Line width collisional

G Millot, A Boutahar, B Lavorel, C Wenger, R Saint-Loup, H Berger. Measurements of collisional line widths in the stimulated Raman Q-branch of the p band of silane. J Raman Spectrosc 21 803-808, 1990. 

Expressed in wavelength and by using molar masses Ma, (g/mol). Equation 2.10 gives the FWHM for collisional broadening, the so-called collisional line width A Ac ... 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

The major requirement of the light source for atomic absorption is that it should emit the characteristic radiation (the spectrum) of the element to be determined at a half-width less than that of the absorption line. The natural absorption line width is about 10 4 (A), but due to broadening factors such as Doppler and collisional broadening, the real or total width for most elements at temperatures between 2000 ° and 3000 °K is typically 0.02 — 0.1 A. Hence, a high resolution monochromator is not required. 

It is essential to correctly evaluate the absorption cross-section a relative to the laser line profile, the spectral resolution of the light collection optics, and the natural HO line width as influenced by Doppler, Voigt, or collisional broadening. The principles governing absorption measurements of HO over a distance through the atmosphere are discussed by Hiibler et al. (38). 

While collisional resonances 5 MHz wide are interesting for spectroscopic purposes, what makes them most interesting is that the 5 MHz line width implies that the collision lasts at least 200 ns, a time not much less than the 1 fxs period allowed for the collisions to occur. If the collision linewidths can be reduced to the inverse of the time allowed for the collisions to occur, the collisional resonances become transform limited, and we know when each collision begins and ends. 

In Eq. (10), E nt s(u) and Es(in) are the s=x,y,z components of the internal electric field and the field in the dielectric, respectively, and p u is the Boltzmann density matrix for the set of initial states m. The parameter tmn is a measure of the line-width. While small molecules, N<pure solid show well-defined lattice-vibrational spectra, arising from intermolecular vibrations in the crystal, overlap among the vastly larger number of normal modes for large, polymeric systems, produces broad bands, even in the crystalline state. When the polymeric molecule experiences the molecular interactions operative in aqueous solution, a second feature further broadens the vibrational bands, since the line-width parameters, xmn, Eq. (10), reflect the increased molecular collisional effects in solution, as compared to those in the solid. These general considerations are borne out by experiment. The low-frequency Raman spectrum of the amino acid cystine (94) shows a line at 8.7 cm- -, in the crystalline solid, with a half-width of several cm-- -. In contrast, a careful study of the low frequency Raman spectra of lysozyme (92) shows a broad band (half-width 10 cm- -) at 25 cm- -,... 

Vapor-phase linewidth studies of benzophenone in this interesting spectral region have not been carried out. Nevertheless, it may be possible to make some predictions on the variation of linewidths with pressure. The pressure dependence or collisional deactivation may be qualitatively described by assigning a linewidth At, which is assumed proportional to pressure, to the triplet levels. Thus, the line-widths are given by... 

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. 

Collisional or pressure broadening. Collisions shorten the lifetime of the excited state and thus broaden the spectroscopic line width. 

Since the homogeneous width y of the Lamb-dip profile increases with pressure p, the maximum allowed deflection angle in (13.1) also increases with p. A comparison of pressure-induced effects on the kernel and on the background profile of the Lamb dips and on the Doppler profile therefore yields more detailed information on the collision processes. Velocity-selective optical pumping allows the measurement of the shape of velocity-changing collisional line kernels over the full thermal range of velocity changes [13.21]. 

Moreover, the line profiles are consistent with models of bow shocks e.g. Hartigan et al., 1987), seen with a range of projection angles. The line width ves the shock velocity in such models, yielding the speed of the bullet and time since ejection. The [FeII line ratios are typical of collisional excitation in gas of electron density 10 cm. The overall spectrum is characteristic of excitation in fast (> lOOkm/s), dissociative J-shocks e.g. HoUenbach McKee, 1989), although some detailed differences await explanation, such as the weakness of the [Cl] and [N lines. This may in part be due to the shock speeds being hi er than has been modelled. 

Ideally, the emission line used should have a half-width less than that of the corresponding absorption line otherwise equation (8.4) will be invalidated. The most suitable and widely used source which fulfils this requirement is the hollow-cathode lamp, although interest has also been shown in microwave-excited electrodeless discharge tubes. Both sources produce emission lines whose halfwidths are considerably less than absorption lines observed in flames because Doppler broadening in the former is less and there is negligible collisional broadening. 

Apparently, within each branch, rotational lines are not resolved. This is due to the short interaction time of the collisional pair which renders individual lines rather diffuse, with half-widths that are much greater than the rotational spacings of O2 and N2 at temperatures around 300 K. 

Fig. 1.3. Collision-induced profile - schematic. Shown is the transition frequency Vo ( line center ), a sum of molecular transition frequencies, (AEA + AEs)/h. At higher frequencies, translational energies of relative motion of the collisional pair are increased, at lower frequencies decreased see Eq. 1.7. The average width is given by Eq. 1.5.

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