Collisional line broadening

Collisional line broadening can be written in a form similar to Eq. (5.6)... 

The most important source of line broadening in microwave studies of bulk gas samples is collisional or pressure broadening, the theory of which was first developed by Van Vleck and Weisskopf [77], They developed the line shape function... 

So far, this discussion of selection rules has considered only the electronic component of the transition. For molecular species, vibrational and rotational structure is possible in the spectrum, although for complex molecules, especially in condensed phases where collisional line broadening is important, the rotational lines, and sometimes the vibrational bands, may be too close to be resolved. Where the structure exists, however, certain transitions may be allowed or forbidden by vibrational or rotational selection rules. Such rules once again use the Born-Oppenheimer approximation, and assume that the wavefunctions for the individual modes may be separated. Quite apart from the symmetry-related selection rules, there is one further very important factor that determines the intensity of individual vibrational bands in electronic transitions, and that is the geometries of the two electronic states concerned. Relative intensities of different vibrational components of an electronic transition are of importance in connection with both absorption and emission processes. The populations of the vibrational levels obviously affect the relative intensities. In addition, electronic transitions between given vibrational levels in upper and lower states have a specific probability, determined in part... 

For optical depth t 1 the observed interstellar molecular lines usually have a gaussian shape. This is to be expected, since collisional broadening, which causes the Lorentzian line profile, should be negligible and become important only at gas densities 1012 — 1014 cm- 3. If thermal motions of the molecules were the only source of line broadening the line half power width (i.e. the width between half power points) would be given by... 

In order to demonstrate the physical significance of asymjjtotic nonadiabatic transitions and especially the aiialj-tical theory developed an application is made to the resonant collisional excitation transfer between atoms. This presents a basic physical problem in the optical line broadening [25]. The theoretical considerations were mad( b( for< [25, 27, 28, 29, 25. 30] and their basic id( a has bec n verified experimentally [31]. These theoretical treatments assumed the impact parameter method and dealt with the time-dependent coupled differenticil equations imder the common nuclear trajectory approximation. At that time the authors could not find any analytical solutions and solved the coupled differential equations numerically. The results of calculations for the various cross sections agree well with each other and also with experiments, confirming the physical significance of the asymptotic type of transitions by the dipole-dipole interaction. 

Doppler broadening has a Gaussian lineshape, and its convolution with the Lorentzian natural lineshape yields a Voigt profile. In typical experiments, this effect can be neglected since the Doppler width is usually much smaller than the resolution of the apparatus. Collisional line broadening is also Lorentzian, and the Lorentzian component of measured lines must be carefully extrapolated to zero pressure. 

Olson and Innes, who observed tht B- - X system of in absorption, studied the extensively predissociated level v = 3 of the B state by observations of line broadening in the 3-1 absorption band, using Fabry-Perot interferometry. (The gross perturbation in the v = 3 level was first identified by Brown and Oibson. ) An estimated B state radiative lifetime of (0.98 0.10) /weak heterogeneous predissociation is suggested to contribute to linewidths for levels of low Fluorescence decay gives a non-collisional lifetime of 0.5 /us for v = 1,2. ... 

High-Resolution Laser Spectroscopy of Collisional Line Broadening and Line Shifts... 

Often the collisional broadening of the Lamb dip and of the Doppler profile can be measured simultaneously. A comparison of both broadenings allows the separate determination of the different contributions to line broadening. For phase-changing collisions there is no difference between the broadenings of the two different line profiles. However, velocity-changing collisions do affect the Lamb-dip profile (see above), but barely affect the Doppler profile because they mainly cause a redistribution of the velocities but do not change the temperature. 

An alternative way of trying to estimate the onset of collisional randomisation is to use known collisional broadening factors for example, in methane, the magnitude of the line broadening is 0.086 cm atm for one of the observed transitions [79.G] this translates into just over 10 cm" Torr , not inconsistent with the earlier entries in Table 7.2. 

The spectral line broadening is a sum of the natural, Dopplei and collisional broadening however, the natural broadening is relatively small and can be neglected. 

Fig. 3.10. Illustration of collisional line broadening explained with the potential curves of the collision pair AB...

Inelastic collisions of A with molecules B of the liquid host may cause radiationless transitions from the level Ei populated by optical pumping to lower levels En. These radiationless transitions shorten the lifetime of Ei and cause collisional line broadening. In liquids the mean time between successive inelastic collisions is of the order of 10 to 10 s. Therefore the spectral line Ei Ek is greatly broadened with a homogeneously broadened profile. When the line broadening becomes larger than the separation of the different spectral lines, a broad... 

Complete active space SCF calculations on BNe, BAr, and BKr indicated that anomalous line-broadening of boron emission by certain of the noble gases results from collisional excitation of boron atoms via avoided crossings in the boron-noble gas interaction potentials [6]. Ab initio molecular orbital theory at the HF/6-31G level has been used to investigate the structure of BAr(2ri) the B-Ar distance is 4.321 A [22]. 

Tiesinga E, Crampton SB, Verhaar BJ, Stoof HTC. (1993) Collisional frequency shifts and line broadening in the cryogenic deuterium maser. Phys. Rev. A 47 4342-4347. 

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