Collapse of the spectral doublet

However, for the La example, where T = 2p, the minimum is not pronounced. In fact for F/p 2 the minimum is not obvious and the spectrum of such doublets looks like it is continuously broadened with increase of the collision rate proportional to n. In contrast, for 1 F/p 2 the minimum is much deeper. In the extreme case 

In this manner the necessary condition (4.16) of the line narrowing effect is satisfied only for the doublet that belongs to the Q-branch. This result reflects the fact that a rotational phase shift does not affect Q-branch 

The situation is rather different for the other doublet which models P-R exchange. Rates 

Both lines are broadened independently and solely by adiabatic phase shift as in Lorentz and Weisskopf theories. They are Lorentzians of width (1 — cosa) and frequency shift (sin a). In general off-diagonal elements of f are not zero though they are less than diagonal elements. Consequently, the spectrum may collapse even in the adiabatic case when A 1/tc. However, adiabatic collapse is hardly ever achieved in the gas phase where l/rc l/t0 jS since A 1/tc j8 and hence only the resolved doublet limit is available. 

Fortunately most molecules, except H2 and D2, are non-adiabatically broadened. Only small corrections for rotational adiabaticity are required for such molecules as N2, but in the first approximation even these may be neglected. In this extreme, which is valid at A C 1/tc, the S-matrices are real and therefore yi = W = fa as in the Q-branch. This approximation is similar to the classical 7-diffusion model. The non-adiabatic impact operator 

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