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Physical Review A

Temperature Dependence of the e−Na and e−Rb Spin-Exchange Cross Sections

Steve J. Davis, L. C. Balling

Published Aug 1, 1973• 4 citations
Publisher

Abstract

The $e\ensuremath{-}\mathrm{R}\mathrm{b}$ and $e\ensuremath{-}\mathrm{N}\mathrm{a}$ spin-exchange cross sections have been measured in a spin-exchange optical-pumping experiment as a function of temperature over the range 300-660 \ifmmode^\circ\else\textdegree\fi{}K for Rb and 400-725 \ifmmode^\circ\else\textdegree\fi{}K for Na. Within experimental error, the cross sections are essentially constant as a function of temperature. Measurements at 293 \ifmmode^\circ\else\textdegree\fi{}K give ${\ensuremath{\sigma}}_{\mathrm{SE}}(\mathrm{Rb})=(7.0\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ and measurements at 403 \ifmmode^\circ\else\textdegree\fi{}K give ${\ensuremath{\sigma}}_{\mathrm{SE}}(\mathrm{Na})=(3.2\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$.

DOI
10.1103/physreva.8.1136

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The e\ensuremath−Rbe\ensuremath{-}\mathrm{R}\mathrm{b}e\ensuremath−Rb and e\ensuremath−Nae\ensuremath{-}\mathrm{N}\mathrm{a}e\ensuremath−Na spin-exchange cross sections have been measured in a spin-exchange optical-pumping experiment as a function of temperature over the range 300-660 \ifmmode^\circ\else\textdegree\fi{}K for Rb and 400-725 \ifmmode^\circ\else\textdegree\fi{}K for Na. Within experimental error, the cross sections are essentially constant as a function of temperature. Measurements at 293 \ifmmode^\circ\else\textdegree\fi{}K give \ensuremathσSE(Rb)=(7.0\ifmmode±\else\textpm\fi2.0)\ifmmode×\else\texttimes\fi10\ensuremath−14{\ensuremath{\sigma}}_{\mathrm{SE}}(\mathrm{Rb})=(7.0\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\ensuremathσSE​(Rb)=(7.0\ifmmode±\else\textpm\fi2.0)\ifmmode×\else\texttimes\fi10\ensuremath−14 cm2{\mathrm{cm}}^{2}cm2 and measurements at 403 \ifmmode^\circ\else\textdegree\fi{}K give \ensuremathσSE(Na)=(3.2\ifmmode±\else\textpm\fi1.0)\ifmmode×\else\texttimes\fi10\ensuremath−14{\ensuremath{\sigma}}_{\mathrm{SE}}(\mathrm{Na})=(3.2\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\ensuremathσSE​(Na)=(3.2\ifmmode±\else\textpm\fi1.0)\ifmmode×\else\texttimes\fi10\ensuremath−14 cm2{\mathrm{cm}}^{2}cm2.
A spin-exchange optical-pumping experiment to study the temperature dependence of the electron-rubidium spin-exchange cross section is reported. In this experiment, electrons were polarized in a weak magnetic field by spin-exchange collisions with optically pumped Rb atoms. The electron-Rb collisions were the principal source of the electron-spin-resonance linewidth, and they also produced a shift in the resonance frequency. The magnitudes of the linewidth and frequency shift are functions of the electron-Rb-scattering phase shifts. The electron linewidth at fixed Rb density was essentially constant over the temperature range 200-840 \ifmmode^\circ\else\textdegree\fi{}K indicating the spin-exchange cross section is well approximated by a 1v\frac{1}{v}v1​ velocity dependence. The ratio of the frequency shift to linewidth was 0.075\ifmmode\pm\else\textpm\fi{}0.005 at 300 \ifmmode^\circ\else\textdegree\fi{}K with an estimated Rb polarization of (20\ifmmode\pm\else\textpm\fi{}10)%, and the ratio was 0.027\ifmmode\pm\else\textpm\fi{}0.007 at 600 \ifmmode^\circ\else\textdegree\fi{}K with a Rb polarization of (10\ifmmode\pm\else\textpm\fi{}5)%.
The spin-exchange cross section for Rb85{\mathrm{Rb}}^{85}Rb85-Rb87{\mathrm{Rb}}^{87}Rb87 collisions has been measured to be (1.70\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2 using the techniques of optical pumping and an interferometric method for measuring the Rb vapor density. The Rb87{\mathrm{Rb}}^{87}Rb87 constituent in a vapor of natural Rb was polarized through absorption of circularly polarized resonance radiation, and the Rb87{\mathrm{Rb}}^{87}Rb87 polarization was partially transferred to the Rb85{\mathrm{Rb}}^{85}Rb85 constituent through spin-exchange collisions. A phenomenological theory of the optical pumping plus the exchange polarization process which neglects nuclear spin was used to relate the cross section to the ratio of the signal strengths for the Rb87{\mathrm{Rb}}^{87}Rb87 and Rb85{\mathrm{Rb}}^{85}Rb85 Zeeman resonances, the relaxation time, and the Rb87{\mathrm{Rb}}^{87}Rb87 vapor density. The density was measured by comparing spectral profiles of the resonance radiation transmitted through the optical pumping cell at room temperature with the resonance radiation transmitted at the temperature at which the signal strengths were measured. These spectral profiles were obtained through use of a scanning Fabry-Perot interferometer.
In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for Rb87{\mathrm{Rb}}^{87}Rb87-Rb87{\mathrm{Rb}}^{87}Rb87 and Rb87{\mathrm{Rb}}^{87}Rb87-Cs133{\mathrm{Cs}}^{133}Cs133 collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Rb}}^{87})=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2 and $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Cs}}^{133})=(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2. A large difference between the ground-state hyperfine populations was established by pumping with light absorbable by atoms in only one hyperfine level. In the presence of a second unpumped species, the resulting polarization relaxed with a characteristic rate of $\frac{1}{\ensuremath{\tau}}=\frac{1}{T}+\frac{1}{{T}_{S1}}+\frac{1}{{T}_{E1}}$, where TTT is the non-spin-exchange relaxation time and TS1{T}_{S1}TS1​ and TE1{T}_{E1}TE1​ are the self- and cross-exchange times. Then $\ensuremath{\tau}$ was obtained by fitting the signal to a single exponential and applying a small correction ($\ensuremath{\approx}10%$) to account for the fact that the signal is only approximately proportional to the polarization (and hence to a single exponential). The relaxation measurement utilized rapid data accumulation with a Kerr-cell shutter and pulse-height analyzer. The cross section can be easily deduced from the relaxation times if the corresponding densities are known. Each density was measured by determining the integral over all frequencies of the absorption coefficient by means of a scanning Fabry-Perot interferometer. We describe how to remove the effect of the Fabry-Perot on the true emission and absorption profiles.
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