Physical Review A

Diffusion and excitation transfer of excited alkali-metal atoms

Moncef Bouledroua, A. Dalgarno, Robin Côté

Published Dec 5, 2001• 11 citations

Abstract

We report calculations of diffusion, excitation transfer, width, and shift cross sections. We use these cross sections to obtain the diffusion coefficient and the width and line shift due to collisions of alkali-metal atoms in the impact approximation. The results are compared to analytical expressions obtained from semiclassical treatments, and with measured widths for sodium atoms. Extension to other alkali metal atoms is also given.

DOI: 10.1103/physreva.65.012701

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Broadening and Shifting of the Alkali-Metal Resonance Lines by Collisions of Like Monatoms

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Physical Review A

Diffusion and excitation transfer of excited alkali-metal atoms

Moncef Bouledroua, A. Dalgarno, Robin Côté

Published Dec 5, 2001• 11 citations

Publisher

Abstract

DOI: 10.1103/physreva.65.012701

Related papers

Broadening and Shifting of the Alkali-Metal Resonance Lines by Collisions of Like Monatoms

Moncef Bouledroua, A. Dalgarno, E Robin

The purpose of this work is the evaluation of the linewidth w and lineshift d of the sodium resonance line 3p − → 3s when the excited atoms are evolving in their parent gas. Assuming the Baranger impact approximation, these two quantities are given in terms of the phase shifts of the ground Na(3s) + Na(3s) and the excited Na(3p)+Na(3s) states. The quantal calculations and the semi-classical method, developed by Mott and Massey and Landau and Lifshitz, show that the cross sections σ and λ vary with the energy like E−1/2, the width w and the shift d do not depend on the temperature, the long-range interactions have a big influence on w and d, and the rate coefficients depend on the dispersion coefficients like w/n ≈ +7.298 × 10−8C3(Σ) and d/n ≈ +8.893 × 10−9C3(Σ). The study also shows that the sodium results can be extended to the other alkali-metal atoms (Li, K, Rb, Cs, and Fr) by a simple scaling. Keywords: potential energy curve, broadening cross section, rate coefficient, linewidth, lineshift, dispersion coefficientThe purpose of this work is the evaluation of the linewidth w and lineshift d of the sodium resonance line 3p − → 3s when the excited atoms are evolving in their parent gas. Assuming the Baranger impact approximation, these two quantities are given in terms of the phase shifts of the ground Na(3s) + Na(3s) and the excited Na(3p)+Na(3s) states. The quantal calculations and the semi-classical method, developed by Mott and Massey and Landau and Lifshitz, show that the cross sections σ and λ vary with the energy like E−1/2, the width w and the shift d do not depend on the temperature, the long-range interactions have a big influence on w and d, and the rate coefficients depend on the dispersion coefficients like w/n ≈ +7.298 × 10−8C3(Σ) and d/n ≈ +8.893 × 10−9C3(Σ). The study also shows that the sodium results can be extended to the other alkali-metal atoms (Li, K, Rb, Cs, and Fr) by a simple scaling. Keywords: potential energy curve, broadening cross section, rate coefficient, linewidth, lineshift, dispersion coefficient

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Cross sections for energy transfer in collisions between two excited sodium atoms

John Huennekens, Alan Gallagher

We have measured cross sections, ${\ensuremath{\sigma}}_{\mathrm{nL}}$, for the excitation transfer process $\mathrm{Na}(3P)+\mathrm{Na}(3P)\ensuremath{\rightarrow}\mathrm{Na}(3S)+\mathrm{Na}(\mathrm{nL})$, where $\mathrm{nL}$ is the $4D$ or $5S$ level. Our results are ${\ensuremath{\sigma}}_{4D}=23 {\AA{}}^{2}\ifmmode\pm\else\textpm\fi{}35%$ and ${\ensuremath{\sigma}}_{5S}=16 {\AA{}}^{2}\ifmmode\pm\else\textpm\fi{}35%$ at $T\ensuremath{\sim}600$ K. To obtain these cross sections we have used pulsed excitation and measured the intensities of $4D$ , $5S$ , and $3P$ fluorescence emissions, and the spatial distribution of excited atoms resulting from radiation diffusion, as well as the excited atom density as a function of time. Additionally, we have accounted for (time-dependent) radiation trapping of $3P$ and $\mathrm{nL}$ level radiation and for the resulting anisotropies of these fluorescence emissions. Comparisons of our results with theory have been made, and their relevance to other experiments is discussed.We have measured cross sections, ${\ensuremath{\sigma}}_{\mathrm{nL}}$, for the excitation transfer process $\mathrm{Na}(3P)+\mathrm{Na}(3P)\ensuremath{\rightarrow}\mathrm{Na}(3S)+\mathrm{Na}(\mathrm{nL})$, where $\mathrm{nL}$ is the $4D$ or $5S$ level. Our results are ${\ensuremath{\sigma}}_{4D}=23 {\AA{}}^{2}\ifmmode\pm\else\textpm\fi{}35%$ and ${\ensuremath{\sigma}}_{5S}=16 {\AA{}}^{2}\ifmmode\pm\else\textpm\fi{}35%$ at $T\ensuremath{\sim}600$ K. To obtain these cross sections we have used pulsed excitation and measured the intensities of $4D$, $5S$, and $3P$ fluorescence emissions, and the spatial distribution of excited atoms resulting from radiation diffusion, as well as the excited atom density as a function of time. Additionally, we have accounted for (time-dependent) radiation trapping of $3P$ and $\mathrm{nL}$ level radiation and for the resulting anisotropies of these fluorescence emissions. Comparisons of our results with theory have been made, and their relevance to other experiments is discussed.

Physical Review AFeb 1, 198374 citations

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John M. Pitre, L. Krause

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Владимир Сергеевич Лебедев, V. S. Marchenko

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Journal of Physics B Atomic and Molecular PhysicsNov 28, 198724 citations

Inelastic Collisions of Slow Atoms

J. Callaway, Ernest Bauer

A general approximate method for computing the cross sections for certain inelastic collision processes is developed. It is based on the possibility of obtaining, with the use of the impact-parameter method, an exact expression for the transition amplitude in a special case. The dependence of the cross section on the parameters of coupling constant, velocity, and energy difference between states is discussed for a two-level model. Detailed calculations are made of cross section for collisions of the type $A(^{2}P_{\frac{3}{2}})+B\ensuremath{\rightleftharpoons}A(^{2}P_{\frac{1}{2}})+B$, where $A$ is an excited atom of an alkali metal and $B$ is an atom of a noble gas. An Appendix contains a review of the effective long-range interaction of atoms.A general approximate method for computing the cross sections for certain inelastic collision processes is developed. It is based on the possibility of obtaining, with the use of the impact-parameter method, an exact expression for the transition amplitude in a special case. The dependence of the cross section on the parameters of coupling constant, velocity, and energy difference between states is discussed for a two-level model. Detailed calculations are made of cross section for collisions of the type $A(^{2}P_{\frac{3}{2}})+B\ensuremath{\rightleftharpoons}A(^{2}P_{\frac{1}{2}})+B$, where $A$ is an excited atom of an alkali metal and $B$ is an atom of a noble gas. An Appendix contains a review of the effective long-range interaction of atoms.

Physical ReviewNov 15, 1965134 citations

Collision-Induced Mixing in the First Excited States of Sodium and Potassium

J. A. Jordan, P. A. Franken

The cross sections for the collision-induced transfer of excitation from the $^{2}P_{\frac{3}{2}}$ level to the $^{2}P_{\frac{1}{2}}$ level of the first excited states of the alkali atoms have been measured for several alkali-noble gas systems. The cross sections were determined with a conventional resonance fluorescence technique in which the radiation from a spectral source was absorbed and re-emitted by an alkali vapor at low pressure (\ensuremath{\sim}${10}^{\ensuremath{-}6}$ Torr), and the scattered light analyzed with a scanning spectrometer. Provision was made for the introduction of various noble gases at controlled pressures into the alkali vapor. The determined cross sections are (in units of ${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ ): Na-He, 41.1\ifmmode\pm\else\textpm\fi{}2.9; Na-Ne, 36.1\ifmmode\pm\else\textpm\fi{}2.5; Na-Ar, 64.6\ifmmode\pm\else\textpm\fi{}5.2; Na-Kr, 68.2\ifmmode\pm\else\textpm\fi{}5.5; Na-Xe, 61.8\ifmmode\pm\else\textpm\fi{}4.9; K-He, 52.8\ifmmode\pm\else\textpm\fi{}5.8; K-Ne, 14.0\ifmmode\pm\else\textpm\fi{}1.2; K-Ar, 34.0\ifmmode\pm\else\textpm\fi{}3.1. The quoted errors are estimated 70% confidence intervals. The measurements are compared with other experimental results and with various estimated cross sections.The cross sections for the collision-induced transfer of excitation from the $^{2}P_{\frac{3}{2}}$ level to the $^{2}P_{\frac{1}{2}}$ level of the first excited states of the alkali atoms have been measured for several alkali-noble gas systems. The cross sections were determined with a conventional resonance fluorescence technique in which the radiation from a spectral source was absorbed and re-emitted by an alkali vapor at low pressure (\ensuremath{\sim}${10}^{\ensuremath{-}6}$ Torr), and the scattered light analyzed with a scanning spectrometer. Provision was made for the introduction of various noble gases at controlled pressures into the alkali vapor. The determined cross sections are (in units of ${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$): Na-He, 41.1\ifmmode\pm\else\textpm\fi{}2.9; Na-Ne, 36.1\ifmmode\pm\else\textpm\fi{}2.5; Na-Ar, 64.6\ifmmode\pm\else\textpm\fi{}5.2; Na-Kr, 68.2\ifmmode\pm\else\textpm\fi{}5.5; Na-Xe, 61.8\ifmmode\pm\else\textpm\fi{}4.9; K-He, 52.8\ifmmode\pm\else\textpm\fi{}5.8; K-Ne, 14.0\ifmmode\pm\else\textpm\fi{}1.2; K-Ar, 34.0\ifmmode\pm\else\textpm\fi{}3.1. The quoted errors are estimated 70% confidence intervals. The measurements are compared with other experimental results and with various estimated cross sections.

Physical ReviewFeb 4, 196639 citations

\mathrm{nL}

is the

4D

5S

level. Our results are ${\ensuremath{\sigma}}_{4D}=23 {\AA{}}^{2}\ifmmode\pm\else\textpm\fi{}35%$ and ${\ensuremath{\sigma}}_{5S}=16 {\AA{}}^{2}\ifmmode\pm\else\textpm\fi{}35%$ at $T\ensuremath{\sim}600$ K. To obtain these cross sections we have used pulsed excitation and measured the intensities of

4D

5S

, and

3P

fluorescence emissions, and the spatial distribution of excited atoms resulting from radiation diffusion, as well as the excited atom density as a function of time. Additionally, we have accounted for (time-dependent) radiation trapping of

3P

and

\mathrm{nL}

level radiation and for the resulting anisotropies of these fluorescence emissions. Comparisons of our results with theory have been made, and their relevance to other experiments is discussed.

A

is an excited atom of an alkali metal and

B

is an atom of a noble gas. An Appendix contains a review of the effective long-range interaction of atoms.

The cross sections for the collision-induced transfer of excitation from the

^{2}P_{\frac{3}{2}}

level to the

^{2}P_{\frac{1}{2}}

level of the first excited states of the alkali atoms have been measured for several alkali-noble gas systems. The cross sections were determined with a conventional resonance fluorescence technique in which the radiation from a spectral source was absorbed and re-emitted by an alkali vapor at low pressure (\ensuremath{\sim}${10}^{\ensuremath{-}6}$ Torr), and the scattered light analyzed with a scanning spectrometer. Provision was made for the introduction of various noble gases at controlled pressures into the alkali vapor. The determined cross sections are (in units of ${10}^{\ensuremath{-}16}$

{\mathrm{cm}}^{2}

): Na-He, 41.1\ifmmode\pm\else\textpm\fi{}2.9; Na-Ne, 36.1\ifmmode\pm\else\textpm\fi{}2.5; Na-Ar, 64.6\ifmmode\pm\else\textpm\fi{}5.2; Na-Kr, 68.2\ifmmode\pm\else\textpm\fi{}5.5; Na-Xe, 61.8\ifmmode\pm\else\textpm\fi{}4.9; K-He, 52.8\ifmmode\pm\else\textpm\fi{}5.8; K-Ne, 14.0\ifmmode\pm\else\textpm\fi{}1.2; K-Ar, 34.0\ifmmode\pm\else\textpm\fi{}3.1. The quoted errors are estimated 70% confidence intervals. The measurements are compared with other experimental results and with various estimated cross sections.