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Physical Review Letters

Observation of Non-Lorentzian Spectral Line Shapes in Na-Noble-Gas Systems

Robert E. Walkup, Annie Spielfiedel, David E. Pritchard

Published Sep 22, 1980• 42 citations
Publisher

Abstract

This Letter reports observations showing that the spectral line shape in the core region of collision-broadened lines contains a dispersion component in addition to the usual Lorentzian. The physical origin of this component is the finite duration of the collisions. For the Na $D$ lines and Xe perturbers, the dispersion component produces an 8% asymmetry 0.1 \AA{} from line center. Calculations based on recent line-broadening theories predict a dispersion component with an amplitude comparable to our experimental results.

DOI
10.1103/physrevlett.45.986

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This Letter reports observations showing that the spectral line shape in the core region of collision-broadened lines contains a dispersion component in addition to the usual Lorentzian. The physical origin of this component is the finite duration of the collisions. For the Na DDD lines and Xe perturbers, the dispersion component produces an 8% asymmetry 0.1 \AA{} from line center. Calculations based on recent line-broadening theories predict a dispersion component with an amplitude comparable to our experimental results.
Degenerate four-wave mixing in sodium vapor in the presence of a noble gas is measured and calculated for large detunings from resonance, where the collisional impact approximation is no longer applicable. The measurement thus probes the non-impact collisional potential of the Na-noble gas system. When the noble gas is Xe, and the detuning is to the red of the Na D 1 resonance, an avoided crossing between the quasi-molecular potentials results in a satellite in the absorption lineshape, which can be detected in the four wave mixing signal. We calculate collisional lineshapes with several available sets of Na-Xe interaction potentials using the quasi-static and semi-classic line broadening theories, and find that the available potentials do not yield line shapes which agree with the measurements. The lineshape derived from the measured degenerate four wave mixing signal shows good agreement with theoretical calculations, only if the non-adiabatic nature of the level crossing is considered. Based on our experimental lineshape and a non-adiabatic level crossing theory, we derive corrections to the Na-Xe potentials, near the level crossing, that is for interatomic separations in the range of 0.55–0.75 nm.
The quantum-mechanical Baranger-Kolb-Griem theory of pressure broadening is reexamined in order to include both the effects due to overlapping lines and finite duration of collision. A general line-shape formula is derived which for near wings can be presented as a linear combination of the Lorentzian and dispersion profiles. The asymmetry parameter is expressed by means of evolution operators for the initial and final states. It is shown that in the weak-coupling case only the resultant asymmetry parameter can be approximately given as the sum of parameters describing the asymmetry due to line mixing and finite collision time.
The shapes of the thallium (Tl) 535- and 377.6-nm resonance lines broadened by 500-1500 Torr of noble gases have been measured at 743 K. The reported normalized emission intensities yield absorption coefficients in absolute units for all portions of the line. The shift and broadening of the Lorentzian-shaped line cores, the wavelengths of the transition to non-Lorentzian wings, wing shapes, and satellite positions, shapes, and intensities are reported. As an example, a pair of excited and ground-state interaction potentials are given for the Xe case to explain the shift, width, and intensities in all portions of the line wings.
The thermally averaged collision-broadened line shape is written in terms of a detuning-dependent broadening rate ${\ensuremath{\gamma}}_{c}(\ensuremath{\Delta})$ which is evaluated numerically for van der Waals potentials using classical straight trajectories. The results are presented in terms of reduced variables that make it easy to calculate the line shape for any system with arbitrary van der Waals coefficient and temperature. The results show how the line shape makes a smooth transition from a Lorentzian profile in the impact region to the dramatically asymmetric far line wings. The transition zone is characterized by $|\ensuremath{\Delta}|{T}_{d}\ensuremath{\sim}1$, where $\ensuremath{\Delta}$ is the frequency detuning from resonance and Td{T}_{d}Td​ is a characteristic collision duration. The lowest-order correction to the Lorentzian line shape due to finite collision duration describes the dominant behavior for $|\ensuremath{\Delta}|{T}_{d}\ensuremath{\sim}1$. The numerical results are compared with analytic approximations and recent experiments. Averaging over a thermal distribution of relative velocities is shown to alter the line-shape asymmetry substantially, improving agreement between theory and experiment. The temperature dependence of the overall line shape is presented and discussed.