Broadening collisional

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. 

Spectral lines are fiirther broadened by collisions. To a first approximation, collisions can be drought of as just reducing the lifetime of the excited state. For example, collisions of molecules will connnonly change the rotational state. That will reduce the lifetime of a given state. Even if die state is not changed, the collision will cause a phase shift in the light wave being absorbed or emitted and that will have a similar effect. The line shapes of collisionally broadened lines are similar to the natural line shape of equation (B1.1.20) with a lifetime related to the mean time between collisions. The details will depend on the nature of the intemrolecular forces. We will not pursue the subject fiirther here. 

Natural linewidths are broadened by several mechanisms. Those effective in the gas phase include collisional and Doppler broadening. Collisional broadening results when an optically active system experiences perturbations by other species. Collisions effectively reduce the natural lifetime, so the broadening depends on a characteristic impact time, that is typically 1 ps at atmospheric pressure ... 

Fig. 5.6. Collisional broadening of N2 rotational components, (a) In Q-branch, calculated by purely non-adiabatic theory at 300 K (1) and with adiabatic corrections at 300 K (2) and at 100 K (3) [215]. (b) In S-branch, calculated in [191] with adiabatic corrections using the recipe of Eq. (5.56). The experimental data (+) are from [214].

Fig. 5.10. Argon collisional broadening coefficients for nitrogen Q-branch components measured in [227] ( ), [228] ( ) and calculated with PLBC potential ( ) and KDV potential (o).

Kozlov D. N., Pykhov R. L., Smirnov V. V., Vereschagin K. A., Burshtein A. I., Storozhev A. V. Rotational relaxation of nitrogen in argon collisional broadening of Q-branch components in coherent Raman spectra of cooled gas, J. Raman Spectr. 22, 403-7 (1991). 

Jongerius MJ, Van Bergen ARD, Hollander T, Alkemade CTH (1981) An experimental study of the collisional broadening of the Na-D lines by Ar, N2 and H2 perturbers in flames and vapor cells—I. The line core. J Quant Spectrosc Radiat Transfer 25 1-18... 

Mullamphy DFT, Peach G, Venturi V, Whittingham IB, Gibson SJ (2007) Collisional broadening of alkali doublets by helium perturbers. J Phys B 40 1141-1152... 

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. 

In flames, only Doppler and, to a lesser extent, collisional broadening contribute significantly to the overall linewidth. 

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. 

Formulations for SMD of secondary droplets have also been derived by other researchers, for example, O Rourke and Amsden)3101 and Reitz.[316] O Rourke and Amsden[310] used the % -square distri-bution[317] for determining size distribution of the secondary droplets. They speculated that a breakup process may result in a distribution of droplet sizes because many modes are excited by aerodynamic interactions with the surrounding gas. Each mode may produce droplets of different sizes. In addition, during the breakup process, there might be collisions and coalescences of the secondary droplets, giving rise to collisional broadening of the size distribution. 

In passing it is interesting to note that Fig. 5 qualitatively explains the reason for the difference in the effect of motion on spectral lines in radiofrequency and optical spectroscopy. In radiofrequency spectroscopy one refers to motional narrowing, while collisional broadening is used to... 

UV absorption bands have fine structure due to the presence of vibrational sub-levels, but this is rarely observed in solution due to collisional broadening. As the transitions are associated with changes of electron orbitals, they are often described in terms of the orbitals involved, e.g. 

The effects of such collisionally induced kicks are treated within the so-called pressure broadening (sometimes called collisional broadening) model by modifying the free-rotation correlation function through the introduction of an exponential damping factor exp( -Itl/x) ... 

The full width at half height of these Lorentzian peaks is 2/x. One says that the individual peaks have been pressure or collisionally broadened. 

When the Doppler broadening can not be neglected relative to the collisional broadening, the above integral... 

If no collision interferes with the emission process, the line is very sharp. In the presence of collisions, on the other hand, the line will be broadened. The intensity at the line center may rise by several orders of magnitude, depending on various factors, such as the presence of unresolved hyperfine structure components, etc. [119]. The core of the line still remains sharp the collisional broadening is most striking in the wings, especially the far wings where the intensities have fallen off by orders of magnitude. 

Collisional redistribution of radiation. A system A + B of two atoms /molecules may be excited by absorption of an off-resonant photon, in the far wing of the (collisionally) broadened resonance line of species A. One may then study the radiation that has been redistributed into the resonance line - a process that may be considered the inverse of pressure-broadened emission. Interesting polarization studies provide additional insights into the intermolecular interactions [118, 388]. 

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). 

When the excited atoms can be deactivated by collisions with other atoms in competition with the emission of light, there is the additional process of collisional broadening (also known as pressure broadening, since collisions become more frequent as the pressure of a gas increases). The shorter excited state lifetime leads to a wider spread of excited state energies. 

Fig. 12.6 The 3s —> ns and 3s — nd collisional broadening cross sections derived from tri-level echo decay data are shown plotted vs the principal quantum number of the upper state of the transition. The curved line corresponds to the calculation of Omont (ref. 16). The flat part of the line is also calculated by Alekseev and Sobelman (ref. 3). The errors shown are typical and represent the statistical error in the data (from ref. 7).

Having explicit formulas for a number of first moments we can approximately restore the envelope line of the radiation spectrum without its detailed calculations. If lines in the spectrum have one symmetric maximum, then its envelope line is approximated by a normal function whose reconstruction requires only the mean energy and variance of the spectrum. Such an approach is useful for the case of complex spectra consisting of many lines, which, due to low resolutions as well as Doppler and collisional broadening or large natural width, form continuous or quasi-continuous bands. Studies of variation of these statistical characteristics along isoelectronic sequences give a wealth of information on intra-atomic interactions. 

The width of the spectral line equals the sum of the widths of initial and final levels. Due to the short lifetime of highly excited states with an inner vacancy, their widths, conditioned by spontaneous transitions, are very broad. The other reasons for broadening of X-ray and electronic lines (apparatus distortions, Doppler and collisional broadenings) usually lead to small corrections to natural linewidth. 

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