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Physical Review

Resonance Broadening of the Sodium D Lines

Kenichi Watanabe

Published Jan 15, 1941• 42 citations
Publisher

Abstract

By direct measurement of the contours of the line wings, the resonance broadening of the sodium $D$ 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 $N$; 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.

DOI
10.1103/physrev.59.151

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Resonance Broadening of the Sodium D-Lines in Absorption

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The resonance broadening of the sodium D-lines in absorption was determined by measuring the contour of the line wings directly. The vapor pressures of sodium ranged from 10-3 to 75 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. Δν1/2/N = 0.78 x 10-7 sec-1cm3 --the constant being about twice that predicted by Houston, but much less than the experimental result by Hughes and LLoyd. Above 5 mm pressure, the half-intensity width appeared to increase slightly faster than N. Somewhat in contradiction to theory, the relative width, Δν1/2,s/Δν1/2,1' was 1.16. The natural width measured was, within experimental error, consistent with previous values. The inverse square contour for the absorption coefficient was satisfactory up to 5 mm Hg; beyond this pressure an inverse cube contour fitted better. No definite evidence of van der Waal force was observed at high pressures; likewise, no appreciable shifts and asymmetries. MgO windows were used and the temperature determination was made reliable.

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Self-broadening of the sodium resonance lines and excitation transfer between the 3P32 and 3P12 levels

John Huennekens, A. Gallagher

Sodium vapor, in the density range ${10}^{13}$ to 5 \ifmmode\times\else\texttimes\fi{} ${10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, was excited by a cw dye laser, tuned 20-150 GHz from either the ${D}_{1}$ or ${D}_{2}$ 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 $D$-line self-broadening rate coefficients [${k}_{\mathrm{br}}=4.67\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{cm}}^{3}$${\mathrm{s}}^{\ensuremath{-}1}$ (\ifmmode\pm\else\textpm\fi{}15%) for the ${D}_{2}$ line and ${k}_{\mathrm{br}}=3.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ ${\mathrm{cm}}^{3}$${\mathrm{s}}^{\ensuremath{-}1}$ (\ifmmode\pm\else\textpm\fi{}15%) for the ${D}_{1}$ line]. Asymmetry in the self-broadened line wings due to fine-structure recoupling was observed. The measured intensity ratio of the $D$ 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$${\mathrm{\AA{}}}^{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.

Physical Review A•Apr 1, 1983•68 citations
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{10}^{\ensuremath{-}3}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., \ensuremathΔ\ensuremathν12N=0.80\ifmmode×\else\texttimes\fi10\ensuremath−7\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2}}}{N}=0.80\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}N\ensuremathΔ\ensuremathν21​​​=0.80\ifmmode×\else\texttimes\fi10\ensuremath−7 sec.\ensuremath−1{\mathrm{sec}.}^{\ensuremath{-}1}sec.\ensuremath−1 cm\ensuremath−3{\mathrm{cm}}^{\ensuremath{-}3}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, \ensuremathΔ\ensuremathν12\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2}}\ensuremathΔ\ensuremathν21​​ 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, \ensuremathΔ\ensuremathν12,8\ensuremathΔ\ensuremathν12,l\frac{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2},8}}{\ensuremath{\Delta}{\ensuremath{\nu}}_{\frac{1}{2},l}}\ensuremathΔ\ensuremathν21​,l​\ensuremathΔ\ensuremathν21​,8​​ 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.
The resonance broadening of the sodium D-lines in absorption was determined by measuring the contour of the line wings directly. The vapor pressures of sodium ranged from 10-3 to 75 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. Δν1/2/N = 0.78 x 10-7 sec-1cm3 --the constant being about twice that predicted by Houston, but much less than the experimental result by Hughes and LLoyd. Above 5 mm pressure, the half-intensity width appeared to increase slightly faster than N. Somewhat in contradiction to theory, the relative width, Δν1/2,s/Δν1/2,1' was 1.16. The natural width measured was, within experimental error, consistent with previous values. The inverse square contour for the absorption coefficient was satisfactory up to 5 mm Hg; beyond this pressure an inverse cube contour fitted better. No definite evidence of van der Waal force was observed at high pressures; likewise, no appreciable shifts and asymmetries. MgO windows were used and the temperature determination was made reliable.
The broadening of the resonance lines of rubidium in absorption under pressures up to 150 mm of its own homogeneous vapor was studied by means of a 21-foot grating. Under pressures below 1 mm the broadening of the lines was very symmetrical and the line contours could be described by the dispersion formula, but when the pressure was high the lines exhibited asymmetrical broadening of van der Waals type. The 2P12^{2}P_{\frac{1}{2}}2P21​​ component showed red, while the 2P32^{2}P_{\frac{3}{2}}2P23​​ component showed violet asymmetry. Both lines showed the proportionality of the width with NNN, the concentration of Rb atoms. The experimental width at half-maximum is greater than that predicted by Houston's theory by a factor of 1.5 and the width of the transition from 3P32^{3}P_{\frac{3}{2}}3P23​​ is greater than that from 3P12^{3}P_{\frac{1}{2}}3P21​​ by a factor of 1.6. A narrow diffuse band was observed near the shorter wave-length side of the 2P12^{2}P_{\frac{1}{2}}2P21​​ component and a similar one near the longer wave-length side of the 2P32^{2}P_{\frac{3}{2}}2P23​​ component.
The resonance broadening of homogeneous Cs vapor in absorption was studied by means of the contour method. The intensities were obtained via the method of "astigmatic photometry" by utilizing the astigmatism of the Rowland grating. The pressure of the homogeneous absorbing vapor ranged from ${10}^{\ensuremath{-}2}$ to 17.5 mm Hg. The half breadth $\ensuremath{\gamma}$ varied rather linearly with the number of atoms per unit volume, with $(\frac{{\ensuremath{\gamma}}_{1}}{N})\ifmmode\times\else\texttimes\fi{}{10}^{7}=1.45$, $(\frac{{\ensuremath{\gamma}}_{2}}{N})\ifmmode\times\else\texttimes\fi{}{10}^{7}$ for the 2P32^{2}P_{\frac{3}{2}}2P23​​ and 2P12^{2}P_{\frac{1}{2}}2P21​​ eomponents of the resonance lines, respectively. The average value of the ratio of half breadths $\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}$ was found to be 1.8. The experimental half-width $\ensuremath{\gamma}$ is found to be about 1\textonehalf{} times larger than that predicted by W. V. Houston. Below pressures of 10 mm Hg the lines exhibited symmetrical broadening according to the "dispersion" formula. At higher pressures indications of a violet and red asymmetry are present for the 2P32^{2}P_{\frac{3}{2}}2P23​​ and 2P12^{2}P_{\frac{1}{2}}2P21​​ components, respectively. A definite band on the red side of the 2P32^{2}P_{\frac{3}{2}}2P23​​ and one on the violet side of the 2P12^{2}P_{\frac{1}{2}}2P21​​ was observed.
Spectrograms of the DDD lines of sodium in absorption were obtained and measured on a densitometer, thus determining an optical constant which was uncertain in former work. Absolute contours in terms of transmitted intensity against wave-length were obtained. Possible sources of error were studied in detail. The observed contours were compared with the classical formula. The contours were found to have the theoretical inverse square variation of opacity with wave-length distance from resonance; they showed the theoretical variation of width with the square root of the number of atoms in the line of sight, and the 2:1 ratio between the two DDD lines. The width of the lines was, however, about five times that which classical radiation damping accounts for. A detailed further experimental study of this discrepancy is planned.
We studied the line shape of Rb D1{D}_{1}D1​ and D2{D}_{2}D2​ resonance lines in the presence of 1--10 amg of several gases: 3{}^{3}3He, 4{}^{4}4He, N2{}_{2}2​, and Xe. We found that the line cores are well described by the asymmetric line shape expected for a van der Waals interatomic potential. The width and shift of the lines is proportional to the density of the foreign gas with high degree of accuracy, while the asymmetry is independent of the density. The constants of proportionality for pressure broadening and shift were measured with much higher accuracy than in previous experiments. We also studied the density dependence of the oscillator strength of the transitions.
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.