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

Physical Review

Quantum Theory of Collision-Induced Absorption in Rare-Gas Mixtures

Howard B. Levine

Published Aug 5, 1968• 2 citations
Publisher

Abstract

A theoretical calculation of the collision-induced far-infrared absorption, which has been observed in rare-gas mixtures, is carried out using the quantum-mechanical expression for the absorption coefficient. Using a simple empirical form to describe the variation of the collision-induced dipole moment with internuclear separation, and using plane-wave eigenstates (i.e., assuming straight-line collision paths), an analytic expression is obtained for the spectrum which agrees well with the experiments. Comparison with a previous classical calculation based upon the same model shows that quantum effects are small at room temperature except in the high-frequency wing of the spectrum. A number of analytic integrations allow us to derive simple expressions for the correlation function, relaxation time, static dielectric constant, and other spectral invariants.

DOI
10.1103/physrev.172.241.3

Related papers

Unified Theory of Spectral Line Broadening in Gases

Robert P. Futrelle

A quantum-mechanical unified theory of foreign-gas pressure broadening of atomic lines which includes the impact and statistical theories and duration-of-collision effects is developed. The model consists of an absorber atom with two internal states $u$ (upper) and $l$ (lower) interacting with a structureless perturber gas via two spherical pairwise additive potentials ${V}_{u}(\mathcal{r})$ and ${V}_{l}(\mathcal{r})$, e.g., a simple model of an alkali-atom line perturbed by a rare gas. The dipolemoment correlation function is analyzed in the time domain using Liouville (tetradic) techniques. The correlation function reduces exactly to a two-body form $\ensuremath{\varphi}(t)$ containing the proper thermal weight factors. Detailed balance is obeyed and no $|\frac{\ensuremath{\hbar}(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0})}{\mathrm{kT}}|<1$ restriction is required. The impact theory follows from a long-time analysis of $\ensuremath{\varphi}(t)$. Sum rules or spectral moments are used to study short-time behavior revealing conventional statistical-theory effects (including satellite bands) and the important duration-of-collision effects which link the statistical and impact regimes. The sum rules are expressed as quadratures involving potential functions and the quantum-mechanical radial distribution function. Unified methods for calculating the total line shapes are suggested: (1) Pad\'e approximants (ratios of polynomials) can be used to interpolate from the known short-time behavior to the known long-time beahvior; this requires the least computational effort; (2) exact results for this model may be obtained numerically from the overlap integrals of radial wave functions (Franck-Condon factors) for the two potentials ${V}_{u}$ and ${V}_{l}$; (3) classical phase (trajectory) expressions are given which are reasonable approximations in both the impact and statistical limits. A number of related topics are discussed including diabatic effects, collision-induced absorption, non-Lorentzian wings of molecular vibration-rotation bands, and the Condon approximation for the dipole-moment transition strength vs $\mathcal{r}$. The use of line shapes to probe atomic interactions, especially in excited states, is emphasized and the suggestion made that experiments be done over as wide a temperature range as possible with the measured line shapes in computer-readable form. The entire line-shape problem is described as the study of the spectrum of an atom-perturber "quasimolecule" (with primarily unbound states).

Physical Review A•May 1, 1972•40 citations

Far-wing study of laser-induced collisional energy transfer

M. Matera, Marina Mazzoni, Roberto Buffa +2 more

An experimental study of laser-induced collisional energy transfer in a mixture of europium and strontium vapors is reported. The profile of the excitation spectrum in the static wing has been measured with high accuracy and compared with available calculations, demonstrating that simple two-level models are inadequate to describe the transfer process. A comparison with the predictions of a three-level model assuming dipole-dipole interaction, recently developed by Bambini and Berman, shows for the first time agreement between theory and experiment.

Physical Review A•Aug 1, 1987•33 citations

Light absorption during a resonant or near-resonant collision: Study of the cross section in the far-wing

Stefano Cavalieri, Milva Celli

We have studied the absorption of light induced by a resonant or near-resonant collision between two atoms. The calculations have been performed by taking into account also the magnetic sublevels, which makes our theoretical predictions more applicable to realistic cases. Analytical expressions for the far wing absorption cross-section have been obtained.

AIP conference proceedings•Jan 1, 1997•0 citations

Light absorption by interacting atomic gas in quantum optical regime

Андрій Сіжук, Konstantin E. Dorfman, C. H. Raymond Ooi

Quantum optical theory of absorption properties of interacting atoms is developed. The concept of local absorptance is introduced as a derivative of the logarithm of intensity with respect to the distance in the vicinity of a given spatial point and a moment of time. The intensity is represented by the quantum and statistically averaged normal product of creation and annihilation operators of the electromagnetic field. The development of an analytical method of the estimation for the kinetic and optical parameters for the system is proposed here. The calculation method of the absorption coefficient includes thermal atomic motion, Doppler effect, and the short-range interaction between atoms. The absorption coefficient explicitly takes into account the quantum nature of the optical field. The ability of the system to absorb or emit quanta is quantitatively expressed through the special form of interaction integrals. The specific form of integrals results from the structure of the quantum brackets. The interplay between the collective (virtual photon exchange) and binary (optically induced inter-particle bonding) processes determines the system behavior. The spectral profile of the local absorption coefficient for different atomic densities and time intervals is simulated for realistic parameters.

The Journal of Chemical Physics•Jul 27, 2021•0 citations

Quantum Theory of Spectral Line Broadening

Stanley Bloom, Henry Margenau

Simple radiation theory is used to derive a formula proposed earlier by P. W. Anderson, for calculating the intensity within a collision-broadened spectral line. The problem is considered, first from the point of view of molecular transitions, and then by computing the work done by the light wave. The general result for absorption is stated in Eq. (18), wherein the first double integral represents true absorption, the second induced emission.

Physical Review•Jun 1, 1953•60 citations

Theory of two-atom coherence in gases. II. Continuous-wave spectra

A. Ben‐Reuven

General expressions are derived for the spectral line shapes of resonance absorption and scattering of coherent radiation in collision-broadened gases, taking into account effects of coherent excitation of two or more atoms (or molecules), as steady-state solutions of a hierarchy of master equations described in a previous publication (paper I). Coupling between the coherent motions of the atoms, provided by a Bethe-Salpeter---type effective interaction, in the binary-collision approximation, forms the essential mechanism for introducing cooperative coherent effects into the steady-state spectra. Explicit expressions are given for the effects of two-atom coherence in the binary-collision approximation, in which the Bloch-type dressed-atom self-energy superoperator is modified by the presence of collisions in which both atoms retain memory of their coherent propagation before the collision. The self-energies include the effects of resonance exchange symmetrization in self-broadening, and are renormalized by the coincidence of radiative transitions during the collisions. The impact (near-resonance) and the quasistatic (line-wing) limits of the applied-frequency detunings are discussed. In the quasistatic limit, coherent many-atom excitations become irrelevant; however, interactions of both collision partners with the radiation during the collision accounts for such phenomena as collision-induced absorption or radiative collisions. In the impact limit, the inclusion of the Bethe-Salpeter interactions allows for the appearance of two-atom resonances. Magnitude estimates of these effects are discussed. Effects of higher-rank (many-body) coherences are formally discussed with the help of a diagrammatic method, leading into implicit bootstrap equations that can be solved by iterative or other procedures.

Physical Review A•Dec 1, 1980•9 citations
A theoretical calculation of the collision-induced far-infrared absorption, which has been observed in rare-gas mixtures, is carried out using the quantum-mechanical expression for the absorption coefficient. Using a simple empirical form to describe the variation of the collision-induced dipole moment with internuclear separation, and using plane-wave eigenstates (i.e., assuming straight-line collision paths), an analytic expression is obtained for the spectrum which agrees well with the experiments. Comparison with a previous classical calculation based upon the same model shows that quantum effects are small at room temperature except in the high-frequency wing of the spectrum. A number of analytic integrations allow us to derive simple expressions for the correlation function, relaxation time, static dielectric constant, and other spectral invariants.
A quantum-mechanical unified theory of foreign-gas pressure broadening of atomic lines which includes the impact and statistical theories and duration-of-collision effects is developed. The model consists of an absorber atom with two internal states uuu (upper) and lll (lower) interacting with a structureless perturber gas via two spherical pairwise additive potentials Vu(r){V}_{u}(\mathcal{r})Vu​(r) and Vl(r){V}_{l}(\mathcal{r})Vl​(r), e.g., a simple model of an alkali-atom line perturbed by a rare gas. The dipolemoment correlation function is analyzed in the time domain using Liouville (tetradic) techniques. The correlation function reduces exactly to a two-body form $\ensuremath{\varphi}(t)$ containing the proper thermal weight factors. Detailed balance is obeyed and no $|\frac{\ensuremath{\hbar}(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0})}{\mathrm{kT}}|<1$ restriction is required. The impact theory follows from a long-time analysis of $\ensuremath{\varphi}(t)$. Sum rules or spectral moments are used to study short-time behavior revealing conventional statistical-theory effects (including satellite bands) and the important duration-of-collision effects which link the statistical and impact regimes. The sum rules are expressed as quadratures involving potential functions and the quantum-mechanical radial distribution function. Unified methods for calculating the total line shapes are suggested: (1) Pad\'e approximants (ratios of polynomials) can be used to interpolate from the known short-time behavior to the known long-time beahvior; this requires the least computational effort; (2) exact results for this model may be obtained numerically from the overlap integrals of radial wave functions (Franck-Condon factors) for the two potentials Vu{V}_{u}Vu​ and Vl{V}_{l}Vl​; (3) classical phase (trajectory) expressions are given which are reasonable approximations in both the impact and statistical limits. A number of related topics are discussed including diabatic effects, collision-induced absorption, non-Lorentzian wings of molecular vibration-rotation bands, and the Condon approximation for the dipole-moment transition strength vs r\mathcal{r}r. The use of line shapes to probe atomic interactions, especially in excited states, is emphasized and the suggestion made that experiments be done over as wide a temperature range as possible with the measured line shapes in computer-readable form. The entire line-shape problem is described as the study of the spectrum of an atom-perturber "quasimolecule" (with primarily unbound states).
An experimental study of laser-induced collisional energy transfer in a mixture of europium and strontium vapors is reported. The profile of the excitation spectrum in the static wing has been measured with high accuracy and compared with available calculations, demonstrating that simple two-level models are inadequate to describe the transfer process. A comparison with the predictions of a three-level model assuming dipole-dipole interaction, recently developed by Bambini and Berman, shows for the first time agreement between theory and experiment.
Quantum optical theory of absorption properties of interacting atoms is developed. The concept of local absorptance is introduced as a derivative of the logarithm of intensity with respect to the distance in the vicinity of a given spatial point and a moment of time. The intensity is represented by the quantum and statistically averaged normal product of creation and annihilation operators of the electromagnetic field. The development of an analytical method of the estimation for the kinetic and optical parameters for the system is proposed here. The calculation method of the absorption coefficient includes thermal atomic motion, Doppler effect, and the short-range interaction between atoms. The absorption coefficient explicitly takes into account the quantum nature of the optical field. The ability of the system to absorb or emit quanta is quantitatively expressed through the special form of interaction integrals. The specific form of integrals results from the structure of the quantum brackets. The interplay between the collective (virtual photon exchange) and binary (optically induced inter-particle bonding) processes determines the system behavior. The spectral profile of the local absorption coefficient for different atomic densities and time intervals is simulated for realistic parameters.
General expressions are derived for the spectral line shapes of resonance absorption and scattering of coherent radiation in collision-broadened gases, taking into account effects of coherent excitation of two or more atoms (or molecules), as steady-state solutions of a hierarchy of master equations described in a previous publication (paper I). Coupling between the coherent motions of the atoms, provided by a Bethe-Salpeter---type effective interaction, in the binary-collision approximation, forms the essential mechanism for introducing cooperative coherent effects into the steady-state spectra. Explicit expressions are given for the effects of two-atom coherence in the binary-collision approximation, in which the Bloch-type dressed-atom self-energy superoperator is modified by the presence of collisions in which both atoms retain memory of their coherent propagation before the collision. The self-energies include the effects of resonance exchange symmetrization in self-broadening, and are renormalized by the coincidence of radiative transitions during the collisions. The impact (near-resonance) and the quasistatic (line-wing) limits of the applied-frequency detunings are discussed. In the quasistatic limit, coherent many-atom excitations become irrelevant; however, interactions of both collision partners with the radiation during the collision accounts for such phenomena as collision-induced absorption or radiative collisions. In the impact limit, the inclusion of the Bethe-Salpeter interactions allows for the appearance of two-atom resonances. Magnitude estimates of these effects are discussed. Effects of higher-rank (many-body) coherences are formally discussed with the help of a diagrammatic method, leading into implicit bootstrap equations that can be solved by iterative or other procedures.