Collision broadening impact approximation

In the framework of the impact approximation of pressure broadening, the shape of an ordinary, allowed line is a Lorentzian. At low gas densities the profile would be sharp. With increasing pressure, the peak decreases linearly with density and the Lorentzian broadens in such a way that the area under the curve remains constant. This is more or less what we see in Fig. 3.36 at low enough density. Above a certain density, the l i(0) line shows an anomalous dispersion shape and finally turns upside down. The asymmetry of the profile increases with increasing density [258, 264, 345]. Besides the Ri(j) lines, we see of course also a purely collision-induced background, which arises from the other induced dipole components which do not interfere with the allowed lines its intensity varies as density squared in the low-density limit. In the Qi(j) lines, the intercollisional dip of absorption is clearly seen at low densities, it may be thought to arise from three-body collisional processes. The spectral moments and the integrated absorption coefficient thus show terms of a linear, quadratic and cubic density dependence,... 

For gases at normal pressures and temperatures (STP) impact broadening is also negligible when compared to broadening in condensed systems. However, if collisions could be approximated by crystal lattice vibrations in condensed systems, half-widths according to interruption broadening could range to 1500 cm 1. 

The phase shift produced by one collision is calculated and the result is averaged over all impact parameters. The impact approximation is used to describe the line broadening at pressures from 0-100 Torr. From equations (8.19) and (8.20) we see that the impact approximation should work best at low pressures, where is long, and high temperatures, where v is large. 

As charge-dipole interaction between the electron and the atom is small, the perturbation theory expansion may be used to estimate f. The odd terms of this expansion disappear after averaging over impact parameters due to isotropy of collisions. In the second order approximation only those elements of P that are bilinear in V are non-zero. Straightforward calculation showed [176] that all components of the Stark structure are broadened but only those for which m = 0 interfere with each other ... 

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