecular electron transfer reactions in D-A molecules, traditionally observed in solutions, are amenable to a detailed spectroscopic study. One should note, however, the difference between the possible energy dissipation processes in jet-cooled clusters and in solution. Since molecular clusters are produced in the gas phase under collision-free conditions, they are free of perturbations from many-body interactions or macro-molecular structures inherent for molecules in the condensed phase. In addition, they are frozen out in their minimum energy conformations which may differ from those relevant at room temperature. Another important aspect of the condensed phase is its role as a heat bath. Thus, excess energy in a molecule may be dissipated to the bulk on a picosecond time-scale. On the other hand, in a cluster excess energy may only be dissipated to a restricted number of oscillators and the cluster may fragment by losing solvent molecules. 

Various experimental methods used to investigate the H-bonded clusters in gas phase are described in the earlier reviews [150-152]. Since molecular clusters are produced in supersonic beams in the gas phase under collision free conditions, they are free from perturbation of many-body interactions. The spectroscopic characterization of these clusters has less complexity. Hence, high level quantum chemical calculations on these clusters can be directly compared with the experimental values. Due to advent of laser-based techniques, it is currently possible to study the size and mass selective molecular clusters produced in supersonic beam. The combination of high resolution spectroscopy along with the mass and size selective strategies has enabled the scientific community to look at the intrinsic features of H-bonding. Principles behind the method of size selection, beam spectroscopy, and experimental setup have also been thoroughly described in an earlier thematic issue in chemical review [105, 150-152]. 

Fig.3.11a-c. Phase perturbation of an oscillator by collisions (a) classical path approximation of colliding particles (b) frequency change of the oscillator A(t) during the collision (c) resulting phase shift... 

So far, we have neglected the fact that collisions also change the velocity of both collision partners. If the velocity component of a molecule is altered by an amount during the collision, the molecule is transferred from one subgroup (u Au ) within the Doppler profile to another subgroup vz+Uz EAv ). This causes a shift of its absorption or emission frequency from CO to co- -kuz (Fig. 3.21). This shift should not be confused with the line shift caused by phase-perturbing elastic collisions that also occurs when the velocity of the oscillator does not noticeably change. 

In liquids, the distances / /(A, By) show random fluctuations analogous to the situation in a high-pressure gas. The linewidth Acoik is therefore determined by the probability distribution P(Rj) of the mutal distances i y (A, Bj) and the correlation between the phase perturbations at A caused by elastic collisions during the lifetime of the levels /, Ej (see the analogous discussion in Sect. 3.3). 

This causes a shift of its absorption or emission frequency from co to co kuz (Fig. 3.20). This shift should not be confused with the line shift caused by phase-perturbing elastic collisions that also occurs when the velocity of the oscillator does not noticeably change. 

In this model of the phase-perturbed oscillator, both line broadening and line shift are proportional to the density N of collision partners and to the mean relative velocity v. The line broadening is determined by the cross section and the line shift by cjg (Fig.3.12). 

Natural linewidths are broadened by several mechanisms. Those effective in the gas phase include collisional and Doppler broadening. Collisional broadening results when an optically active system experiences perturbations by other species. Collisions effectively reduce the natural lifetime, so the broadening depends on a characteristic impact time, that is typically 1 ps at atmospheric pressure ... 

Relations (2.46) and (2.47) are equivalent formulations of the fact that, in a dense medium, increase in frequency of collisions retards molecular reorientation. As this fact was established by Hubbard within Langevin phenomenology [30] it is compatible with any sort of molecule-neighbourhood interaction (binary or collective) that results in diffusion of angular momentum. In the gas phase it is related to weak collisions only. On the other hand, the perturbation theory derivation of the Hubbard relation shows that it is valid for dense media but only for collisions of arbitrary strength. Hence the Hubbard relation has a more general and universal character than that originally accredited to it. 

In order to reduce the complexity of the problem, several approximation schemes have been developed. In the BGK model, the collision integral is replaced by a simple local term ensuring that the well-known Maxwell distribution is reached at thermal equilibrium [16]. The linearization method assumes that the phase space distribution is given by a small perturbation h on top of a (local) Maxwell distribu-tion/o (see, e.g., [17, 18]) ... 

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