Soft collision

Figure C3.3.7. In the upper half of the figure are shown typical measured Doppler profiles for molecules scattered into the (OO O J= 72) or (OO l J = 17) states of CO2 by collisions with hot pyrazine having an energy of 40 640 cm In the lower half of the figure is shown a typical intennolecular potential identifying the hard and soft collision regimes and the kind of energy transfer they effect.

Figure C3.3.8. A typical trajectory for a soft collision between a hot pyrazine molecule and a CO2 bath molecule in which the CO 2 becomes vibrationally excited.

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. 

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.

The value of AE /AEa) may be either positive or negative here, depending upon the relative signs of va, v-r, and ubc, since the picture of hard-sphere collisions requires an instantaneous interaction. For real molecules, however, we can think in terms of a soft collision taking place over a finite period of time in which several vibrational cycles of the molecule BC occur (i.e., B and C change directions with respect to each other), and we can time-average results such as that of equation (2-32). 

Assumption (a) is appropriate for violent collisions. Violent collisions between atoms of reasonably high energy range (keV) require the collision partners to approach very closely, so that the probability of a collision between three or more atoms is small. Soft collisions can take place at large distances and therefore can involve more than two atoms simultaneously. However, soft collisions usually can be treated by perturbation theory (the momentum or impulse approximation), in which case no restriction to binary collisions is necessary. At lower energies (below 1 keV), collective effects become increasingly important and assumption... 

In Vol. 1, Sect. 3.3. we discussed how elastic and inelastic collisions contribute to the broadening and shifts of spectral lines. In a semiclassical model of a collision between partners A and B, the particle B travels along a definite path r(t) in a coordinate system with its origin at the location of A. The path r t) is completely determined by the initial conditions r(0) and (dr/df)o and by the interaction potential V(r, Ex, E-b), which may depend on the internal energies Ex and b of the collision partners. In most models a spherically symmetric potential V r) is assumed, which may have a minimum at r = ro (Fig. 8.1). If the impact parameter b is large compared to tq the collision is classified as a soft collision, while for b hard collisions occur. 

Fig. 8.1 Interaction potential V r) and semiclassical model for soft collisions with impact parameter b ro and hard collisions (b

V sinO < y/k, the molecule after the collision is still in resonance with the standing light wave inside the laser resonator. Such soft collisions with deflection angles 0 < therefore do not appreciably change the absorption probability of a molecule. Because of their statistical phase jumps (Vol. 1, Sect. 3.3) they do, however, contribute to the linewidth. The line profile of the Lamb dip broadened by soft collisions remains Lorentzian. 

The combined effect of both kinds of collisions gives a line profile with a kernel that can be described by a Lorentzian profile slightly broadened by soft collisions. The wings, however, form a broad background caused by velocity-changing collisions. The whole profile cannot be described by a single Lorentzian function. In Fig. 8.4 such a line profile is shown for the Lamb peak in the laser output Pl(co) at... 

Collision effects (discussed in more detail in Section 111,E) may be well described in terms of collision-induced transitions from mixed v levels with a nonnegligible s content to pure triplet levels. Since mixed states are grouped in narrow, sparsely spaced bands, the transfer to pure triplet states (equivalent to the loss of the s character, i.e., to the fluorescence quenching) will occur even in very soft collisions. Much harder collisions, inducing large energy losses will be efficient for the vibrational relaxation within the / manifold, i.e., for induction of thermally equilibrated phosphorescence (van der Werf et al., 1976). 

If V sin < y/k, the molecule after the collision is still in resonance with the standing light wave inside the laser resonator. Such soft collisions with deflection angles 0 < therefore do not appreciably change the absorption... 

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