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Determination of Oscillator Strengths by Direct Measurement of the Line Widths of a Source of Finite Optical Density

L. M. Biberman

Published Jan 1, 1962• 0 citations
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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.

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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 ${\mathrm{cm}}^{\ensuremath{-}3}$. 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{} ${10}^{\ensuremath{-}7}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{sec}}^{\ensuremath{-}1}$ are obtained for 8521 and 8944 \AA{} lines. Here $\ensuremath{\gamma}$ is the collisional (or Lorentzian) half-width and fff 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=5.9L=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.
The connection between dephasing of optical coherence and the measured spectral density of the pure solvent is made through measurements and calculations of photon echo signals. 2-pulse photon echo measurements of a cyanine dye in polar solvents are presented. Signals are recorded for both phase matched directions enabling accurate determination of the echo signal time shift. Echo signals are calculated by two approaches that employ the response function description of nonlinear spectroscopy; (i) a single Brownian oscillator line shape model, and (ii) the line shape obtained using the solvent spectral density. The strongly overdamped Brownian oscillator model incorporates only a single adjustable parameter while the experimental data present two fitting constraints. The second model incorporates the measured solvent spectral density. Both give very good agreement with the experimental results. The significance of the second method lies in this being a new approach to calculate nonlinear spectroscopic signals, for comparison with experimental data, that uses directly the measured spectrum of equilibrium fluctuations of the solvent. This approach also provides a better conceptual perspective for deriving insight into the nature of the solute–solvent coupling mechanism. Comparing the parameters for the strength of interaction in a variety of polar solvents it is found that the coupling involves the solvent polarizability and not the solvent polarity. The interaction mechanism cannot be deduced from the Brownian oscillator calculations.