The absorption coefficient can be defined in a very general form as a product of
The latter is a Fourier transform of the autocorrelation function of molecular dipole.
In a simplest hypothetical case of 2-level molecules, the molecular dipole produces a train of
harmonic oscillations between two successive collisions. Averaging over gas (autocorrelation) gives
a almost exponentially decreasing envelop of the oscillations. Its spectrum is a well known
bell-shaped function at the frequency of oscillations having width equal to the reversed duration
- the number of molecules that are able to absorb radiation quantum;
- the so-called radiation field term;
- spectral function.
Within the impact approximation (instant collisions), a collisional line shape is very close to the
Lorentz one. It fits well the real line near its center. Actually, collision takes finite time.
The train of oscillations breaks down smoothly. This leads to exponential decay of the far line
wings (sub-Lorentz behavior). The breaking function of the oscillation train is determined by
interaction potential that is unknown as a rule. Fortunately, the difference in the line shape of
the impact approximation and the real case becomes noticeable only at very significant frequency
detuning from the line center. So, the line is usually divided into a resonance part and a pedestal,
which is usually attributed to continuum absorption. Note that the major collisional lineshape
parameters such as pressure shifting, collisional broadening and its speed dependence, collsional
coupling etc. are also determined by the same interaction potential, in particular, by its
long-range part. The number of collisions per unit time varies linearly with molecular number
density (or pressure). Therefore, all collisional parameters also vary linearly with pressure.
This linearity is experimentally confirmed in a very broad range of pressures.
It was believed that the line wing at large detuning is always sub-Lorentzian and that
“super-Lorentzian line shape is not supported by any known physics”.
We found the missing mechanism. If the dipole oscillation breaking function is not monotonous
(a light molecule can make several full turns during typical collision time), then the corresponding
line wing has a broad hill at detuning equal to the characteristic frequency of this non-monotonic
behavior. The width of the hill is determined by collision duration. See
[Ref. 4, 2017] and references therein for more