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Physical Review

Resonance Broadening of Caesium

Chris Gregory

Published Apr 1, 1942• 45 citations
Publisher

Abstract

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 $^{2}P_{\frac{3}{2}}$ and $^{2}P_{\frac{1}{2}}$ 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 $^{2}P_{\frac{3}{2}}$ and $^{2}P_{\frac{1}{2}}$ components, respectively. A definite band on the red side of the $^{2}P_{\frac{3}{2}}$ and one on the violet side of the $^{2}P_{\frac{1}{2}}$ was observed.

DOI
10.1103/physrev.61.465

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Pressure Effects of Homogeneous Rubidium Vapor on Its Resonance Lines

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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.

Physical Review•Nov 15, 1940•40 citations

Resonance Broadening of the Sodium D Lines

Kenichi Watanabe

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.

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Resonance Broadening of the Sodium D-Lines in Absorption

Kenichi Watanabe

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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Rb and Cs broadening of the Na resonance lines

B. Kamke, W. Kamke, Kay Niemax +1 more

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 ${k}_{1}$ and ${k}_{2}$ for the ${D}_{1}$ and ${D}_{2}$ resonance lines are ${k}_{1}(\mathrm{Rb})=(6.2\ifmmode\pm\else\textpm\fi{}0.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$, ${k}_{2}(\mathrm{Rb})=(5.5\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$, ${k}_{1}(\mathrm{Cs})=(6.9\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$, and ${k}_{2}(\mathrm{Cs})=(5.5\ifmmode\pm\else\textpm\fi{}0.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$ 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.

Physical Review A•Oct 1, 1983•11 citations

SELECTIVE REFLECTION FROM THE VAPORS OF THE ALKALI METALS

A. C. Lauriston, H. L. Welsh

Selective reflection from sodium, potassium, rubidium, and caesium vapors in the neighborhood of the resonance lines was observed for vapor pressures between 10 mm. and 1 atm., using a steel tube with a window of transparent magnesium oxide. Reflecting power as a function of frequency was measured by using incident light of continuous spectral distribution. The reflection contour for pressures up to ½ atm. is in good agreement with the theory of reflection from an absorbing medium. For each line the damping constant in the dispersion equations varies as the square root of the number of atoms per cubic centimeter, as was found previously for mercury and cadmium. For the two members of the resonance doublet the damping constants are proportional to the square roots of the oscillator strengths. In a region about 5 cm.−1 wide about each resonance frequency the reflected intensity measured experimentally is greater than that calculated. These lines of residual intensity may be due to a second kind of selective reflection. At pressures above ½ atm. the observed reflection contour cannot be explained by the simple anomalous dispersion theory.

Canadian Journal of Physics•May 1, 1951•20 citations

New aspects in the self-broadening of alkali resonance lines

Kay Niemax, Goran Pichler

In addition to previous absorption measurements of Cs resonance lines, new investigations on Na, K and Rb also showed definitely that beyond symmetrical Lorentzian central parts of the lines, the stronger components of the resonance lines have blue and the weaker components red asymmetry. This behaviour can be explained by a quasistatic treatment of the self-broadening mechanism taking interatomic interaction potentials into account. But with additional data it is now possible to give a different interpretation of the origin of observed asymmetries than suggested in the previous paper on Cs resonance lines (see abstr. A5740 of 1975). The asymmetries are shown to arise from the mutual repulsion of two potential curves of the same species.

Journal of Physics B Atomic and Molecular Physics•Feb 1, 1975•62 citations
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{10}^{\ensuremath{-}2}10\ensuremath−2 to 17.5 mm Hg. The half breadth \ensuremathγ\ensuremath{\gamma}\ensuremathγ varied rather linearly with the number of atoms per unit volume, with (\ensuremathγ1N)\ifmmode×\else\texttimes\fi107=1.45(\frac{{\ensuremath{\gamma}}_{1}}{N})\ifmmode\times\else\texttimes\fi{}{10}^{7}=1.45(N\ensuremathγ1​​)\ifmmode×\else\texttimes\fi107=1.45, (\ensuremathγ2N)\ifmmode×\else\texttimes\fi107(\frac{{\ensuremath{\gamma}}_{2}}{N})\ifmmode\times\else\texttimes\fi{}{10}^{7}(N\ensuremathγ2​​)\ifmmode×\else\texttimes\fi107 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 \ensuremathγ1\ensuremathγ2\frac{{\ensuremath{\gamma}}_{1}}{{\ensuremath{\gamma}}_{2}}\ensuremathγ2​\ensuremathγ1​​ was found to be 1.8. The experimental half-width \ensuremathγ\ensuremath{\gamma}\ensuremathγ 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.
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.
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 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.
Selective reflection from sodium, potassium, rubidium, and caesium vapors in the neighborhood of the resonance lines was observed for vapor pressures between 10 mm. and 1 atm., using a steel tube with a window of transparent magnesium oxide. Reflecting power as a function of frequency was measured by using incident light of continuous spectral distribution. The reflection contour for pressures up to ½ atm. is in good agreement with the theory of reflection from an absorbing medium. For each line the damping constant in the dispersion equations varies as the square root of the number of atoms per cubic centimeter, as was found previously for mercury and cadmium. For the two members of the resonance doublet the damping constants are proportional to the square roots of the oscillator strengths. In a region about 5 cm.−1 wide about each resonance frequency the reflected intensity measured experimentally is greater than that calculated. These lines of residual intensity may be due to a second kind of selective reflection. At pressures above ½ atm. the observed reflection contour cannot be explained by the simple anomalous dispersion theory.
In addition to previous absorption measurements of Cs resonance lines, new investigations on Na, K and Rb also showed definitely that beyond symmetrical Lorentzian central parts of the lines, the stronger components of the resonance lines have blue and the weaker components red asymmetry. This behaviour can be explained by a quasistatic treatment of the self-broadening mechanism taking interatomic interaction potentials into account. But with additional data it is now possible to give a different interpretation of the origin of observed asymmetries than suggested in the previous paper on Cs resonance lines (see abstr. A5740 of 1975). The asymmetries are shown to arise from the mutual repulsion of two potential curves of the same species.