On the theory of linear absorption line shapes in gases

A detailed theory of the line shape in linear absorption spectroscopy of low-pressure gases is developed. The goal is to take into account all effects that come into play in the determination of Boltzmann's constant from measurements of the Doppler width. We demonstrate that there is no additional broadening from finite transit time across the laser beams. The molecular recoil and the second-order Doppler effect are included in the line shape thanks to a complete quantum treatment. The Mössbauer–Lamb–Dicke narrowing of Doppler lines by collisions is also included and the special cases of Galatry and Nelkin–Ghatak profiles are presented. To cite this article: C.J. Bordé, C. R. Physique 10 (2009).     

Widths and shifts of HF vibration-rotation absorption lines induced by pressure of rare gases

Widths and shifts of the HF vibration-rotation absorption spectrum, induced by the pressure of rare gases, have been calculated using the Kolb-Griem-Baranger theory, for the pure rotation, 0–1, and 0–2 bands. Agreement between the calculated and experimental widths is good in general, but the calculated shifts, though having a qualitatively correct m-dependence for the most part, exceed the experimental values by a factor of 1·3-2·0. Isotropic effects are included to all orders, leading to three major consequences: (1) a criticism is made regarding one of the assumption underlying Anderson's approximation number two, (2) a reason is provided for the differences in widths of R and P branch lines of the same ∣m∣ within a given band, and (3) the previously unexplained increase in widths with increasing ∣m∣ in the 0–2 band with xenon is explained.     

Resonant acousto-optical interaction under realistic conditions of a broadened absorption line

A theory of the resonant acousto-optical interaction has been constructed for spectral line broadening of arbitrary character. Account is taken of the strongest of the mechanisms of resonant photoelasticity, associated with the potential-deformation interaction of light and sound. It is shown that when inhomogeneous broadening is present the maximum efficiency of the acoustooptical interaction over the optical absorption length is not not reached at exact resonance, as in the case of homogeneously broadened lines, but at some separation from it, at a distance of about the half-width of the absorption line. It is shown that a combined study of the diffraction efficiency of the acousto-optical interaction and the optical absorption coefficient at near-resonant frequencies would make it possible to obtain information on the contributions of homogeneous and inhomogeneous broadening in a real resonance and thus assess the quality of the material. Fiz. Tverd. Tela (St. Petersburg) 39, 1354–1357 (August 1997)     

Atom-atom potential in rotational line broadening for molecular gases: Application to CO lines broadened by CO,N2, O2 and NO

Linewidths in CO-CO, CO-N₂, CO-C₂ and CO-NO collisions have been calculated using an improved potential for atom-atom interactions in addition to the first-order terms of the electrostatic interaction. The energy parameters characterizing the Lennard-Jones potential have been estimated previously from second virial coefficients. Overall agreement between calculated and experimental linewidths (particularly for CO-O₂ mixtures for which the electrostatic contributions are weak) is thus obtained without any adjustable parameters. It is concluded that the atom-atom potential describes the angular dependence of the short-range forces in molecular collisions fairly adequately.     

Calculated pressure effects on spectral lines for long-range interatomic potentials: Rb and Cs with heavy rare gases

We have calculated the impact broadening and shift of the first and second doublets of Rb and Cs. The interaction potential of the collision pair is assumed to be a long-range van der Waals potential. The van der Waals constants involved are provided by recent theoretical calculations. We obtain good agreement between the calculated and experimental values for both the P_{$\text{1}\text{2}$} and P_{$\text{3}\text{2}$} component. Comparison of our calculated values is also made with those of Granier, Granier and Schuller.     

Alkali rare-gas line profiles in a square-well potential approximation: Width,shift, and asymmetry

We have studied the profiles of spectral lines of alkalies perturbed by rare gases using the Anderson and Talman theory of line broadening with a square-well potential, chosen for its simplicity in order to understand the influence of potential parameters on the profiles. Although it is obvious that such a simple potential is not able to give an exact quantitative fit to the experimentally measured results, we have been able to give a complete and satisfactory explanation of the variations of width, shift and asymmetry with density by applying previously established results, for the case of well-resolved satellites, to the case of unresolved satellites often encountered experimentally.     

Experimental and theoretical studies of room-temperature sub-millimetre CH3 35Cl line shapes broadened by H2

Hydrogen-broadening coefficients of methyl chloride rotational lines J?=?6?→?7, 10?→?11, 17?→?18, 22?→?23 and 31?→?32 at 296?K are measured as functions of the quantum number K using a sensitive frequency-modulation technique. As expected for this light perturber, the observed line shapes are well described by Voigt profile model. A clear dependence of the collisional broadening on K is observed for most transitions. From a detailed study of the K-components of the transition J?=?6?→?7 situated at 186?GHz no variation of the broadening of the hyperfine components related to ³⁵Cl quadrupole is stated. Given the absence of refined ab initio computed potential energy surfaces and the impracticality of quantum-mechanical calculations for the considered molecular system, theoretical values of these broadening coefficients are estimated by a semi-classical approach with exact trajectories and a model interaction potential including both long-range and short-range (atom-atom) interactions of the active molecule rigorously treated as a symmetric top. It is shown that the short-range forces yield important contributions to the collisional line width for all values of the rotational quantum numbers J and K. Various models are also tested for the isotropic part of the interaction potential which governs the relative translational motion. It is demonstrated that for the very light perturbing molecule H₂ the calculated line widths, practically independent from the rotational quantum number J (for K?≤?J), are particularly sensitive to the position and slope of the repulsive wall. Modifications required in the semi-classical formalism for a correct application of the cumulant expansion are also tested and it is stated that no difference is observed for the CH₃Cl–H₂ system characterised by quite weak interactions.     

Dicke-narrowed spectral line shapes of CO in Ar: Experimental results and a revised interpretation

The shapes of Dicke-narrowed spectral lines in the fundamental P-branch of CO in Ar are studied by comparing high-resolution measurements and theoretical calculations. The measured spectra were recorded at temperatures between 214 and 324 K, and at pressures between 0.025 and 1 atm. The calculations are based on solving a transport/relaxation equation for the appropriate off-diagonal element of the density matrix; they use a realistic intermolecular potential to determine the speed-dependent collisional broadening, and a rigid sphere potential to determine the Dicke narrowing. It is found that the calculations can reproduce the measured spectra within the experimental noise under all conditions, but that the magnitude of the Dicke narrowing in the measured spectra is 70-90% less than predicted from the mass diffusion constant. A revised view of the collision operator resolves the discrepancy in principle, and leads to a better understanding of the line shape problem in general.     

Broadening and shift of neutral chromium absorption lines by various perturbing gases

The broadening and shift of the absorption lines (a⁷S-z⁷P°, a⁷S-y⁷P° and a⁵S-z⁵P°) of the neutral chromium atom were observed at various temperatures (1500–1800 K) and densities (0.24-3.2x 10¹⁹/cm³) of foreign perturbers (He, Ar, N₂, H₂). The dependence of width and shift on temperature and density was studied. The collisional broadening and shift rates were determined from the profile measurements. The results are interpreted in terms of the Lindholm-Foley interaction potential between radiating atom and perturbers. Semi-quantitative agreement of theory and experiment was found in some cases for the temperature dependence of width and shift and for the differences of attractive constants ΔC₆ between upper and lower states of chromium lines.     

The line shapes of a tumbling triplet

The line shapes of a triplet spin system which interacts simultaneously with the molecular environment and with an externally applied field depend on the relative strengths of these interactions and on the motion of the molecule relative to the laboratory. In this paper line shapes are reported for zero, low, intermediate and strong applied fields, assuming that the molecular motion is due to strong collisions and that the tumbling rate is slow or intermediate.     

Integrated absorption of a spectral line with the Voigt profile

A simple approximation has been found for the integrated absorpton of a spectral line with Voigt profile. It is expressed in terms of the integrated absorption of the Doppler and Lorentz profiles. The maximum error is 8%.     

The white line inL absorption spectra of rare earth oxides

The method of curve fitting of the experimentally obtained absorption edge has been developed and successfully adopted to study the precise variation in the density of states responsible for the occurrence of the white line associated with theL _II andL _III absorption discontinuities of rare earth (RE) in their sesquioxides. The theoretical equation and the curve fitting routine is flexible enough to include all the transitions responsible for XANES as well as other phenomena such as, screening effect, variation in the potential around the metal ion due to surrounding ligand ion, charge transfer etc. An erratum to this article is available at .     

Three-body interaction-induced light scattering in krypton gas: a computer simulation of the spectral line shapes

The two-, three- and four-body effective collision induced scattering spectral line shapes are calculated for dense gaseous krypton using the pairwise additivity (PA) approximation and different polarizability models. These spectra and several interaction induced spectra calculated at various densities are compared with the experimental measurements of Barocchi et al. [1988, Europhys. Lett., 5, 607]. The potential effect on the spectrum is found to be weak. The results obtained with the Meinander et al. [1986, J. chem. Phys., 84, 3005] empirical polarizability model and molecular dynamics fit well the experimental two- and three-body spectral shapes. The irreducible contribution to the spectral shape is evaluated using the dipole induced dipole irreducible polarizability [buckingham, A. D., and Hands, I. D., 1991, Chem. Phys. Lett., 185, 544]. This contribution is found to be relatively weak for the anisotropic spectra in the frequency and density range studied, explaining the good agreement between the pairwise approximation calculations and the experimental data. The spectra radiated by the quasi-molecules Kr₂, Kr₃, and Kr₄ (the total spectrum within the PA approximation) are also simulated.     

A formulation of the saturation of absorption lines,which are partially homogeneous broadened by collision processes

With considering the influence of velocity changing collisions a is given. The result including also effects of the frequency detuning from the line center is between the known limiting cases of homogeneous and inhomogeneous broadening.     

Nonlinear collapse of an isolated,homogeneously broadened,spectral line as a result of coherent collisions

The collisional exchange between an off-diagonal element of the density matrix and its complex conjugate results in the collapse of a homogeneously broadened spectral line. The case when such exchange is due to the polarization of the heat bath on account of two-photon absorption is studied. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 599–603 (10 November 1996)