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Physical Review

Spin-Exchange Cross Section for Rb85 - Rb87 Collisions

Steven Jarrett

Published Jan 6, 1964• 36 citations
Publisher

Abstract

The spin-exchange cross section for ${\mathrm{Rb}}^{85}$-${\mathrm{Rb}}^{87}$ collisions has been measured to be (1.70\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$ using the techniques of optical pumping and an interferometric method for measuring the Rb vapor density. The ${\mathrm{Rb}}^{87}$ constituent in a vapor of natural Rb was polarized through absorption of circularly polarized resonance radiation, and the ${\mathrm{Rb}}^{87}$ polarization was partially transferred to the ${\mathrm{Rb}}^{85}$ 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 ${\mathrm{Rb}}^{87}$ and ${\mathrm{Rb}}^{85}$ Zeeman resonances, the relaxation time, and the ${\mathrm{Rb}}^{87}$ 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.

DOI
10.1103/physrev.133.a111

Related papers

Spin-Exchange Cross Sections for Rb87 - Rb87 and Rb87 - Cs133 Collisions

Hyatt M. Gibbs, Robert J. Hull

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.

Physical Review•Jan 5, 1967•69 citations

SPIN-EXCHAHGE CROSS SECTIONS FOR Rb87 -Rb87 AND Rb87 -Cs133

Hyatt M. Gibbs, Robert J. Hull

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.

•Apr 1, 1966•0 citations

Measurement of Spin-Exchange Cross Sections for Cs133 , Rb87 , Rb85 , K39 , and Na23

N Ressler, Richard H. Sands, Thomas Edison. Stark

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 ${\mathrm{Cs}}^{133}$, ${\mathrm{Rb}}^{87}$, ${\mathrm{Rb}}^{85}$, ${\mathrm{K}}^{39}$, and ${\mathrm{Na}}^{23}$. 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 ${10}^{15}$ 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 ${\mathrm{Cs}}^{133}$ and ${\mathrm{Rb}}^{87}$, 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 ${\mathrm{Cs}}^{133}$ and ${\mathrm{Rb}}^{87}$. Relative cross sections, referred to that of ${\mathrm{Na}}^{23}$, are also given.

Physical Review•Aug 5, 1969•69 citations

Temperature Dependence of the Electron-Rubidium Spin-Exchange Cross Section

Steve J. Davis, L. C. Balling

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 $\frac{1}{v}$ 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)%.

Physical Review A•Oct 1, 1972•6 citations

High-field measurement of the 129Xe−Rb spin-exchange rate due to binary collisions

Yuan‐Yu Jau, Nicholas N. Kuzma, W. Happer

We have measured the binary spin-exchange rate coefficient for collisions between Rb and ${}^{129}\mathrm{Xe}$ atoms at a magnetic field $B=9.4\mathrm{T}$ and in the temperature range $160<T<200\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}.$ The longitudinal spin-relaxation rate ${1/T}_{1}$ of ${}^{129}\mathrm{Xe}$ is dominated by ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}$ binary collisions. We measured ${1/T}_{1}$ 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 $\ensuremath{\kappa}{=d(1/T}_{1})/d[\mathrm{Rb}]=(1.75\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{\mathrm{cm}}^{3}/\mathrm{s}.$

Physical Review A•Nov 15, 2002•40 citations

Optical pumping of Rb in the presence of high-pressure He3 buffer gas

B. Larson, O. Häusser, P. P. J. Delheij +2 more

A cryogenic technique has been used to produce polarized $^{3}\mathrm{He}$ targets of up to relative density p=12 atm (\ensuremath{\approxeq}3\ifmmode\times\else\texttimes\fi{}${10}^{20}$ $^{3}\mathrm{He}$ atoms/${\mathrm{cm}}^{3}$; p=1 atm corresponds to 760 Torr or 101.3 kPa pressure at 273 K). In these targets $^{3}\mathrm{He}$ nuclei are polarized by spin-exchange collisions with optically pumped rubidium atoms. From transmission measurements at wavelengths of 790--800 nm, we have determined pressure shifts, linewidths, and line-shape asymmetries for the Rb 5${\mathit{S}}_{1/2}$\ensuremath{\rightarrow}5${\mathit{P}}_{1/2}$ D1 transition. The Rb spin-destruction rate was found to exhibit a quadratic increase versus $^{3}\mathrm{He}$ pressure, which indicates the importance of Rb${\mathrm{\ensuremath{-}}}^{3}$He${\mathrm{\ensuremath{-}}}^{3}$He collision processes. The transmission results for circularly polarized light are well described by a model that predicts the dependence of the average Rb polarization on Rb density, $^{3}\mathrm{He}$ pressure, light intensity, and cell geometry. The Rb${\mathrm{\ensuremath{-}}}^{3}$He spin-exchange cross section, 〈${\mathrm{\ensuremath{\sigma}}}_{\mathrm{SE}}$v〉=6.1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}20}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, was found to be independent of $^{3}\mathrm{He}$ pressure up to p=12.1 atm. Maximum $^{3}\mathrm{He}$ polarizations of 72--79% were observed with cells of 17 ${\mathrm{cm}}^{3}$ volume that contained $^{3}\mathrm{He}$ at p=6--9 atm.

Physical Review A•Sep 1, 1991•80 citations
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{10}^{\ensuremath{-}14}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.
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.
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{\mathrm{Cs}}^{133}Cs133, Rb87{\mathrm{Rb}}^{87}Rb87, Rb85{\mathrm{Rb}}^{85}Rb85, K39{\mathrm{K}}^{39}K39, and Na23{\mathrm{Na}}^{23}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 XXX-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{10}^{15}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{\mathrm{Cs}}^{133}Cs133 and Rb87{\mathrm{Rb}}^{87}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{\mathrm{Cs}}^{133}Cs133 and Rb87{\mathrm{Rb}}^{87}Rb87. Relative cross sections, referred to that of Na23{\mathrm{Na}}^{23}Na23, are also given.
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)%.
We have measured the binary spin-exchange rate coefficient for collisions between Rb and 129Xe{}^{129}\mathrm{Xe}129Xe atoms at a magnetic field B=9.4TB=9.4\mathrm{T}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{1/T}_{1}1/T1​ of 129Xe{}^{129}\mathrm{Xe}129Xe is dominated by ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}$ binary collisions. We measured 1/T1{1/T}_{1}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 $\ensuremath{\kappa}{=d(1/T}_{1})/d[\mathrm{Rb}]=(1.75\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{\mathrm{cm}}^{3}/\mathrm{s}.$
A cryogenic technique has been used to produce polarized 3He^{3}\mathrm{He}3He targets of up to relative density p=12 atm (\ensuremath{\approxeq}3\ifmmode\times\else\texttimes\fi{}1020{10}^{20}1020 3He^{3}\mathrm{He}3He atoms/cm3{\mathrm{cm}}^{3}cm3; p=1 atm corresponds to 760 Torr or 101.3 kPa pressure at 273 K). In these targets 3He^{3}\mathrm{He}3He nuclei are polarized by spin-exchange collisions with optically pumped rubidium atoms. From transmission measurements at wavelengths of 790--800 nm, we have determined pressure shifts, linewidths, and line-shape asymmetries for the Rb 5S1/2{\mathit{S}}_{1/2}S1/2​\ensuremath{\rightarrow}5P1/2{\mathit{P}}_{1/2}P1/2​ D1 transition. The Rb spin-destruction rate was found to exhibit a quadratic increase versus 3He^{3}\mathrm{He}3He pressure, which indicates the importance of Rb${\mathrm{\ensuremath{-}}}^{3}$He${\mathrm{\ensuremath{-}}}^{3}$He collision processes. The transmission results for circularly polarized light are well described by a model that predicts the dependence of the average Rb polarization on Rb density, 3He^{3}\mathrm{He}3He pressure, light intensity, and cell geometry. The Rb${\mathrm{\ensuremath{-}}}^{3}$He spin-exchange cross section, 〈${\mathrm{\ensuremath{\sigma}}}_{\mathrm{SE}}$v〉=6.1\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}20}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, was found to be independent of 3He^{3}\mathrm{He}3He pressure up to p=12.1 atm. Maximum 3He^{3}\mathrm{He}3He polarizations of 72--79% were observed with cells of 17 cm3{\mathrm{cm}}^{3}cm3 volume that contained 3He^{3}\mathrm{He}3He at p=6--9 atm.