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Journal of Applied Physics

Evaluating modeling approaches for Rb-129Xe spin-exchange optical pumping and the effect of Rb vapor density heterogeneity

James Ball, Jim M. Wild, Graham Norquay

Published Dec 24, 2024• 4 citations
Publisher

Abstract

The applicability of commonly used 129Xe nuclear polarization (PXe) buildup models to large optical cell polarizers, which operate at lower gas pressures when compared to small cell polarizers for which spin-exchange optical pumping (SEOP) models were originally developed, has yet to be systematically evaluated. In addition, spatial heterogeneity of Rb vapor density ([Rb]) and its impact on SEOP in low pressure, large optical cell polarizers remains poorly understood. In this theoretical study, it was shown that 1D analytical and numerical PXe buildup models yield diverging PXe and critical flow rate values at low flow rates and high laser absorption, contributing to the discrepancy between theoretical and experimentally measured production rates. Additionally, it was found that [Rb] heterogeneity leads to lower PXe buildup and an undesirable increase in optimal cell temperature, while the optimal laser absorption remains relatively unchanged. The updated simulation framework presented here can be utilized to model other SEOP systems.

DOI
10.1063/5.0233678

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The applicability of commonly used 129Xe nuclear polarization (PXe) buildup models to large optical cell polarizers, which operate at lower gas pressures when compared to small cell polarizers for which spin-exchange optical pumping (SEOP) models were originally developed, has yet to be systematically evaluated. In addition, spatial heterogeneity of Rb vapor density ([Rb]) and its impact on SEOP in low pressure, large optical cell polarizers remains poorly understood. In this theoretical study, it was shown that 1D analytical and numerical PXe buildup models yield diverging PXe and critical flow rate values at low flow rates and high laser absorption, contributing to the discrepancy between theoretical and experimentally measured production rates. Additionally, it was found that [Rb] heterogeneity leads to lower PXe buildup and an undesirable increase in optimal cell temperature, while the optimal laser absorption remains relatively unchanged. The updated simulation framework presented here can be utilized to model other SEOP systems.
The ability to produce liter volumes of highly-spin-polarized 129Xe^{129}\mathrm{Xe}129Xe enables a wide range of investigations, most notably in the fields of materials science and biomedical magnetic resonance imaging. However, for nearly all polarizers built to date, both peak 129Xe^{129}\mathrm{Xe}129Xe polarization and the rate at which it is produced fall far below those predicted by the standard model of Rb metal vapor, spin-exchange optical pumping (SEOP). In this work we comprehensively characterized a high-volume flow-through 129Xe^{129}\mathrm{Xe}129Xe polarizer using three different SEOP cells with internal volumes of 100, 200, and 300cm3300\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{3}300cm3 and two types of optical sources: a broad-spectrum 111-W laser [full width at half maximum (FWHM) equal to 1.92 nm] and a line-narrowed 71-W laser (FWHM equal to 0.39 nm). By measuring 129Xe^{129}\mathrm{Xe}129Xe polarization as a function of gas flow rate, we extracted the peak polarization and polarization production rate across a wide range of laser absorption levels. Peak polarization for all cells consistently remained a factor of 2--3 times lower than predicted at all absorption levels. Moreover, although production rates increased with laser absorption, they did so much more slowly than predicted by the standard theoretical model and basic spin-exchange efficiency arguments. Underperformance was most notable in the smallest optical cells. We propose that all these systematic deviations from theory can be explained by invoking the presence of paramagnetic Rb clusters within the vapor. Cluster formation within saturated alkali-metal vapors is well established and their interaction with resonant laser light was recently shown to create plasmalike conditions. Such cluster systems cause both Rb and 129Xe^{129}\mathrm{Xe}129Xe depolarization, as well as excess photon scattering. These effects were incorporated into the SEOP model by assuming that clusters are activated in proportion to excited-state Rb number density and by further estimating physically reasonable values for the nanocluster-induced velocity-averaged spin-destruction cross section for Rb $(\ensuremath{\langle}{\ensuremath{\sigma}}_{\text{cluster-Rb}}v\ensuremath{\rangle}\phantom{\rule{0.16em}{0ex}}\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1})$, the 129Xe^{129}\mathrm{Xe}129Xe relaxation cross section $(\ensuremath{\langle}{\ensuremath{\sigma}}_{\text{cluster-Xe}}v\ensuremath{\rangle}\phantom{\rule{0.16em}{0ex}}\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1})$, and a non-wavelength-specific photon-scattering cross section $({\ensuremath{\sigma}}_{\mathrm{cluster}}\phantom{\rule{0.16em}{0ex}}\ensuremath{\approx}\phantom{\rule{0.16em}{0ex}}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2})$. The resulting modified SEOP model now closely matches experimental observations.
We have studied the efficiency of spin-exchange optical pumping (SEOP) in cells that contain either pure rubidium, mixtures of rubidium and potassium, or pure potassium. Optical pumping was performed with spectrally narrowed diode array lasers operating at either the wavelength of the Rb $5{s}_{1∕2}\ensuremath{-}5{p}_{1∕2}$ transition (795nm)(795\phantom{\rule{0.3em}{0ex}}\mathrm{nm})(795nm) or the K $4{s}_{1∕2}\ensuremath{-}4{p}_{1∕2}$ transition (770nm)(770\phantom{\rule{0.3em}{0ex}}\mathrm{nm})(770nm). Calculations of the expected efficiency are shown for practical conditions and compared to measurements. We have measured the vapor density ratio in Rb-K mixture cells using absorption of white light. Our focus is on the conditions that are relevant for neutron spin filters, but the results are relevant to all applications of SEOP. We find that both Rb-K and pure K cells yield improvements in the spin-exchange efficiency, and each approach has its own advantages. Overall, the best results for high polarizing rate with high polarization were obtained with mixture cells with K-Rb vapor density ratios between 2 and 6.
Analytical model for polarization transfer during gas-phase collision events in spin-exchange optical pumping: Spin-12\frac{1}{2}21​ 129^{129}129Xe versus spin-32\frac{3}{2}23​ 131^{131}131Xe
Spin-exchange optical pumping (SEOP) is a method for producing spin-hyperpolarized noble gas nuclei, such as 129Xe and 131Xe, which are used in various magnetic resonance applications from fundamental physics to quantum sensing and medical imaging. In SEOP, optically polarized alkali-metal atoms transfer their spin polarization to the noble gas nuclei in gas-phase collision events via the hyperfine coupling (HFC) between the alkali valence electron and the noble gas nucleus. While the polarization transfer physics of spin I=1/2I = 1/2I=1/2 nuclei, such as 129Xe, is relatively well understood, that of spin I>1/2I > 1/2I>1/2 nuclei, such as 131Xe (I=3/2I = 3/2I=3/2), has been far less studied, and no rigorous theoretical model has been presented to date. To this end, we derive a simple analytical model for the upper limit, neglecting relaxation, of the SEOP polarization transfer, applicable to noble gases with arbitrary nuclear spin. Analytical evaluation of the Baker-Campbell-Hausdorff expansion for the time evolution of the spin density operator ρ^(t)\hatρ(t)ρ^​(t) reveals that only even-order terms in the HFC contribute to the polarization transfer, with the leading-order quadratic term being the most significant. We obtain a result similar to that derived for the spin-exchange cross section by Herman [Phys. Rev. 137, A 1062 (1965)], but in a more general framework for the time evolution of ρ^(t)\hatρ(t)ρ^​(t) that is also more familiar to magnetic resonance researchers. The model is applied to understand the difference in the polarization transfer efficiency between 129Xe and 131Xe, yielding results in agreement with previous experiments. We also validate the model by comparison to detailed numerical multiscale simulations of the SEOP process, where full quantum-chemically computed spin Hamiltonians sampled from molecular dynamics simulations of the gas-phase collision events are used to propagate the spin dynamics.
We present a design for a spin-exchange optical pumping system to produce large quantities of highly polarized 129Xe. Low xenon concentrations in the flowing gas mixture allow the laser to maintain high Rb polarization. The large spin-exchange rate between Rb and 129Xe through the long-lived van der Waals molecules at low pressure, combined with a high flow rate, results in large production rates of hyperpolarized xenon. We report a maximum polarization of 64% achieved for a 0.3 l/h Xe flow rate, and maximum magnetization output of 6 l/h at 22% polarization. Our findings regarding the polarization dependence on temperature, nitrogen partial pressure, and gas mixture flow velocity are also reported.
We present a design for a spin-exchange optical pumping system to produce large quantities of highly polarized 129Xe and 131Xe. Low xenon concentrations in the flowing gas mixture which allow the laser to maintain high Cs polarization. The large spin-exchange rate between Cs and Xe through the long-lived van der Waals molecules at low pressure, combined with a high flow rate, results in large production rates of hyperpolarized xenon. The fast rates make it possible to obtain large nuclear polarizations after several minutes of optical pumping with a laser.At high Xe pressures. According to the theory, the longitudinal spin-elaxation rate 1T1 of Xe in a high-pressure sample containing only Xe and Cs vapor has the simple form is the velocity averaged binary spin-exchange cross section, It is the relaxation rate due to wall collisions and perhaps magnetic field inhomogeneities. Our results complement earlier studies performed at 129Xe pressures of about 20 Torr and 131Xe pressures of about 20 Torr and N2 pressures of 600 Torr . This work is useful for predicting spin-exchange rates between polarized Cs atoms and Xe nuclei.
To increase the 129Xe polarization for emerging biomedical applications, the Rb polarization on which the 129Xe directly depends must be first optimized. Radiation trapping is a form of Rb depolarization thought to be quenched by the N2 added to SEOP gas mixtures. Here we use absorption spectroscopy to measure the Rb density, optical spectroscopy to monitor the fraction of Rb atoms involved in radiation trapping, and field cycling to measure the Rb polarization. We find that radiation trapping is still present during spin-exchange optical pumping and appears to limit the achievable Rb polarization.