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

Self-Broadening of Optical Double Resonance Lines in Cadmium

F. W. Byron, Mark N. McDermott, Robert Novick

Published May 4, 1964• 67 citations
Publisher

Abstract

Collision broadening studies have been made of optical double resonance lines in cadmium. The results indicate that the collision frequency is velocity dependent, contrary to the usual theory of resonance self-broadening. This result supports the suggestion that the broadening results from interactions involving a number of intermediate states rather than only the initial and final states of the optical transition, because of the small oscillator strength ($f=0.002$) for transitions between the ${(5s)}^{2}^{1}S_{0}$ ground state and the excited state in question $(5s5p)^{3}P_{1}$. The cross section in this case has a $\frac{1}{{{\overline{v}}_{12}}^{\frac{2}{5}}}$ velocity dependence, so the collision frequency varies as ${{\overline{v}}_{12}}^{\frac{3}{5}}$. Measurements show that under this assumption the self-broadening cross section for cadmium is ${\ensuremath{\sigma}}_{\mathrm{coll}}=(1.9\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\mathrm{cm}}^{2}/{{\overline{v}}_{12}}^{\frac{2}{5}},$ where ${\overline{v}}_{12}$ is the average relative velocity in cm/sec. In the course of this work, the lifetime of the $(5s, 5p)^{3}P_{1}$ state was redetermined and found to be (2.39\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}6}$ sec.

DOI
10.1103/physrev.134.a615

Related papers

Theory of Collision Broadening in the Sudden Approximation

F. W. Byron, Henry M. Foley

A method is developed for calculating the cross section for line broadening in the limiting case in which important collisions may be considered to occur very rapidly with respect to the periods corresponding to the transitions in question. This method is essentially an extension of the familiar "sudden" approximation; reference is made throughout to the particular example of optical double resonance only for definiteness and because there are available experimental results for comparison with the theory. Assuming the impact model and considering the case when the energy levels in question are well resolved with respect to their width, an exact expression is found for resonant self-broadening in the usual weak rf field limit of interest in double resonance. For the case of very small oscillator strengths for the optical transition (intercombination lines), the resonant broadening becomes sufficiently small so that second-order, intermediate-state processes dominate, and approximations must be made to effect sums over intermediate states. Here the broadening is of the same sort as foreign gas broadening, and in many cases of interest, the approximations can be made in a sufficiently realistic manner to obtain useful expressions for the broadening. It is shown that the resonant cross section and this "second-order" cross section are not additive, but that the one which is larger dominates the total cross sections very strongly. Finally, we evaluate explicitly the self-broadening and foreign gas broadening (by the noble gases) of double resonance lines in the group II metals and the self-broadening in the optical spectrum of helium. In all cases our theoretical predictions are in good agreement with measurements which have been made.

Physical Review•May 4, 1964•97 citations

Resonant Broadening of Double-Resonance and Level-Crossing Signals: Application to the P13 State in Mercury

A. Omont, J. Meunier

A detailed calculation of the relaxation matrix of resonance atomic states by resonant collisions is carried out in the semiclassical impact theory. The validity of the different approximations is discussed. These results have been tested by observing self-broadening of level-crossing curves in high field and in zero field, in the $6^{3}P_{1}$ state in mercury. Observation of these signals at high pressures is very difficult with a pure isotope because of strong absorption and trapping of resonance light in the vapor; it is made very easy by observing level-crossing signals of one isotope in a very low concentration in the vapor of another isotope. Collisions between the different pairs of mercury isotopes have been thus systematically studied. Results are in excellent agreement (10%) with theory, both for the absolute value of cross sections and for the ratio of orientation broadening to alignment broadening.

Physical Review•May 5, 1968•78 citations

Breakdown of the impact approximation as seen in collision broadening at high densities of the (6p7s)P103 state of lead

Joshua B. Halpern, Ahmed Baghdadi, E. B. Saloman

The Hanle effect has been used to measure the resonant pressure broadening of the $(6p7s)^{3}P_{1}^{0}$ excited state of lead over a density range from ${10}^{14}$ to 4 \ifmmode\times\else\texttimes\fi{} ${10}^{16}$ atom/${\mathrm{cm}}^{3}$. Below ${10}^{16}$ atom/${\mathrm{cm}}^{3}$ the results agree with theories based on the impact approximation and the experimental results of Happer and Saloman. For densities above ${10}^{16}$ atom/${\mathrm{cm}}^{3}$ it is shown that the broadening should have the form $\overline{v}{\ensuremath{\sigma}}_{0}^{(L)}[N\ensuremath{-}\ensuremath{\beta}{N}^{2}]$, where $\overline{v}$ is the mean relative velocity of the atoms, ${\ensuremath{\sigma}}_{0}^{(L)}$ is the resonant-collision-broadening cross section for the L th multipole element of the excited-state density matrix, $N$ is the atomic density, and $\ensuremath{\beta}$ is a measure of the correlation of the atoms which represents the breakdown of the impact approximation. $\ensuremath{\beta}$ has been determined to be equal to 3.8(6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}18}$ ${\mathrm{cm}}^{3}$.

Physical Review A•Feb 1, 1974•1 citation

Resonant Collision Broadening of the (6s26p7s)P13∘ State in Lead

W. Happer, E. B. Saloman

Orientation and alignment depolarization cross sections have been measured for the $(6{s}^{2}6p7s){^{3}P_{1}}^{\ensuremath{\circ}}$ excited state of lead. The cross sections are characteristic of resonance collision broadening; ${\ensuremath{\sigma}}_{\mathrm{al}}=7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ ${\mathrm{cm}}^{2}$ for ${v}_{\mathrm{rel}}=5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ cm/sec. The ratio of orientation broadening to alignment broadening was found to be $\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}=1.21(5)$. Expressions are derived for the signal shapes in Hanle-effect, optical-double-resonance, and light-beat experiments that show which components of the signals depend on orientation and alignment relaxation times, respectively.

Physical Review•Aug 5, 1967•68 citations

Semiclassical theory of two-photon polarization-dependent fractional optical collisions: Application to the Mg−He(3s21S0→3p1P1→5s1S0, 4d1D2) optical collision

Dmitriy V. Kupriyanov, Igor M. Sokolov, A. V. Slavgorodskii +1 more

We have analyzed by perturbation theory technique two-photon polarization-dependent fractional optical collisions. In its general form the cross section of the collision is expressed as the overlap integral of its spectral profile with the spectrum of the second order correlation function of the electromagnetic field. Based on the semiclassical expansion of radial wave functions and of a retarded Green function we have expressed the spectral profile of the cross section in terms of well understood semiclassical characteristics of the process such as the rotational transformations of the transition dipole moments and the transition amplitudes describing the adiabatic or nonadiabatic dynamics of the electronic subsystem along classical trajectories. As a practical example, we have calculated the Mg-He ${(3s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}3p{}^{1}{P}_{1}\ensuremath{\rightarrow}5s{}^{1}{S}_{0},4d{}^{1}{D}_{2})$ fractional optical collision cross section. The partial wave analysis for excitation up to the $5s{}^{1}{S}_{0}$ state has shown the nonvalidity of quasistatic approximation based on successive single-photon transitions for some frequency detunings. For example, for the positive detuning from two-photon atomic resonance we have obtained the dominant contribution coming from the direct two-photon Franck-Condon transitions. Such a contribution gives the magnitude of the polarization ratio, characterizing the dependence of the cross section on mutual laser polarizations at the first and at the second steps of the photoexcitation, different than for successive single-photon Franck-Condon transitions. In the more complicated case of excitation up to the $4d{}^{1}{D}_{2}$ state of magnesium the role of the interference between different photoexcitation channels becomes important. The polarization ratio has a stable value close to $\frac{1}{7}$ in a broad spectral range in the blue wing of the second frequency detuning. There is a strong dependence of the polarization ratio in the red wing of the second detuning. Such spectral behavior can be explained by the partial selection in the red wing of the atomic resonance line, perturbed by the collisions of those Zeeman transitions in which contributions in the polarization ratio have different orders and different signs.

Physical Review A•Sep 1, 1999•2 citations

Rubidium and Cesium Excitation Transfer in Nearly Adiabatic Collisions with Inert Gases

Alan C. Gallagher

The cross sections for rubidium $5^{2}P_{\frac{1}{2}}\ensuremath{\rightleftarrows}5^{2}P_{\frac{3}{2}}$ and cesium $6^{2}P_{\frac{1}{2}}\ensuremath{\rightleftarrows}6^{2}P_{\frac{3}{2}}$ excitation transfer due to inert-gas collisions have been measured. The temperature of the collision vessel has been varied from 300\ifmmode^\circ\else\textdegree\fi{}K to 900\ifmmode^\circ\else\textdegree\fi{}K in order to partially establish the velocity dependence of these cross sections (the alkali resonance-line optical depths were always much less than 1). The various cross sections exhibit a systematic behavior that can be combined to find the general shape of a "universal" cross section that ranges across six orders of magnitude, starting just below the threshold for "sudden" collisions. The surprisingly large influence of optical line broadening on these excitation-transfer measurements has been removed as a source of error.

Physical Review•Aug 5, 1968•111 citations
Collision broadening studies have been made of optical double resonance lines in cadmium. The results indicate that the collision frequency is velocity dependent, contrary to the usual theory of resonance self-broadening. This result supports the suggestion that the broadening results from interactions involving a number of intermediate states rather than only the initial and final states of the optical transition, because of the small oscillator strength (f=0.002f=0.002f=0.002) for transitions between the {(5s)}^{2}^{1}S_{0} ground state and the excited state in question (5s5p)3P1(5s5p)^{3}P_{1}(5s5p)3P1​. The cross section in this case has a 1v‾1225\frac{1}{{{\overline{v}}_{12}}^{\frac{2}{5}}}v12​52​1​ velocity dependence, so the collision frequency varies as v‾1235{{\overline{v}}_{12}}^{\frac{3}{5}}v12​53​. Measurements show that under this assumption the self-broadening cross section for cadmium is \ensuremathσcoll=(1.9\ifmmode±\else\textpm\fi0.3)\ifmmode×\else\texttimes\fi10\ensuremath−12cm2/v‾1225,{\ensuremath{\sigma}}_{\mathrm{coll}}=(1.9\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}{\mathrm{cm}}^{2}/{{\overline{v}}_{12}}^{\frac{2}{5}},\ensuremathσcoll​=(1.9\ifmmode±\else\textpm\fi0.3)\ifmmode×\else\texttimes\fi10\ensuremath−12cm2/v12​52​, where v‾12{\overline{v}}_{12}v12​ is the average relative velocity in cm/sec. In the course of this work, the lifetime of the (5s,5p)3P1(5s, 5p)^{3}P_{1}(5s,5p)3P1​ state was redetermined and found to be (2.39\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}10\ensuremath−6{10}^{\ensuremath{-}6}10\ensuremath−6 sec.
A method is developed for calculating the cross section for line broadening in the limiting case in which important collisions may be considered to occur very rapidly with respect to the periods corresponding to the transitions in question. This method is essentially an extension of the familiar "sudden" approximation; reference is made throughout to the particular example of optical double resonance only for definiteness and because there are available experimental results for comparison with the theory. Assuming the impact model and considering the case when the energy levels in question are well resolved with respect to their width, an exact expression is found for resonant self-broadening in the usual weak rf field limit of interest in double resonance. For the case of very small oscillator strengths for the optical transition (intercombination lines), the resonant broadening becomes sufficiently small so that second-order, intermediate-state processes dominate, and approximations must be made to effect sums over intermediate states. Here the broadening is of the same sort as foreign gas broadening, and in many cases of interest, the approximations can be made in a sufficiently realistic manner to obtain useful expressions for the broadening. It is shown that the resonant cross section and this "second-order" cross section are not additive, but that the one which is larger dominates the total cross sections very strongly. Finally, we evaluate explicitly the self-broadening and foreign gas broadening (by the noble gases) of double resonance lines in the group II metals and the self-broadening in the optical spectrum of helium. In all cases our theoretical predictions are in good agreement with measurements which have been made.
A detailed calculation of the relaxation matrix of resonance atomic states by resonant collisions is carried out in the semiclassical impact theory. The validity of the different approximations is discussed. These results have been tested by observing self-broadening of level-crossing curves in high field and in zero field, in the 63P16^{3}P_{1}63P1​ state in mercury. Observation of these signals at high pressures is very difficult with a pure isotope because of strong absorption and trapping of resonance light in the vapor; it is made very easy by observing level-crossing signals of one isotope in a very low concentration in the vapor of another isotope. Collisions between the different pairs of mercury isotopes have been thus systematically studied. Results are in excellent agreement (10%) with theory, both for the absolute value of cross sections and for the ratio of orientation broadening to alignment broadening.
The Hanle effect has been used to measure the resonant pressure broadening of the (6p7s)3P10(6p7s)^{3}P_{1}^{0}(6p7s)3P10​ excited state of lead over a density range from 1014{10}^{14}1014 to 4 \ifmmode\times\else\texttimes\fi{} 1016{10}^{16}1016 atom/cm3{\mathrm{cm}}^{3}cm3. Below 1016{10}^{16}1016 atom/cm3{\mathrm{cm}}^{3}cm3 the results agree with theories based on the impact approximation and the experimental results of Happer and Saloman. For densities above 1016{10}^{16}1016 atom/cm3{\mathrm{cm}}^{3}cm3 it is shown that the broadening should have the form $\overline{v}{\ensuremath{\sigma}}_{0}^{(L)}[N\ensuremath{-}\ensuremath{\beta}{N}^{2}]$, where v‾\overline{v}v is the mean relative velocity of the atoms, ${\ensuremath{\sigma}}_{0}^{(L)}$ is the resonant-collision-broadening cross section for the L th multipole element of the excited-state density matrix, NNN is the atomic density, and $\ensuremath{\beta}$ is a measure of the correlation of the atoms which represents the breakdown of the impact approximation. $\ensuremath{\beta}$ has been determined to be equal to 3.8(6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}18}$ cm3{\mathrm{cm}}^{3}cm3.
Orientation and alignment depolarization cross sections have been measured for the $(6{s}^{2}6p7s){^{3}P_{1}}^{\ensuremath{\circ}}$ excited state of lead. The cross sections are characteristic of resonance collision broadening; ${\ensuremath{\sigma}}_{\mathrm{al}}=7.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm2{\mathrm{cm}}^{2}cm2 for ${v}_{\mathrm{rel}}=5\ifmmode\times\else\texttimes\fi{}{10}^{4}$ cm/sec. The ratio of orientation broadening to alignment broadening was found to be $\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}=1.21(5)$. Expressions are derived for the signal shapes in Hanle-effect, optical-double-resonance, and light-beat experiments that show which components of the signals depend on orientation and alignment relaxation times, respectively.
We have analyzed by perturbation theory technique two-photon polarization-dependent fractional optical collisions. In its general form the cross section of the collision is expressed as the overlap integral of its spectral profile with the spectrum of the second order correlation function of the electromagnetic field. Based on the semiclassical expansion of radial wave functions and of a retarded Green function we have expressed the spectral profile of the cross section in terms of well understood semiclassical characteristics of the process such as the rotational transformations of the transition dipole moments and the transition amplitudes describing the adiabatic or nonadiabatic dynamics of the electronic subsystem along classical trajectories. As a practical example, we have calculated the Mg-He ${(3s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}3p{}^{1}{P}_{1}\ensuremath{\rightarrow}5s{}^{1}{S}_{0},4d{}^{1}{D}_{2})$ fractional optical collision cross section. The partial wave analysis for excitation up to the 5s1S05s{}^{1}{S}_{0}5s1S0​ state has shown the nonvalidity of quasistatic approximation based on successive single-photon transitions for some frequency detunings. For example, for the positive detuning from two-photon atomic resonance we have obtained the dominant contribution coming from the direct two-photon Franck-Condon transitions. Such a contribution gives the magnitude of the polarization ratio, characterizing the dependence of the cross section on mutual laser polarizations at the first and at the second steps of the photoexcitation, different than for successive single-photon Franck-Condon transitions. In the more complicated case of excitation up to the 4d1D24d{}^{1}{D}_{2}4d1D2​ state of magnesium the role of the interference between different photoexcitation channels becomes important. The polarization ratio has a stable value close to 17\frac{1}{7}71​ in a broad spectral range in the blue wing of the second frequency detuning. There is a strong dependence of the polarization ratio in the red wing of the second detuning. Such spectral behavior can be explained by the partial selection in the red wing of the atomic resonance line, perturbed by the collisions of those Zeeman transitions in which contributions in the polarization ratio have different orders and different signs.
The cross sections for rubidium $5^{2}P_{\frac{1}{2}}\ensuremath{\rightleftarrows}5^{2}P_{\frac{3}{2}}$ and cesium $6^{2}P_{\frac{1}{2}}\ensuremath{\rightleftarrows}6^{2}P_{\frac{3}{2}}$ excitation transfer due to inert-gas collisions have been measured. The temperature of the collision vessel has been varied from 300\ifmmode^\circ\else\textdegree\fi{}K to 900\ifmmode^\circ\else\textdegree\fi{}K in order to partially establish the velocity dependence of these cross sections (the alkali resonance-line optical depths were always much less than 1). The various cross sections exhibit a systematic behavior that can be combined to find the general shape of a "universal" cross section that ranges across six orders of magnitude, starting just below the threshold for "sudden" collisions. The surprisingly large influence of optical line broadening on these excitation-transfer measurements has been removed as a source of error.