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Physical Review A

Shift and Broadening of the Rb87 0-0 Line Due to Collisions with Krypton Buffer-Gas Atoms

Francis Hartmann, F. Hartmann-Boutron

Published Nov 1, 1970• 13 citations
Publisher

Abstract

The shift and broadening of the $^{87}\mathrm{Rb}$ 0-0 line (frequency 6.8 GHz) due to collisions with Kr atoms have been studied in the pressure range 0.2-10 Torr. The shift versus pressure has been found to be linear and equal to -542 \ifmmode\pm\else\textpm\fi{} 10 Hz/Torr. The linewidth results from the super-position of several effects which are analyzed, one of the most important being the relaxation due to the spin-orbit interaction experienced by Rb atoms while temporarily bound in van der Waals Rb-Kr molecules.

DOI
10.1103/physreva.2.1885

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The shift and broadening of the 87Rb^{87}\mathrm{Rb}87Rb 0-0 line (frequency 6.8 GHz) due to collisions with Kr atoms have been studied in the pressure range 0.2-10 Torr. The shift versus pressure has been found to be linear and equal to -542 \ifmmode\pm\else\textpm\fi{} 10 Hz/Torr. The linewidth results from the super-position of several effects which are analyzed, one of the most important being the relaxation due to the spin-orbit interaction experienced by Rb atoms while temporarily bound in van der Waals Rb-Kr molecules.
Normalized emission spectra of the optically excited Rb resonance lines (7800 \AA{}, 7948 \AA{}) have been measured in the presence of He, Ne, Ar, Kr, and Xe for about 50 \AA{} on either side of the lines. The perturber gas pressures were in the range 100-1100 Torr and the temperature was 318 \ifmmode^\circ\else\textdegree\fi{}K. The spectra, normalized to the total emission, are shown to be due to binary collisions. Shifts and widths of the Lorentzian cores of the lines were obtained, at pressures sufficiently low for impact theory to apply. The widths are corrected for the Rb hfs and the instrument function. Various power-law fits to the near-wing intensities are presented and compared to theoretical expectations. The red satellites reported by other authors are found to be, in the low-pressure limit, mere shoulders on the line wing for Ar and Kr, while Xe barely produces an actual peak. The measured linewidths and shifts are compared to previous measurements.
Relaxation experiments performed on optically polarized Rb atoms in a rare gas have been previously reported; their detailed interpretation is given below. It is shown that the relaxation governed by the spin-orbit interaction is strongly affected by the formation of chemically unstable Rb-Kr molecules bound by van der Waals forces. Two processes of molecule formation are analyzed: binary resonant collisions leading to metastable states and three-body collisions producing actual bound states. A relaxation model valid for any disorientation probability per single Rb-Kr interaction is developed. Aside from clear evidence for the existence of alkali-rare-gas molecules, the success of the theoretical interpretation of the relaxation experiments yields the equilibrium constant $\mathcal{K}=1.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}22}$ cm3{\mathrm{cm}}^{3}cm3/molecule for the reaction Rb+Kr \ensuremath{\rightleftharpoons} Rb-Kr at 300\ifmmode^\circ\else\textdegree\fi{}K, the average lifetime of a Rb-Kr molecule in the gas phase, $\ensuremath{\tau}=0.65\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ sec, at a krypton pressure of one Torr, and the average spin-orbit coupling constant in a Rb-Kr molecule, $\overline{\ensuremath{\gamma}}{h}^{\ensuremath{-}1}=0.63$ MHz. It is also shown that the spin-orbit potential is predominantly short-range.
We demonstrated the nonlinear dependence of the microwave resonance frequencies of ground-state Rb or Cs atoms on the pressure of the buffer gases Ar and Kr. No nonlinearities were observed in the gases He or N2. These observations strongly suggest that the nonlinearities are due to the van der Waals molecules that form in Ar and Kr, but not in He or N2. We developed a simple model, parameterized by the effective three-body formation rate of molecules and by the effective product of the collisionally-limited lifetime times the shift of the hyperfine coupling coefficient in the molecule, and it explained the data very well.
The total absorption, AG, was measured as a function of absorbing gas pressure, P, for the 1S0–3P1 (1236 Å) and 1S0–1P1 (1165 Å) resonance transitions in Kr. For P=0.006–0.06 torr, self-broadening was negligible compared to the natural width. For P=0.06–0.75 torr, self-broadening contributed significantly to the linewidth, and the line shape was essentially symmetrical. For P = 1.0–7.0 torr, the. asymmetric Van der Waals broadening was apparent. The component of the linewidth due to self-broadening, ΓSB, was calculated from the measurements of AG, for P=0.06–0.75 torr, and was found to vary linearly with the number density of absorbers, N, as predicted by theory. The ratio, ΓSB/N, was found to be in reasonably good agreement with theoretical predictions.
Collisions with chemically inert atoms or molecules change the hyperfine coupling $A\phantom{\rule{0.16em}{0ex}}\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$ of an alkali-metal atom through the hyperfine-shift interaction $\ensuremath{\delta}A\phantom{\rule{0.16em}{0ex}}\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{S}$. This interaction is responsible for the pressure shifts of the microwave resonances of alkali-metal atoms in buffer gases, is an important spin interaction in alkali-metal--noble-gas van der Waals molecules, and is anticipated to enable the magnetoassociation of ultracold molecules such as RbSr. An improved estimate is presented for the long-range asymptote of this interaction for Na, K, Rb, and Cs. To test the results, the change in hyperfine coupling due to a static electric field is estimated and reasonable agreement is found.
We present results of the pressure broadening and shift of the rubidium 5s2S1∕2–6p2P3∕25s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}\text{--}6p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}5s2S1∕2​–6p2P3∕2​ (420.2 nm) spectral line by argon and helium buffer gases at pressures below 10 torr. High-resolution absorption measurements were performed with a single-mode external cavity diode laser, having 20-GHz tuning range and a linewidth of about 1 MHz. Pressure broadening and shift parameters of Lorentzian hyperfine components have been determined. We obtained the redshift of hyperfine spectral lines for He and the blueshift for Ar.