In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for ${\mathrm{Rb}}^{87}$-${\mathrm{Rb}}^{87}$ and ${\mathrm{Rb}}^{87}$-${\mathrm{Cs}}^{133}$ collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Rb}}^{87})=(1.9\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ and $\ensuremath{\sigma}({\mathrm{Rb}}^{87}\ensuremath{-}{\mathrm{Cs}}^{133})=(2.3\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$. 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 $T$ is the non-spin-exchange relaxation time and ${T}_{S1}$ and ${T}_{E1}$ 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.
In a hyperfine-optical-pumping experiment we employed the Franzen transient method to determine the total spin-exchange cross sections for Rb87-Rb87 and Rb87-Cs133 collisions at 78\ifmmode^\circ\else\textdegree\fi{}C. Values determined in this way were: \ensuremathσ(Rb87\ensuremath−Rb87)=(1.9\ifmmode±\else\textpm\fi0.2)\ifmmode×\else\texttimes\fi10\ensuremath−14cm2 and \ensuremathσ(Rb87\ensuremath−Cs133)=(2.3\ifmmode±\else\textpm\fi0.2)\ifmmode×\else\texttimes\fi10\ensuremath−14cm2. 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 \ensuremathτ1=T1+TS11+TE11, where T is the non-spin-exchange relaxation time and TS1 and TE1 are the self- and cross-exchange times. Then \ensuremathτ was obtained by fitting the signal to a single exponential and applying a small correction (\ensuremath≈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.
In a hvperfine optical pumping experiment we employed the Franzen transient method to determine the total spinexhange cross sections for 87 Rb-Rb 7 and Rb 87 .-Cscollisions at 78°C.Values determined in this way were:UCRL-16785 values of the absorption and polarization, corrections (as large as iz% in this experiment) must be made to account for the difference between the relaxation time deduced from the signal and that characterizing the decay of the polarization Corresponding to each total relaxation time T , a density measurement is made with a scanning Fabry-Perot interferometer.The analysis involves a recovery of the.true emission and absorption profiles by removing the effects of the Fabry-Perot from the experimental profiles.The integral over all frequencies of the absorption coefficient, which i proportional to the density n, is then found easily.The cross section is then• proportional to the slope of a plot of 1/'r versus n; the intercept for n = 0 is 1/T • where T is the non-s pin-exchange relaxation time.Observd values of T are in • good agreement with values calculated with the assumption that effusion to and from the sidearms dominates the relaxation.Our experiment differs from the similar one of Bouchiat and Brossel 12 in two fundamental ways.First, in our experiment circularly polarized pumping light was used instead of unpolarized light, and a resonant rf field was applied to the pumped species to destroy the resulting longitudinal polarization.This technique was necessary because it is difficult to destroy the polarization produced by the Kerr cell shutter.Second, our density measurements were made directly rather than estimated from vapor-pressure curves.The experiment is described briefly in Sec.U, the experimental procedure• in Ill, and the apparatus in IV.Data analysis is discussed in Sec.V, and Sec.Vt is a summary of the results.For a more detailed discussion of parts of this research see Ref. 15.However, the density-measurement analysis presented here supersedes the simpler approach of that reference.Also corrections for optical thickness discussed in Section V were not applied to the relaxation-time data in Ref. 15.S.
The spin-exchange cross section for Rb85-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 using the techniques of optical pumping and an interferometric method for measuring the Rb vapor density. The Rb87 constituent in a vapor of natural Rb was polarized through absorption of circularly polarized resonance radiation, and the Rb87 polarization was partially transferred to the 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 and Rb85 Zeeman resonances, the relaxation time, and the 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.
This paper reports measurements to determine the spin-exchange cross section for collisions between like alkali atoms. The spin-exchange cross section is determined for Cs133, Rb87, Rb85, K39, and Na23. The lifetime of the alkali atoms in the Zeeman sublevels of the ground-state hyperfine levels is dominated by spin-exchange collisions. The spin-exchange collision rate is therefore reflected by the linewidth of the microwave absorption spectrum observed in the magnetic dipole transitions between various of the Zeeman sublevels. The measurements employed an X-band electron paramagnetic resonance spectrometer. The alkali metal was distilled into a sample bulb which was placed inside a Dewar in a resonant cavity. The bulb was then heated to a temperature corresponding to an equilibrium vapor density of approximately 1015 alkali atoms/c.c. and the microwave absorption spectrum was recorded. In order to relate the spin-exchange rate to a cross section, it is necessary to determine the alkali density. This was done by comparing the intensity of the alkali EPR absorption to that of a weighed and oriented copper sulfate crystal. For Cs133 and Rb87, interpretation of the linewidth data is complicated by the fact that the transitions occur in a region where there is appreciable mixing of the high-field spin states by the hyperfine interaction. A density-matrix description of spin exchange which corrects for this intermediate field mixing is discussed, and the corrections are applied to the measured cross sections for two transitions in Cs133 and Rb87. Relative cross sections, referred to that of Na23, are also given.
The hyperfine relaxation of a population difference, produced by optical pumping, between the F=1mF=0 and F=2mF=0 energy levels of the ground state of Rb87, has been studied in cells containing neon, argon, helium, or krypton as a buffer gas. The relaxation times T1 and T2 have been measured as a function of the rubidium vapor pressure in the cell. The relaxation rate due to spin exchange in Rb87-Rb87 collisions has been found equal to 65 ${\mathrm{sec}}^{\ensuremath{-}1}$ at 44\ifmmode^\circ\else\textdegree\fi{}C, and the diffusion coefficients of Rb87 atoms in He, Ne, and Ar evaluated as 0.6, 0.31, and 0.22 cm2 ${\mathrm{sec}}^{\ensuremath{-}1}$, respectively. The cross section for Rb87-Ne and Rb87-Ar collisions are found to be 1.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$ cm2 and 9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}22}$ cm2. These values are in general agreement with values previously obtained by other methods. The extrapolated values of T21 for zero vapor pressure of rubidium are 185, 237, and 318 ${\mathrm{sec}}^{\ensuremath{-}1}$ for Ne, He, or Ar, respectively. Relaxations by the pumping light or by the magnetic field inhomogeneities are also discussed.
Detailed studies have been made of the light transmitted through rubidium-87 vapor during the optical-pumping process, both with and without buffer gas present. The observed transients are single exponentials with no buffer gas present, and double exponentials with buffer gas present, over a wide range of pumping intensities and relaxation times. These results are in excellent agreement with the predictions based on phenomenological equations in which nuclear spin is included and a single relaxation time is assumed. From a study of the amplitudes of the two exponential components of the optical-pumping transient, an effective cross section ${\ensuremath{\sigma}}_{\mathrm{eff}}$ is deduced for the disorientation of rubidium-87 within the 52P21 state as a result of its collision with a buffer-gas atom. It is shown that ${\ensuremath{\sigma}}_{\mathrm{eff}}={\ensuremath{\sigma}}_{\frac{1}{2}}+{\ensuremath{\sigma}}_{\frac{3}{2}}$, where ${\ensuremath{\sigma}}_{\frac{1}{2}}$ is the cross section for disorientation within the 52P21 level, and ${\ensuremath{\sigma}}_{\frac{3}{2}}$ is the cross section for transfer from the 52P21 level to the 52P23 level by means of collisions with the buffer gas. On the basis of recently measured values for ${\ensuremath{\sigma}}_{\frac{3}{2}}$, values are deduced for ${\ensuremath{\sigma}}_{\frac{1}{2}}$. The cross sections are: ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{H}\mathrm{e})=1.5(0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ cm2, ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{N}\mathrm{e})=4.4(2.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ cm2, and ${\ensuremath{\sigma}}_{\frac{1}{2}}(\mathrm{R}\mathrm{b}\ensuremath{-}\mathrm{A}\mathrm{r})=3.5(1.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ cm2. These cross sections are deduced from a model in which the probabilities for Rb87 to relax from any hyperfine level to any other are all equal. This model gives a better fit with the observed transients than the assumption that the electron spin only is randomized in the P21 state with the nuclear spin unaffected. We show that accurate relaxation-time measurements can be made by measuring the time constants associated with the double exponentials as a function of light intensity, and extrapolating them to zero light intensity. Moreover, since no shutter is required, relaxation times ${10}^{\ensuremath{-}3}$ sec can be easily observed.
We have measured the binary spin-exchange rate coefficient for collisions between Rb and 129Xe atoms at a magnetic field B=9.4T and in the temperature range $160<T<200\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}.$ The longitudinal spin-relaxation rate 1/T1 of 129Xe is dominated by ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}$ binary collisions. We measured 1/T1 using the methods of conventional nuclear magnetic resonance, with no spin enhancement by optical pumping. At the high magnetic field and large gas pressures used in this work, the contribution of ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}$ molecules to the spin-exchange rate was less than 0.1% of the binary-collision rate. The Rb atomic number density [Rb] was measured directly from the large Faraday rotation of the polarization of near-resonant light passing through the sample cells. The rate coefficient is $\ensuremath{\kappa}{=d(1/T}_{1})/d[\mathrm{Rb}]=(1.75\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{\mathrm{cm}}^{3}/\mathrm{s}.$