Pressure broadening theory

Benreuven, A. (1966). Symmetry considerations in pressure broadening theory, Phys. Rev., 141, 34-40. 

Baranger M. Problem of overlapping lines in the theory of pressure broadening, Phys. Rev. Ill, 494—504 (1958). 

J. Van Kranendonk, On the Theory of Pressure-Broadening and Pressure-Induced Absorption, Thesis, University of Amsterdam, Amsterdam, Holland, December 17, 1952. 

Heijmen TGA, Moszynski R, Wormer PES, Van der Avoird A, Rudert AD, Halpern JB, Martin J, Gao WB, Zacharias H (1999) Rotational state-to-state rate constants and pressure broadening coefficients for He— C2H2 collisions Theory and experiment. J Chem Phys 111 2519—2531... 

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... 

It is possible to formulate a general theory of pressure broadening of line profiles, but because the problem is a many-body problem, the formal... 

Relation of such empirical calibration to quantitative spectroscopic theory was pursued with two of the different source lamps by determining their spectral distributions from high resolution spectro-graphic plates made by repeated flashes, combined with numerical evaluation of Tji via equation (2.3) using the band transition probability factor or /-number, and the pressure broadening factor, as well as the absorber temperature, as selectable parameters. Uncertainty concerning the presence of continuum radiation between the OH lines in the source spectrum ultimately limited the definiteness of this calibration procedure. 

Basic Theory. We consider first an ideal resonance lamp, emitting a non-reversed Doppler-shaped line at a Boltzmann temperature T,. Since most actual lamps operate at low pressures, pressure-broadening is small, as is natural broadening. 

J. Ward, J. Cooper, Correlation effects in the theory of combined Doppler and pressure broadening. J. Quant. Spectrosc. Radiat. Transf. 14, 555 (1974)... 

Fig. 4. Pressure dependence of rf resonance linewidths (HWHM) of AM- and FM-Raman heterodyne signals for xenon and helium collision partners. Experimental points are given by crosses the full curves correspond to fits that are based on a theory including velocity diffusion processes. Dashed lines, initial slopes for the AM-RHS pressure broadening giving YvcC dash-dotted lines, asymptotic slopes for FM-RHS linewidths giving Yc-...

This article reviews the basic theory of the pressure broadening of spectral lines. 

If Other fall-off broadening factors arising m unimolecular rate theory can be neglected, the overall dependence of the rate coefficient on pressure or, equivalently, solvent density may be represented by the expression [1, 2]... 

Chapter 3 is devoted to pressure transformation of the unresolved isotropic Raman scattering spectrum which consists of a single Q-branch much narrower than other branches (shaded in Fig. 0.2(a)). Therefore rotational collapse of the Q-branch is accomplished much earlier than that of the IR spectrum as a whole (e.g. in the gas phase). Attention is concentrated on the isotropic Q-branch of N2, which is significantly narrowed before the broadening produced by weak vibrational dephasing becomes dominant. It is remarkable that isotropic Q-branch collapse is indifferent to orientational relaxation. It is affected solely by rotational energy relaxation. This is an exceptional case of pure frequency modulation similar to the Dicke effect in atomic spectroscopy [13]. The only difference is that the frequency in the Q-branch is quadratic in J whereas in the Doppler contour it is linear in translational velocity v. Consequently the rotational frequency modulation is not Gaussian but is still Markovian and therefore subject to the impact theory. The Keilson-... 

It should be noted that there is a considerable difference between rotational structure narrowing caused by pressure and that caused by motional averaging of an adiabatically broadened spectrum [158, 159]. In the limiting case of fast motion, both of them are described by perturbation theory, thus, both widths in Eq. (3.16) and Eq (3.17) are expressed as a product of the frequency dispersion and the correlation time. However, the dispersion of the rotational structure (3.7) defined by intramolecular interaction is independent of the medium density, while the dispersion of the vibrational frequency shift (5 12) in (3.21) is linear in gas density. In principle, correlation times of the frequency modulation are also different. In the first case, it is the free rotation time te that is reduced as the medium density increases, and in the second case, it is the time of collision tc p/ v) that remains unchanged. As the density increases, the rotational contribution to the width decreases due to the reduction of t , while the vibrational contribution increases due to the dispersion growth. In nitrogen, they are of comparable magnitude after the initial (static) spectrum has become ten times narrower. At 77 K the rotational relaxation contribution is no less than 20% of the observed Q-branch width. If the rest of the contribution is entirely determined by... 

The quasi-classical theory of spectral shape is justified for sufficiently high pressures, when the rotational structure is not resolved. For isotropic Raman spectra the corresponding criterion is given by inequality (3.2). At lower pressures the well-resolved rotational components are related to the quantum number j of quantized angular momentum. At very low pressure each of the components may be considered separately and its broadening is qualitatively the same as of any other isolated line in molecular or atomic spectroscopy. 

Debye s theory, considered in Chapter 2, applies only to dense media, whereas spectroscopic investigations of orientational relaxation are possible for both gas and liquid. These data provide a clear presentation of the transformation of spectra during condensation of the medium (see Fig. 0.1 and Fig. 0.2). In order to describe this phenomenon, at least qualitatively, one should employ impact theory. The first reason for this is that it is able to describe correctly the shape of static spectra, corresponding to free rotation, and their impact broadening at low pressures. The second (and main) reason is that impact theory can reproduce spectral collapse and subsequent pressure narrowing while proceeding to the Debye limit. 

Pressure induced broadening and narrowing of a whole spectrum are described by the quasi-static approximation and the perturbation theory, correspondingly. Comparing inequalities (6.13) and (2.53) one can see that the border between the stages is determined by the criterion coij 1,... 

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