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Physical Review

Pressure Effects of Homogeneous Rubidium Vapor on Its Resonance Lines

Shang-Yi Ch'en

Published Nov 15, 1940• 40 citations
Publisher

Abstract

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 $^{2}P_{\frac{1}{2}}$ component showed red, while the $^{2}P_{\frac{3}{2}}$ component showed violet asymmetry. Both lines showed the proportionality of the width with $N$, 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 $^{3}P_{\frac{3}{2}}$ is greater than that from $^{3}P_{\frac{1}{2}}$ by a factor of 1.6. A narrow diffuse band was observed near the shorter wave-length side of the $^{2}P_{\frac{1}{2}}$ component and a similar one near the longer wave-length side of the $^{2}P_{\frac{3}{2}}$ component.

DOI
10.1103/physrev.58.884

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Physical Review A•Dec 1, 1997•208 citations
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.
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.
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 displacement, asymmetry, and broadening of the second doublet of the rubidium principal series perturbed by pure helium, neon and argon up to 13 atmospheres are observed. The displacement as well as the broadening of the doublet components are not the same. The 2P12^{2}P_{\frac{1}{2}}2P21​​ component shifts and broadens more conspicuously than the 2P112^{2}P_{1\frac{1}{2}}2P121​​ component (an exception being the broadening by argon). The departure from linear relationship between the shift and the density of the perturbing gas is quite manifest. Both for helium and for neon the line contour shows a distinct asymmetry towards the violet, while for argon the line contour shows a very strong red asymmetry. For helium and neon the violet asymmetries of the 2P12^{2}P_{\frac{1}{2}}2P21​​ component are stronger than that of the 2P112^{2}P_{1\frac{1}{2}}2P121​​ component; the reverse is true for argon. The relationship between the half-width and the relative density is linear for foreign gas concentrations of relative densities up to 8 so far applied.
In the presence of heavy foreign gases, such as Kr and Xe, diffused absorption bands were observed at both the short wavelength and the long wavelength side of the first four absorption doublets of the Rb principal series. The red bands were observable when the Rb vapor pressure in the absorption tube was relatively low (10−3 to 10−2 mm Hg). The violet bands were not intense enough until the Rb vapor pressure was increased to 0.1–1 mm Hg. With other lighter gases (H2, He, Ne, A, N2) only violet bands were observed. The positions and the absorption contours of the bands in relation to the member of the absorption series and to the nature of the foreign gases are discussed.
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.