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Physical Review A

Measurement of spin-exchange rate constants between Xe129 and alkali metals

Wenjin Shao, Guodong Wang, E. W. Hughes

Published Aug 17, 2005• 25 citations
Publisher

Abstract

By measuring the relaxation rates of the nuclear spin polarization of $^{129}\mathrm{Xe}$ in the presence of alkali-metal vapor at different densities, we have extracted the spin-exchange rates between $^{129}\mathrm{Xe}$ and the three alkali metals K, Rb, and Cs. By studying the alkali-metal--$^{129}\mathrm{Xe}$ spin-exchange rates as functions of the cell number density from 0.2 to 0.7 amagat, the binary collision and van der Waals molecular terms are separated, and constants governing both mechanisms are determined. The results from our work can be used to optimize the parameter space for polarizing $^{129}\mathrm{Xe}$, a promising agent for magnetic resonance imaging and other applications.

DOI
10.1103/physreva.72.022713

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By measuring the relaxation rates of the nuclear spin polarization of 129Xe^{129}\mathrm{Xe}129Xe in the presence of alkali-metal vapor at different densities, we have extracted the spin-exchange rates between 129Xe^{129}\mathrm{Xe}129Xe and the three alkali metals K, Rb, and Cs. By studying the alkali-metal--129Xe^{129}\mathrm{Xe}129Xe spin-exchange rates as functions of the cell number density from 0.2 to 0.7 amagat, the binary collision and van der Waals molecular terms are separated, and constants governing both mechanisms are determined. The results from our work can be used to optimize the parameter space for polarizing 129Xe^{129}\mathrm{Xe}129Xe, a promising agent for magnetic resonance imaging and other applications.
By analyzing the measured spin-relaxation transients of 129Xe^{129}\mathrm{Xe}129Xe nuclear spins and alkali-metal-atomic spins in mixtures of alkali-metal-atom vapors, Xe gas, and larger amounts of N2{\mathrm{N}}_{2}N2​ gas, we have determined the three-body formation rates and the spin-transfer probabilities for alkali- metal--noble-gas van der Waals molecules. Three parameters, in addition to the spin quantum numbers of the alkali-metal and noble-gas nuclei, are needed to predict the spin-transfer rates. These parameters, which we have determined from experimental measurements, are x=\ensuremath{\gamma}N/\ensuremath{\alpha}, the ratio of the spin-rotation interaction \ensuremath{\gamma}N to the spin-exchange interaction \ensuremath{\alpha}; p0{p}_{0}p0​, the third-body pressure for which the molecular breakup rate ${\ensuremath{\tau}}^{\mathrm{\ensuremath{-}}1}$ is equal to the spin-rotation frequency \ensuremath{\gamma}N/h; and Z, the three-body rate constant for forming van der Waals molecules.
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We report the first measurement of the spin-exchange rate coefficient for binary collisions between Cs and 129Xe^{129}\mathrm{Xe}129Xe atoms in the temperature range $110<T<150\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ at a $9.4\text{\ensuremath{-}}\mathrm{T}$ magnetic field. Under these conditions, binary spin-exchange collisions dominate the longitudinal nuclear spin-relaxation rate 1∕T11∕{T}_{1}1∕T1​ of 129Xe^{129}\mathrm{Xe}129Xe gas. We measured 1∕T11∕{T}_{1}1∕T1​ of a thermally polarized Xe gas using the saturation-recovery of conventional nuclear magnetic resonance. We also directly measured the Cs atomic number density [Cs] by using Faraday rotation of the linear polarization of a probing laser beam passing through the sample. The measured rate coefficient is $\ensuremath{\kappa}(9.4\phantom{\rule{0.3em}{0ex}}\mathrm{T})=d(1∕{T}_{1})∕d[\mathrm{Cs}]=(2.81\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$, which is about a factor of 1.6 higher than the previously measured spin-exchange rate coefficient of $^{129}\mathrm{Xe}\text{\ensuremath{-}}\mathrm{Rb}$ binary collisions. Using a calculated magnetic decoupling factor, we extrapolate our result to zero magnetic field: $\ensuremath{\kappa}(0\phantom{\rule{0.3em}{0ex}}\mathrm{T})=(4.1\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$.
The spin-exchange rates due to binary collisions and due to the formation of van der Waals molecules between 83Kr^{83}\mathrm{Kr}83Kr nuclei and optically pumped rubidium-metal vapor have been determined using a technique that relies on the simultaneous observation of frequency shifts of nuclear magnetic resonance lines of noble-gas atoms and corresponding frequency shifts of electron paramagnetic resonance lines of alkali-metal atoms. In contrast, earlier studies have relied on the observation of the spin-relaxation rate of either the alkali-metal atoms or the noble-gas atoms.
We present a comprehensive theory of nuclear spin polarization of 3He{}^{3}\mathrm{He}3He and 129Xe{}^{129}\mathrm{Xe}129Xe gases by spin-exchange collisions with optically pumped alkali-metal vapors. The most important physical processes considered are (1) spin-conserving spin-exchange collisions between like or unlike alkali-metal atoms; (2) spin-destroying collisions of the alkali-metal atoms with each other and with buffer-gas atoms; (3) electron-nuclear spin-exchange collisions between alkali-metal atoms and 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe atoms; (4) spin interactions in van der Waals molecules consisting of a Xe atom bound to an alkali-metal atom; (5) optical pumping by laser photons; (6) spatial diffusion. The static magnetic field is assumed to be small enough that the nuclear spin of the alkali-metal atom is well coupled to the electron spin and the total spin is very nearly a good quantum number. Conditions appropriate for the production of large quantities of spin-polarized 3He{}^{3}\mathrm{He}3He or 129Xe{}^{129}\mathrm{Xe}129Xe gas are assumed, namely, atmospheres of gas pressure and nearly complete quenching of the optically excited alkali-metal atoms by collisions with N2{\mathrm{N}}_{2}N2​ or H2{\mathrm{H}}_{2}H2​ gas. Some of the more important results of this work are as follows: (1) Most of the pumping and relaxation processes are sudden with respect to the nuclear polarization. Consequently, the steady-state population distribution of alkali-metal atoms is well described by a spin temperature, whether the rate of spin-exchange collisions between alkali-metal atoms is large or small compared to the optical pumping rate or the collisional spin-relaxation rates. (2) The population distributions that characterize the response to sudden changes in the intensity of the pumping light are not described by a spin temperature, except in the limit of very rapid spin exchange. (3) Expressions given for the radio-frequency (rf) resonance linewidths and areas can be used to make reliable estimates of the local spin polarization of the alkali-metal atoms. (4) Diffusion effects for these high-pressure conditions are mainly limited to thin layers at the cell surface and at internal resonant surfaces generated by radio-frequency magnetic fields when the static magnetic field has substantial spatial inhomogeneities. The highly localized effects of diffusion at these surfaces are described with closed-form analytic functions instead of the spatial eigenmode expansions that are appropriate for lower-pressure cells.