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Physical Review A

Magnetic decoupling of 129Xe−Rb and 129Xe−Cs binary spin exchange

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

Published Feb 28, 2003• 23 citations
Publisher

Abstract

We report calculations of the magnetic decoupling of the nuclear spin relaxation rate of ${}^{129}\mathrm{Xe}$ atoms caused by binary collisions with Rb or Cs atoms in a gas. A semiclassical approximation, using a classical path for the collision and treating the spin interactions quantum mechanically, gives results that differ by no more than 2% from calculations with the distorted-wave Born approximation. Both computational methods show that the relaxation rate decreases substantially for magnetic fields of a few tens of teslas. For ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb},$ where recent experimental measurements are available, the calculated rate coefficients at the experimental field of 9.4 T are about 80% of the calculated values at zero field. At 9.4 T, the calculated rate coefficient for ${}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}$ is about one-half of the experimentally observed value. This discrepancy is probably due to inaccuracies in the van der Waals and spin-dependent potentials used in the calculations.

DOI
10.1103/physreva.67.022720

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We report the first studies of magnetic decoupling of the spin relaxation of alkali-metal atoms due to binary collisions with buffer gases. When binary collisions are the dominant relaxation mechanism, the relaxation and its magnetic decoupling are well described by the $S$-damping rate ${\ensuremath{\Gamma}}_{\mathrm{SD}}$ due to the spin-rotation interaction $\ensuremath{\gamma}\mathbf{N}\ifmmode \dot{}\else \.{}\fi{}\mathbf{S}$, the spin exchange rate ${\ensuremath{\Gamma}}_{\mathrm{EX}}$ for collisions between alkali atoms, and a new ``Carver rate'' ${\ensuremath{\Gamma}}_{\mathrm{C}}$, due to the pressure-shift interaction $\ensuremath{\delta}A\mathbf{I}\ifmmode \dot{}\else \.{}\fi{}\mathbf{S}$, which can substantially broaden the magnetic decoupling curve while having no influence on the zero-field rates.

Physical Review Letters•Feb 15, 2002•37 citations
We report calculations of the magnetic decoupling of the nuclear spin relaxation rate of 129Xe{}^{129}\mathrm{Xe}129Xe atoms caused by binary collisions with Rb or Cs atoms in a gas. A semiclassical approximation, using a classical path for the collision and treating the spin interactions quantum mechanically, gives results that differ by no more than 2% from calculations with the distorted-wave Born approximation. Both computational methods show that the relaxation rate decreases substantially for magnetic fields of a few tens of teslas. For 129Xe\ensuremath−Rb,{}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb},129Xe\ensuremath−Rb, where recent experimental measurements are available, the calculated rate coefficients at the experimental field of 9.4 T are about 80% of the calculated values at zero field. At 9.4 T, the calculated rate coefficient for 129Xe\ensuremath−Rb{}^{129}\mathrm{Xe}\ensuremath{-}\mathrm{Rb}129Xe\ensuremath−Rb is about one-half of the experimentally observed value. This discrepancy is probably due to inaccuracies in the van der Waals and spin-dependent potentials used in the calculations.
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: $\ensuremath{\kappa}(0\phantom{\rule{0.3em}{0ex}}\mathrm{T})=(4.1\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$.
We present calculations of spin-relaxation rates of alkali-metal atoms due to the spin-axis interaction acting in binary collisions between the atoms. We show that for the high-temperature conditions of interest here, the spin-relaxation rates calculated with classical-path trajectories are nearly the same as those calculated with the distorted-wave Born approximation. We compare these calculations to recent experiments that used magnetic decoupling to isolate spin relaxation due to binary collisions from that due to the formation of triplet van der Waals molecules. The values of the spin-axis coupling coefficients deduced from measurements of binary collision rates are consistent with those deduced from molecular decoupling experiments, and follow a physically plausible scaling law for the spin-axis coupling coefficients.
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 $\ensuremath{\kappa}{=d(1/T}_{1})/d[\mathrm{Rb}]=(1.75\ifmmode\pm\else\textpm\fi{}0.12)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}{\mathrm{cm}}^{3}/\mathrm{s}.$
Abstract The relative spin-exchange efficiencies of Cs and Rb remain an important question in the field of hyperpolarized 129 Xe; however, direct experimental comparisons are still limited. We present measurements of the spin-exchange efficiency for 129 Xe–Cs/Rb in 129 Xe: N 2 = 1 : 50 mixtures. Under low-magnetic-field and short-lifetimes van der Waals molecular regime, we determine the spin-exchange efficiencies of 129 Xe–Cs/Rb by measuring the spin-exchange rate coefficient for 129 Xe–Cs/Rb and the Xe-induced spin-relaxation rate of Cs/Rb. Under identical gas composition and pressure conditions, the spin-exchange efficiency of Cs is approximately 1.2–1.5 times higher than Rb. We also derive an expression that enables the prediction of the spin-exchange efficiency for 129 Xe–Cs/Rb in arbitrary 129 Xe– N 2 mixtures.
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.
We report the first studies of magnetic decoupling of the spin relaxation of alkali-metal atoms due to binary collisions with buffer gases. When binary collisions are the dominant relaxation mechanism, the relaxation and its magnetic decoupling are well described by the SSS-damping rate ${\ensuremath{\Gamma}}_{\mathrm{SD}}$ due to the spin-rotation interaction $\ensuremath{\gamma}\mathbf{N}\ifmmode \dot{}\else \.{}\fi{}\mathbf{S}$, the spin exchange rate ${\ensuremath{\Gamma}}_{\mathrm{EX}}$ for collisions between alkali atoms, and a new ``Carver rate'' ${\ensuremath{\Gamma}}_{\mathrm{C}}$, due to the pressure-shift interaction $\ensuremath{\delta}A\mathbf{I}\ifmmode \dot{}\else \.{}\fi{}\mathbf{S}$, which can substantially broaden the magnetic decoupling curve while having no influence on the zero-field rates.