Theoretical Treatment of Elastic Collisions

The preceding discussion has shown that both elastic and inelastic collisions cause spectral line broadening. The elastic collisions may additionally pro- 

The elastic collisions change not the amplitude, but the phase of the damped oscillator, due to the frequency shift Aw(R) during the collisions. They are often termed phase-perturbing collisions (Fig.3.11). We now give a short outline of a quantitative description based on this model which gives a better insight into the relation between line profile and collision cross sections [3.7,8]. 

As in Sect.3.1, we describe the damped oscillator by its time-dependent amplitude 

When the integration time is long compared to the mean time T = A/v between successive collisions (which depends on the mean-free path A and the mean relative velocity v) the total phase shift rj(t) is the sum of many random phase shifts caused by collisions with different impact parameters 

The inner integral over dr does not depend on our choice of the time origin. We may therefore shift the variable t by an amount r from f+r to t (see the analogous discussion in Sect.2.7.4). Replacing the dummy variable r on the right-hand side of (3.59) by t we can write 

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