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Physical Review

Self-Broadening of Cesium Resonance Lines at 8521 and 8944 Å

C. L. Chen, A. V. Phelps

Published Sep 5, 1968• 55 citations
Publisher

Abstract

Absorption profiles of cesium resonance lines at 8521 and 8944 \AA{} have been measured for the wavelength range from 0.5 to 30 \AA{} from the line centers using a tungsten ribbon light source, cell lengths $L$ from 0.31 to 6.1 cm, and Cs densities $N$ from 2 \ifmmode\times\else\texttimes\fi{} ${10}^{14}$ to 2 \ifmmode\times\else\texttimes\fi{} ${10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The wavelength dependence of the absorption coefficients are consistent with a Lorentzian form and values of $\frac{\ensuremath{\gamma}f}{N}=1.08\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ and 0.30 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}7}$ ${\mathrm{cm}}^{3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ are obtained for 8521 and 8944 \AA{} lines. Here $\ensuremath{\gamma}$ is the collisional (or Lorentzian) half-width and $f$ is the oscillator strength. The values of $\frac{\ensuremath{\gamma}f}{N}$ deduced from total fractional absorption data agree with those determined from the line profiles. Our results agree well (to within 15%) with those of Gregory and with theory, but disagree with more recent data. A source of error in some previous determinations of half-widths is the fact that even when the calculated absorption is very large, the measured transmission at the line center is significant; about 3.5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ compared to \ensuremath{\sim} ${10}^{\ensuremath{-}100,000}$ predicted from our measurements in the wings of the lines for $N=1.14\ifmmode\times\else\texttimes\fi{}{10}^{15}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ and $L=5.9$ cm. This effect is shown to result from transmission through the monochromator at wavelengths in the far wings of the instrument function.

DOI
10.1103/physrev.173.62

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arXiv:0706.0837•Physical Review A•Jul 31, 2007•60 citations
Absorption profiles of cesium resonance lines at 8521 and 8944 \AA{} have been measured for the wavelength range from 0.5 to 30 \AA{} from the line centers using a tungsten ribbon light source, cell lengths LLL from 0.31 to 6.1 cm, and Cs densities NNN from 2 \ifmmode\times\else\texttimes\fi{} 1014{10}^{14}1014 to 2 \ifmmode\times\else\texttimes\fi{} 1016{10}^{16}1016 cm\ensuremath−3{\mathrm{cm}}^{\ensuremath{-}3}cm\ensuremath−3. The wavelength dependence of the absorption coefficients are consistent with a Lorentzian form and values of \ensuremathγfN=1.08\ifmmode×\else\texttimes\fi10\ensuremath−7\frac{\ensuremath{\gamma}f}{N}=1.08\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}N\ensuremathγf​=1.08\ifmmode×\else\texttimes\fi10\ensuremath−7 and 0.30 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−7{10}^{\ensuremath{-}7}10\ensuremath−7 cm3{\mathrm{cm}}^{3}cm3 sec\ensuremath−1{\mathrm{sec}}^{\ensuremath{-}1}sec\ensuremath−1 are obtained for 8521 and 8944 \AA{} lines. Here \ensuremathγ\ensuremath{\gamma}\ensuremathγ is the collisional (or Lorentzian) half-width and fff is the oscillator strength. The values of \ensuremathγfN\frac{\ensuremath{\gamma}f}{N}N\ensuremathγf​ deduced from total fractional absorption data agree with those determined from the line profiles. Our results agree well (to within 15%) with those of Gregory and with theory, but disagree with more recent data. A source of error in some previous determinations of half-widths is the fact that even when the calculated absorption is very large, the measured transmission at the line center is significant; about 3.5 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−2{10}^{\ensuremath{-}2}10\ensuremath−2 compared to \ensuremath{\sim} 10\ensuremath−100,000{10}^{\ensuremath{-}100,000}10\ensuremath−100,000 predicted from our measurements in the wings of the lines for N=1.14\ifmmode×\else\texttimes\fi1015N=1.14\ifmmode\times\else\texttimes\fi{}{10}^{15}N=1.14\ifmmode×\else\texttimes\fi1015 cm\ensuremath−3{\mathrm{cm}}^{\ensuremath{-}3}cm\ensuremath−3 and L=5.9L=5.9L=5.9 cm. This effect is shown to result from transmission through the monochromator at wavelengths in the far wings of the instrument function.
16 lines of the principal series of Cs(6 2 s 1/2 to 7-16 2 p 3/2 and 6 2 s 1/2 to 7-12 2 p 1/2 ) were investigated in absorption. Cesium vapour density was varied from 10 13 up to 10 17 cm -3 . Red asymmetries of all lines (extended red wings) were detected. This can be understood if electron transitions in the long-range interaction region follow the selection rules of molecules. It was established that the red and the blue wings of the lines each can be fitted to lorentzian profiles in small wavelength intervals. With the help of quasistatic theory the interaction constants from the long-range interaction potential Delta omega =C 3 /r 3 multiplied by the oscillator strength were determined from measurements. For all lines the ratio of C 3 (red)/C 3 (blue) was found to equal 2 in accordance with earlier theoretical calculations. In the far line wing, deviation from a lorentzian profile occurs. This was interpreted as a consequence of electron transition in the short-range region of interatomic potentials.
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.
Self-broadening of the 146.96 nm xenon line and 123.58 nm krypton line is studied in the density range 1-100 amagat (2.7 x 1019 — 2.7 × 1021 at. cm-3). The absorption profile is deduced from reflection experiments by a modified Kramers-Krönig analysis. A detailed discussion of the criteria for validity of available theories is given, allowing the determination of the extent to which the cases studied are related to many-body interactions and/or pure resonance forces. The quasistatic theory, in the nearest neighbour approximation, is shown to be valid for interpreting the far wings. Thus it is possible at increasing density, to underline the specific effect of the various kinds of forces : resonance, Van der Waals and repulsive, and to specify the 1u excited state potential which is found weakly attractive for Xe2 and Kr2.
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Saturation effects affecting absorption and fluorescence spectra of an atomic vapor confined in an extremely thin cell (cell thickness $L<1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$) are investigated experimentally and theoretically. The study is performed on the D2{D}_{2}D2​ line $(\ensuremath{\lambda}=852\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ of Cs and concentrates on the two situations $L=\ensuremath{\lambda}∕2$ and $L=\ensuremath{\lambda}$, the most contrasted ones with respect to the length dependence of the coherent Dicke narrowing. For $L=\ensuremath{\lambda}∕2$, the Dicke-narrowed absorption profile simply broadens and saturates in amplitude when increasing the light intensity, while for $L=\ensuremath{\lambda}$, sub-Doppler dips of reduced absorption at the line-center appear on the broad absorption profile. For a fluorescence detection at $L=\ensuremath{\lambda}$, saturation induces narrow dips, but only for hyperfine components undergoing a population loss through optical pumping. These experimental results are interpreted with the help of the various existing models and are compared with numerical calculations based upon a two-level modeling that considers both a closed and an open system.