Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America

Combined Doppler and Collision Broadening*

Joel I. Gersten, Henry M. Foley

Published Jul 1, 1968• 77 citations
Publisher

Abstract

The combined effect of Doppler and collision broadening of spectral lines is studied by means of the statistical correlation function for the time-varying amplitude of classical oscillators. It is shown that at high pressures (mean-free path smaller than wavelength) the line shape is lorentzian with a width which is the sum of the conventional collision broadening and a Doppler contribution which decreases with increasing pressure, consistent with Dicke’s result.

DOI
10.1364/josa.58.000933

Related papers

Comprehensive theory for line broadening in high-resolution and nonlinear spectroscopies: application to the Na D lines

R. M. Herman, E. W. Weber

A general method for analysing line broadening caused by Doppler, phaseshift, inelastic and velocity-changing collisional effects is proposed for transitions at optical wavelengths. In a unified approach Poisson statistics are used to describe collision probabilities randomly distributed in a time interval which can terminate the optical coherence in a combination of the above effects; markoffian independence is assumed for each collision. Then the dipole moment correlation function is obtained in a form which is virtually exact in accounting for all effects of isotropic forces, and which is correct to second-order terms in the anisotropic interaction potentials. Phenomena as diverse as standard optical pressure broadening, broadening due to velocity-changing collisions in nonlinear spectroscopies, and Dicke narrowing of the Doppler contour are described. The implications of the theory are discussed in detail and applied to the case of the NaD lines perturbed by He buffer gas. Numerical calculations reveal that the substantially different lineshift and broadening parameters in nonlinear and in standard optical spectroscopies can be reasonably well understood within the limitations posed by present uncertainties in the Na 3 2 P-He interaction potentials. However, the large differences in shift and width between the D 2 and D 1 lines in saturation spectroscopy cannot be explained within the present theory.

Journal of Physics B Atomic and Molecular Physics•Apr 28, 1983•8 citations

Correlations between Doppler and pressure broadening for the resonance interaction

J. Cooper, Derek N. Stacey

The correlation between Doppler and collisional broadening has been considered in detail for radiation in which the lower level of the transition is broadened by the resonance interaction. It is found that rather than a single Voigt profile, the profile of the radiation is essentially a sum of Voigt profiles. Although the widths of these profiles vary by some 40%, the over-all line shape is very close to the single Voigt shape obtained when correlation effects are neglected.

Physical Review A•Dec 1, 1975•9 citations

Line-mixing and collision-time asymmetry of spectral line shapes

R. Ciuryło, Józef Szudy

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.

Physical Review A•Mar 20, 2001•24 citations

Emission from an oscillator ensemble

Sergei A. Akhmanov, S YU Nikitin

Abstract From the dynamics of an oscillator to the statistics of an ensemble. Non-laser sources of light: intensity, polarization, and radiation directivity pattern. Radiation statistics of independent oscillators. The radiation spectrum. Mechanisms of spectral line broadening. Natural broadening. Doppler broadening. Collision-induced broadening and the shift of a spectral line. Dicke’s effect: collision-induced narrowing of a Doppler spectral line in a dense gas.

•Apr 3, 1997•0 citations

Shapes of pressure- and Doppler-broadened spectral lines in the core and near wings

R. Ciuryło

The Rautian-Sobelman approach describing the collision-Doppler shape of spectral line that takes into account both soft and hard velocity-changing collisions is extended to the case when correlation between Doppler and collision broadening as well as the dispersion line asymmetry should be considered. Numerical calculations show that speed-dependent effects can produce the additional line narrowing as well as broadening and also the line asymmetry. It is shown that speed-dependent profiles based on the soft and hard collision models differ much more one from another than those which omit the speed-dependent effects.

Physical Review A•Aug 1, 1998•151 citations

Theory of velocity-dependent, collision-broadened, Doppler-free line shapes

M. J. O’Callaghan, J. Cooper

Line-shape expressions for two-step resonant excitation in the presence of low-pressure perturbers are derived. These expressions allow for velocity-dependent broadening rates and are well suited for studying the line-shape contributions due to coherent excitation, incoherent excitation (due to dephasing collisions), interference between coherent and incoherent excitation, and velocity-changing collisions. Using the sodium 3S-3P-4D system perturbed by noble-gas atoms as an example and assuming ${C}_{6}$ interaction potentials, line shapes at a variety of laser detunings (Doppler selected atomic velocities) are numerically calculated to study variation in the line shape due to competing excitation paths and speed-dependent collision rates. In order to deal with both the line core and the line wing a composite collision kernel consisting of a Lorentzian kernel for small \ensuremath{\Delta}${v}_{z}$ collisions and a Keilson-Storer kernel for large \ensuremath{\Delta}${v}_{z}$ collisions is used. It is also demonstrated how the inelastic (3${P}_{3/2}$-3${P}_{1/2}$) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.

Physical Review A•Jun 1, 1989•23 citations
The combined effect of Doppler and collision broadening of spectral lines is studied by means of the statistical correlation function for the time-varying amplitude of classical oscillators. It is shown that at high pressures (mean-free path smaller than wavelength) the line shape is lorentzian with a width which is the sum of the conventional collision broadening and a Doppler contribution which decreases with increasing pressure, consistent with Dicke’s result.
A general method for analysing line broadening caused by Doppler, phaseshift, inelastic and velocity-changing collisional effects is proposed for transitions at optical wavelengths. In a unified approach Poisson statistics are used to describe collision probabilities randomly distributed in a time interval which can terminate the optical coherence in a combination of the above effects; markoffian independence is assumed for each collision. Then the dipole moment correlation function is obtained in a form which is virtually exact in accounting for all effects of isotropic forces, and which is correct to second-order terms in the anisotropic interaction potentials. Phenomena as diverse as standard optical pressure broadening, broadening due to velocity-changing collisions in nonlinear spectroscopies, and Dicke narrowing of the Doppler contour are described. The implications of the theory are discussed in detail and applied to the case of the NaD lines perturbed by He buffer gas. Numerical calculations reveal that the substantially different lineshift and broadening parameters in nonlinear and in standard optical spectroscopies can be reasonably well understood within the limitations posed by present uncertainties in the Na 3 2 P-He interaction potentials. However, the large differences in shift and width between the D 2 and D 1 lines in saturation spectroscopy cannot be explained within the present theory.
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 Rautian-Sobelman approach describing the collision-Doppler shape of spectral line that takes into account both soft and hard velocity-changing collisions is extended to the case when correlation between Doppler and collision broadening as well as the dispersion line asymmetry should be considered. Numerical calculations show that speed-dependent effects can produce the additional line narrowing as well as broadening and also the line asymmetry. It is shown that speed-dependent profiles based on the soft and hard collision models differ much more one from another than those which omit the speed-dependent effects.
Line-shape expressions for two-step resonant excitation in the presence of low-pressure perturbers are derived. These expressions allow for velocity-dependent broadening rates and are well suited for studying the line-shape contributions due to coherent excitation, incoherent excitation (due to dephasing collisions), interference between coherent and incoherent excitation, and velocity-changing collisions. Using the sodium 3S-3P-4D system perturbed by noble-gas atoms as an example and assuming C6{C}_{6}C6​ interaction potentials, line shapes at a variety of laser detunings (Doppler selected atomic velocities) are numerically calculated to study variation in the line shape due to competing excitation paths and speed-dependent collision rates. In order to deal with both the line core and the line wing a composite collision kernel consisting of a Lorentzian kernel for small \ensuremath{\Delta}vz{v}_{z}vz​ collisions and a Keilson-Storer kernel for large \ensuremath{\Delta}vz{v}_{z}vz​ collisions is used. It is also demonstrated how the inelastic (3P3/2{P}_{3/2}P3/2​-3P1/2{P}_{1/2}P1/2​) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.