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Physical Review A

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

John Huennekens, A. Gallagher

Published Apr 1, 1983• 68 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.27.1851

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Physical Review•Jan 15, 1941•42 citations
Sodium vapor, in the density range 1013{10}^{13}1013 to 5 \ifmmode\times\else\texttimes\fi{} 1014{10}^{14}1014 cm\ensuremath−3{\mathrm{cm}}^{\ensuremath{-}3}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 [kbr=4.67\ifmmode×\else\texttimes\fi10\ensuremath−7{k}_{\mathrm{br}}=4.67\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}kbr​=4.67\ifmmode×\else\texttimes\fi10\ensuremath−7 {\mathrm{cm}}^{3}$${\mathrm{s}}^{\ensuremath{-}1} (\ifmmode\pm\else\textpm\fi{}15%) for the D2{D}_{2}D2​ line and kbr=3.07\ifmmode×\else\texttimes\fi10\ensuremath−7{k}_{\mathrm{br}}=3.07\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}kbr​=3.07\ifmmode×\else\texttimes\fi10\ensuremath−7 {\mathrm{cm}}^{3}$${\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$${\mathrm{\AA{}}}^{2}(\ifmmode\pm\else\textpm\fi{}18%)] at T\ensuremath≅300\ifmmode∘\else\textdegree\fiT\ensuremath{\cong}300\ifmmode^\circ\else\textdegree\fi{}T\ensuremath≅300\ifmmode∘\else\textdegree\fi C. Our results are compared to other experiments and to theory.
The dencity of sodium was determined from measurement of optical absorption of the resonance line. Sodium vapour, in the dencity 3×10~(11) to 1.2×10~(12)cm~(-3), was excited by a cw dye laser, tuned 70 GHz from D_2 resonance line. We recorded signal intensities, consisting of The Rayleigh component at the laser frequency and the two fluorescence components (direct and sensitized) at the atomic resonance-line frequencies. D_2 line self-broadening rate coefficient [k_(br,2)=5.44×10~(-7)cm~3/s(±15%)] was yielded. Combined with the effective radiative decay rates in the presence of radiation trapping, we measured excitation-transfer rates in different dencities, for the excitation transfer process Na(3P_(3/2))+Na(3S) Na (3P_(1/2))+Na(3S). The fine-structure collisional-mining cross section [σ_(21)(3P_(3/2)→3P_(1/2))=19.9nm~2(±29%)3 at T 184℃ was obtained. Our results were compared to other experiments and to theory.
We have measured the time-dependent fluorescence of the sodium DDD lines following pulsed excitation of one DDD line, in the presence of radiation trapping with optical depths k0L{k}_{0}Lk0​L of \ensuremath{\sim}10 to 2000. When collisional coupling of the 3P123{P}_{\frac{1}{2}}3P21​​ and 3P323{P}_{\frac{3}{2}}3P23​​ levels and different radiative-escape probabilities for each DDD line are taken into account, we obtain excellent agreement with Holstein's theory for the effective radiative decay rates in the Doppler region (${k}_{0}L\ensuremath{\sim}10\ensuremath{-}300$) and in the redistributed Lorentzian region (k0L>1000{k}_{0}L>1000k0​L>1000). For k0L{k}_{0}Lk0​L between these two regions, we observe an abrupt transition between the two limiting formulas. The buildup rate of the sensitized fluorescence signal also yields a $3{P}_{\frac{3}{2}}\ensuremath{\rightarrow}3{P}_{\frac{1}{2}}$ excitation transfer cross section in agreement with our previously reported cw measurement. Additionally, we have measured the dependence of the 3P3P3P fluorescence on laser power and beam diameter, and we explain the observed approach to saturation. We suggest that the previously reported "anomalous" approaches to saturation may be explained in terms of the laser beam burning through the optically thick vapor. Laser-beam spatial intensity variations and self-focusing also contribute to fluorescence signals that deviate from the usual single-atom saturation behavior.
The intensity ratio D2/D1 for the sodium doublet has been measured for radiation from excited sodium atoms which result from the optical dissociation of sodium iodide vapor by ultraviolet light in the 2082→2500 A region. With shorter wavelength ultraviolet light as exciting source, the D2/D1 ratio is 0.98 and increases to above 1.5 with longer exciting wavelengths. Addition of foreign gases cause the observed D2/D1 ratio to increase to 1.89 for large foreign gas pressure. Cross sections for the transfer of excited sodium atoms from the 32P32 to the 32P½ state and vice versa due to collisions with foreign molecules have been measured as they depend on the relative velocity between excited sodium atom and foreign molecule. The Doppler broadening of the separate D lines emitted in the atomic fluorescence of sodium iodide has been estimated from absorption measurements. Both lines show equal broadening within the experimental error of the observations. Measurements were made with a photomultiplier tube. The sodium doublet was resolved with a reflection grating monochromator.
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 ${k}_{1}(\mathrm{Rb})=(6.2\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\ensuremath{-}1}$, ${k}_{2}(\mathrm{Rb})=(5.5\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\ensuremath{-}1}$, ${k}_{1}(\mathrm{Cs})=(6.9\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\ensuremath{-}1}$, and ${k}_{2}(\mathrm{Cs})=(5.5\ifmmode\pm\else\textpm\fi{}0.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\ensuremath{-}1}$ 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.
We have used the resonance radiation pressure from 40 mW of cw dye laser light propagating axially down a tube filled with sodium vapor to increase the sodium pressure (density) up to 50% over a length of 20 cm. The magnitude of the effect agrees well with measurements of the absorbed power. These observations were made with the laser tuned to the low-frequency side of the sodium D2 resonance line; for tuning to the high-frequency side, an additional unexplained effect leading to density decreases was observed.
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.