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Canadian Journal of Physics

Resonance broadening in high density gases

Haider R. Zaidi

Published Jul 15, 1977• 10 citations
Publisher

Abstract

The resonance broadening of a transition between two excited states of a radiator in a high density gas is investigated. The important many body shielding contributions are included to all orders, and the two body correlations for the close collisions are approximately taken into account. Corrections to the line width and shift at moderately high densities are calculated. The results agree with the experimental data for krypton. The density dependence of the width parameter is examined at very high densities also. It is found that this parameter, after reaching a peak value, decreases with further increase in the density. Moreover, the square root dependence of the line widths on the density is not valid over any extended range of gas densities.

DOI
10.1139/p77-160

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Canadian Journal of Physics•Jul 15, 1977•9 citations
The resonance broadening of a transition between two excited states of a radiator in a high density gas is investigated. The important many body shielding contributions are included to all orders, and the two body correlations for the close collisions are approximately taken into account. Corrections to the line width and shift at moderately high densities are calculated. The results agree with the experimental data for krypton. The density dependence of the width parameter is examined at very high densities also. It is found that this parameter, after reaching a peak value, decreases with further increase in the density. Moreover, the square root dependence of the line widths on the density is not valid over any extended range of gas densities.
The line-shape function is expressed in terms of three boundary functions related to the two-particle Green's function. The transverse as well as the longitudinal interaction among atoms is considered, using the photon propagator approach. The broadening of one of the radiative states through the resonance interaction with the ground state is considered in detail. The contributions of multiple transfer of excitation and of two-body scattering are calculated separately. Several validity conditions are also obtained which clarify the approximations in the existing results. The velocity dependence of the width parameter is investigated in some detail; our results differ considerably from the existing results because we have included higher-order contributions. The extreme low-density region [where (collision width) \ensuremath{\sim} (natural width)] is also considered; the linewidth is found to be nonlinear in the number density. The additional contribution of the coupling between the radiative states is also calculated in a special case.
Reports the results of interferometric investigation of collisional broadening and shift of the resonance line of thallium ( lambda =377.68 nm) by krypton and xenon. The measurements were performed at low density of the perturbing gases (3-53*10 16 cm -3 ) and both Doppler and collisional broadening of the line were determined. The results are compared with those calculated on the basis of the van der Waals, Lennard-Jones and Czuchaj-Sienkiewicz potentials. The measured values of the broadening and shift by krypton and xenon are lower than those computed for the van der Waals and Lennard-Jones potentials. Calculations based on realistic potentials reported by Czuchaj and Sienkiewicz give values of the broadening coefficient in good agreement with the experimental data.
Three-photon excitation and multiphoton ionization techniques have been used to measure self-broadening for several resonance lines in xenon and krypton. Tabulations of widths and shifts of the xenon lines at 146.9, 129.6, 119.2, and 117.0 nm were made for pressures between 50 and 900 Torr. Similar measurements were made for the krypton resonance line at 116.5 nm. For pressures less than 500 Torr the widths were found to be in reasonable agreement with theoretical results, which were extrapolated into regions of concentration where the criteria for their validity are at best questionable. We have also found the lines to be shifted to the high-energy side of the unperturbed line. For four of the five lines studied, the blue shifts increased nearly linearly with increasing pressure. In the four cases where the shift could be measured the ratio of shift to width was close to (1/2. Our experimental technique is very simple, but it has yielded what we believe to be the first resonance broadening data based on absorption under conditions where there is strong trapping of the resonance radiation.
Self-broadening of the 146.96 nm xenon line and 123.58 nm krypton line is studied in the density range 1-100 amagat (2.7 x 1019 — 2.7 × 1021 at. cm-3). The absorption profile is deduced from reflection experiments by a modified Kramers-Krönig analysis. A detailed discussion of the criteria for validity of available theories is given, allowing the determination of the extent to which the cases studied are related to many-body interactions and/or pure resonance forces. The quasistatic theory, in the nearest neighbour approximation, is shown to be valid for interpreting the far wings. Thus it is possible at increasing density, to underline the specific effect of the various kinds of forces : resonance, Van der Waals and repulsive, and to specify the 1u excited state potential which is found weakly attractive for Xe2 and Kr2.
It is pointed out that the usual theories of pressure broadening disagree with direct experimental measurements of the widths of resonance-broadened alkali doublet lines, although the theories are at least qualitatively confirmed for the wings of resonance lines and for foreign-gas broadening. There are also two conflicting sets of experimental data (both in strong disagreement with theory). Some qualitative arguments are given for doubting the validity, near the center of a resonance line, of the "two-body" approximation generally used in theoretical treatments, and some formal objections to the usual procedure are also presented. The basic equation relating the susceptibility to a resolvent operator matrix element is derived from a more fundamental point of view than usual; the result contains in principle all effects due to translational motion, to the quantized nature of the radiation field, and to "spatial dispersion." In the limit of large absorber mass it is proved rigorously that the two-body approximation can never be valid near the center of a line, even for very low densities. By using different approximations for the wings and the line center, we obtain satisfactory agreement with experiments in both regions for the alkali doublet lines. We are also able to decide between the two conflicting experiments, favoring the square-root density dependence of the line-width observed by Lauriston and Welsh.
A theory is developed for the resonant dielectric susceptibility of a high density gas which consists of two level atoms interacting through the dipole–dipole potential. A many body collision model, which includes the binary as well as the shielding effects, is investigated. The linear response of the dielectric is given by a generalized transport equation. Self-consistent coupled equations are derived for the various collision operators, using the propagator techniques. In the two limiting cases, the results of the binary collision model and those of the shielded interaction model, respectively, are recovered. The equations are simplified by neglecting the nonresonant contributions. Finally, a solution is obtained in the resonance broadening approximation. The resulting expression for the dielectric susceptibility includes the two body collision as well as the many body shielding effects. In particular, it includes the important collective excitation transfer effects. The proposed many body collision model should be appropriate for the resonant, linear response of high density gases.