Collision broadening

N is the perturbing atom or molecule density, tc is the collisional cross-section in m, and V is the mean relative velocity between the colliding partners. For thermal equilibrium v is given by  

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  

Larkins determined collisional cross-sections for some elements in an air/acetylene 

As well as broadening, a shift of the spectral line appears, which can be towards shorter wavelengths (blue shift) or to longer wavelengths (red shift), depending on the collision partner. For the prominent case of an adiabatic impact, Corney [19] predicted the relationship between shift and broadening to be 0.36. 

The most important sonrce of line broadening in microwave smdies ofbnlk gas samples is collisional or pressnre broadening, the theory of which was first developed by Van Vleck and Weisskopf [77]. They developed the Une shape function 

Av then becomes the half-width at half-peak height. As the gas pressure is increased, however, the second term becomes significant and die line shape departs from the simple Lorentzian. 

When the populations of the two levels involved in a transition are determined by thermal equilibrium conditions, the Van Vleck- Weisskopf line shape function may be 

Ny is the number of molecules per unit volume and fa is the fraction in the lower state a involved in the transition. 

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Harde H, Katzenellenbogen N and Grischkowsky D 1995 Line-shape transition of collision broadened lines Phys. Rev. Lett. 74 1307-10... 

Smith MAH, Rinsland C P and Fridovich B 1985 Intensities and collision broadening parameters from infrared spectra Molecular Spectroscopy Modem Research Volume Hied K N Rao (New York Academic) pp 118-19... 

Lwin N, McCartan DG (1978) Collision broadening of the potassium resonance lines by noble gases. J Phys B 11 3841-3849... 

Doppler broadening. Collisions broadening becomes less important at the lower pressures found at higher altitudes, so that the Lorentzian half-width and the Doppler half-width become comparable at altitudes of approximately 30-40 km. 

Av Avc Rayleigh resolution in wave-number units half-width yc/4rc observed when collision broadening dominates (given in hertz)... 

To consider gas molecules as isolated from interactions with their neighbors is often a useless approximation. When the gas has finite pressure, the molecules do in fact collide. When natural and collision broadening effects are combined, the line shape that results is also a lorentzian, but with a modified half-width at half maximum (HWHM). Twice the reciprocal of the mean time between collisions must be added to the sum of the natural lifetime reciprocals to obtain the new half-width. We may summarize by writing the probability per unit frequency of a transition at a frequency v for the combined natural and collision broadening of spectral lines for a gas under pressure ... 

The function that we obtain is the Voigt function encountered in Section III.C of Chapter 1. With definition of variables and scaling appropriate to the case of combined Doppler, natural, and collision broadening, the Voigt function appears as the probability per unit frequency of observing light at a frequency v ... 

By using the same definitions, the profile for combined Doppler, natural, and collision broadening may be expressed in terms of the Voigt function ... 

In liquids the interactions between neighboring molecules are considerably more complicated than in gases. The resultant broadening obliterates the fine line structure seen in gas spectra, leaving only broad band profiles. There are many possible contributors to this broadening. In some cases, adequate approximation is obtained by assuming that the band contour is established by collisions. Ramsay (1952) has noted that substitution of appropriate molecular density and collision diameter numbers in the collision broadening formula results in realistic band widths for certain liquid-phase systems. In such systems, the bands typically show an approximately Lorentzian profile. Approximate deconvolution of inherently broadened liquid-phase spectra may therefore be obtained on the basis of the assumption of Lorentzian shape (Kauppinen et al., 1981). 

A further factor which affects the shape of a resonance line is the transport of resonance radiation through the. parent gas. Milne s early theory of self-absorption by the imprisonment of resonance radiation has been revised by Holstein (3) and Bichermau (4), taking into account the incoherent scattering of resonance photons. Furthermore, Walsh (" ) has extended the imprisonment lifetime calculation for cases where Doppler and collision broadening of the resonance line are simultaneously present, and in addition this author has examined the complications caused by the, hfs. The line shape, linewidth, and other properties of self-absorbed lines hare been discussed recently bv Tako (6), who summarizes the various effects of self-absorption as follows ... 

S. H. Robertson, N. Snider, and D. M. Wardlaw, J. Phys. Chem., 97, 7556 (1993). Strong Collision Broadening Factors from Theories of Unimolecular Rate Coefficients. 

General Theory of Collision Broadening. A molecular component in an ordinary fluid, in the presence of an electromagnetic field E(w,t) and the collisional perturbation V (u,t), due to interactions with other molecules, will experience a total Hamiltonian ... 

Models for collision-broadened lineshapes have been treated in detail (1-7), in the adiabatic as well as the diabatic limit. 

In spite of the complexity of the analysis of the millimeter-wave and far-infrared spectrum of l CKO, the principal contributor to the bulk attenuation function of typical biological systems in this frequency range, no compelling experimental evidence or theoretical constructs exist to disqualify the assumption that this system is a complex, but typical, collision-broadened system whose fundamental features (1) are well understood. 

As for all the systems relegated to Section 2 the attenuation function for structural H2O in the microwave and far-infrared region, as well as that for free H2O, can be understood in terms of collision-broadened, equilibrium systems. While the average values of the relaxation times, distribution parameters, and the features of the far-infrared spectra for these systems clearly differ, the physical mechanisms descriptive of these interactions are consonant. The distribution of free and structural H2O molecules over molecular environments is different, and differs for the latter case with specific systems, as are the rotational dynamics which govern the relaxation responses and the quasi-lattice vibrational dynamics which determine the far-infrared spectrum. Evidence for resonant features in the attenuation function for structural H2O, which have sometimes been invoked (24-26,59) to play a role in the microwave and millimeter-wave region, is tenuous and unconvincing. 

Nevertheless, in view of the fact that the stability of biopolymers, in respect of their secondary and tertiary (conformational) structure, is strongly influenced by interactions with structural H2O (45), it is of considerable interest to explore further the features discussed in the penultimate paragraph. Even for a totally collision-broadened (relaxation-type) initial step... 

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