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Physical Review A

Rb and Cs broadening of the Na resonance lines

B. Kamke, W. Kamke, Kay Niemax, Alan C. Gallagher

Published Oct 1, 1983• 11 citations
Publisher

Abstract

The broadening of the Na resonance lines, due to collisions with Rb and with Cs, has been measured with the use of the normalized fluorescence-intensity method of Chatham, Lewis, and Gallagher. Several Na resonance-radiation diffusion and absorption corrections were necessary in the Rb case, due to an unavoidable excess of Na density in the Rb vapor. The line-broadening rate coefficients ${k}_{1}$ and ${k}_{2}$ for the ${D}_{1}$ and ${D}_{2}$ resonance lines are ${k}_{1}(\mathrm{Rb})=(6.2\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$, ${k}_{2}(\mathrm{Rb})=(5.5\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$, ${k}_{1}(\mathrm{Cs})=(6.9\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$, and ${k}_{2}(\mathrm{Cs})=(5.5\ifmmode\pm\else\textpm\fi{}0.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$ at $T\ensuremath{\simeq}300$\ifmmode^\circ\else\textdegree\fi{} C. The leading (${C}_{6}{R}^{\ensuremath{-}6}$) dipole-dipole long-range dispersion forces for the Na-Rb and Na-Cs interactions are calculated, and are used in the impact-theory formula to obtain theoretical line-broadening rate coefficients. These are in poor agreement with the measurements, indicating that as suggested by Vadla, the higher-order (${C}_{8}{R}^{\ensuremath{-}8}$) dispersion terms are also important at the very long range responsible for this line broadening.

DOI
10.1103/physreva.28.2254

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The broadening of the Na resonance lines, due to collisions with Rb and with Cs, has been measured with the use of the normalized fluorescence-intensity method of Chatham, Lewis, and Gallagher. Several Na resonance-radiation diffusion and absorption corrections were necessary in the Rb case, due to an unavoidable excess of Na density in the Rb vapor. The line-broadening rate coefficients k1{k}_{1}k1​ and k2{k}_{2}k2​ for the D1{D}_{1}D1​ and D2{D}_{2}D2​ resonance lines are k1(Rb)=(6.2\ifmmode±\else\textpm\fi0.4)\ifmmode×\else\texttimes\fi10\ensuremath−9{k}_{1}(\mathrm{Rb})=(6.2\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}k1​(Rb)=(6.2\ifmmode±\else\textpm\fi0.4)\ifmmode×\else\texttimes\fi10\ensuremath−9 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}s\ensuremath−1, k2(Rb)=(5.5\ifmmode±\else\textpm\fi0.6)\ifmmode×\else\texttimes\fi10\ensuremath−9{k}_{2}(\mathrm{Rb})=(5.5\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}k2​(Rb)=(5.5\ifmmode±\else\textpm\fi0.6)\ifmmode×\else\texttimes\fi10\ensuremath−9 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}s\ensuremath−1, k1(Cs)=(6.9\ifmmode±\else\textpm\fi1.0)\ifmmode×\else\texttimes\fi10\ensuremath−9{k}_{1}(\mathrm{Cs})=(6.9\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}k1​(Cs)=(6.9\ifmmode±\else\textpm\fi1.0)\ifmmode×\else\texttimes\fi10\ensuremath−9 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}s\ensuremath−1, and k2(Cs)=(5.5\ifmmode±\else\textpm\fi0.9)\ifmmode×\else\texttimes\fi10\ensuremath−9{k}_{2}(\mathrm{Cs})=(5.5\ifmmode\pm\else\textpm\fi{}0.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}k2​(Cs)=(5.5\ifmmode±\else\textpm\fi0.9)\ifmmode×\else\texttimes\fi10\ensuremath−9 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}s\ensuremath−1 at T\ensuremath≃300T\ensuremath{\simeq}300T\ensuremath≃300\ifmmode^\circ\else\textdegree\fi{} C. The leading (C6R\ensuremath−6{C}_{6}{R}^{\ensuremath{-}6}C6​R\ensuremath−6) dipole-dipole long-range dispersion forces for the Na-Rb and Na-Cs interactions are calculated, and are used in the impact-theory formula to obtain theoretical line-broadening rate coefficients. These are in poor agreement with the measurements, indicating that as suggested by Vadla, the higher-order (C8R\ensuremath−8{C}_{8}{R}^{\ensuremath{-}8}C8​R\ensuremath−8) dispersion terms are also important at the very long range responsible for this line broadening.
In addition to previous absorption measurements of Cs resonance lines, new investigations on Na, K and Rb also showed definitely that beyond symmetrical Lorentzian central parts of the lines, the stronger components of the resonance lines have blue and the weaker components red asymmetry. This behaviour can be explained by a quasistatic treatment of the self-broadening mechanism taking interatomic interaction potentials into account. But with additional data it is now possible to give a different interpretation of the origin of observed asymmetries than suggested in the previous paper on Cs resonance lines (see abstr. A5740 of 1975). The asymmetries are shown to arise from the mutual repulsion of two potential curves of the same species.
Sodium vapor, in the density range 1013{10}^{13}1013 to 5 \ifmmode\times\else\texttimes\fi{} 1014{10}^{14}1014 ${\mathrm{cm}}^{\ensuremath{-}3}$, was excited by a cw dye laser, tuned 20-150 GHz from either the D1{D}_{1}D1​ or D2{D}_{2}D2​ resonance line. We observed a three-peak scattered spectrum, consisting of the Rayleigh component at the laser frequency, and the two fluorescence components (direct and sensitized) at the atomic resonance-line frequencies. Corrections to the Rayleigh signals for anisotropy and polarization effects, and to the fluorescence signals for radiation trapping, were made in order to obtain the ratio of the sum of the total intensities of the two fluorescence components to that of the Rayleigh component. This ratio combined with a measurement of the line-wing absorption coefficient yields the sodium density and the DDD-line self-broadening rate coefficients [${k}_{\mathrm{br}}=4.67\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ cm3{\mathrm{cm}}^{3}cm3${\mathrm{s}}^{\ensuremath{-}1}$ (\ifmmode\pm\else\textpm\fi{}15%) for the D2{D}_{2}D2​ line and ${k}_{\mathrm{br}}=3.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ cm3{\mathrm{cm}}^{3}cm3${\mathrm{s}}^{\ensuremath{-}1}$ (\ifmmode\pm\else\textpm\fi{}15%) for the D1{D}_{1}D1​ line]. Asymmetry in the self-broadened line wings due to fine-structure recoupling was observed. The measured intensity ratio of the DDD lines, combined with pulsed measurements of the effective radiative decay rates in the presence of radiation trapping, yields the fine-structure collisional-mixing cross section [$\ensuremath{\sigma}(3{P}_{\frac{3}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}})=172$A˚2{\mathrm{\AA{}}}^{2}A˚2(\ifmmode\pm\else\textpm\fi{}18%)] at $T\ensuremath{\cong}300\ifmmode^\circ\else\textdegree\fi{}$ C. Our results are compared to other experiments and to theory.
By direct measurement of the contours of the line wings, the resonance broadening of the sodium DDD lines in absorption was determined for vapor pressures of sodium ranging from ${10}^{\ensuremath{-}3}$ to 70 mm Hg with negligible amount of foreign gases. Over nearly the entire range, the half-intensity width varied linearly with the density of the absorbing atoms; i.e., $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2}}}{N}=0.80\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{sec}.}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}3}$---the constant being 1.6 times that predicted by theory but much less than the corresponding experimental results for potassium. Above 5 mm pressure, $\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2}}$ increased slightly faster than NNN; moreover, the contour for the absorption coefficient was more adequately represented by an inverse cube contour than by the inverse square. Somewhat in contradiction to theory, the relative width, $\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2},8}}{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2},l}}$ was 1.12. No definite evidence of van der Waals force was observed at the higher pressures; likewise no appreciable shifts or asymmetries. The natural width measured was consistent with previous results.