Nuclear spin relaxation of 129Xe due to persistent xenon dimers

We have measured longitudinal nuclear relaxation rates of 129Xe in Xe-N2 mixtures at densities below 0.5 amagats in a magnetic field of 8.0 T. We find that intrinsic spin relaxation in this regime is principally due to fluctuations in the intramolecular spin-rotation (SR) and chemical-shift-anisotropy (CSA) interactions, mediated by the formation of 129Xe-Xe persistent dimers. Our results are consistent with previous work done in one case at much lower applied fields where the CSA interaction is negligible and in another case at much higher gas densities where transient xenon dimers mediate the interactions. We have verified that a large applied field suppresses the persistent-dimer mechanism, consistent with standard relaxation theory, allowing us to measure room-temperature gas-phase relaxation times T1 for 129Xe greater than 25 h at 8.0 T. These data also yield a maximum possible low-field T1 for pure xenon gas at room temperature of 5.45 ± 0.2 h. The coupling strengths for the SR and CSA interactions that we extract are in fair agreement with estimates based both on previous experimental work and on ab initio calculations. Our results have potential implications for the production and storage of large quantities of hyperpolarized 129Xe for use in various applications.

PHYSICAL REVIEW A 74. 063408 (2006) Nuclear spin relaxation of 129Xe due to persistent xenon dimers B. N. Berry-Pusey, B. C. Anger, G. Laicher, and B. Saam Department of Physics, University of Utah, Salt Lake City, Utah 84112-0830, USA (Received 12 September 2006; published 15 December 2006) We have measured longitudinal nuclear relaxation rates of 12<JXe in Xe-N2 mixtures at densities below 0.5 amagats in a magnetic field of 8.0 T. We find that intrinsic spin relaxation in this regime is principally due to fluctuations in the intramolecular spin-rotation (SR) and chemical-shift-anisotropy (CSA) interactions, medi­ated by the formation of 12<JXe-Xe persistent dimers. Our results are consistent with previous work done in one case at much lower applied fields where the CSA interaction is negligible and in another case at much higher gas densities where transient xenon dimers mediate the interactions. We have verified that a large applied field suppresses the persistent-dimer mechanism, consistent with standard relaxation theory, allowing us to measure room-temperature gas-phase relaxation times Tx for 12<JXe greater than 25 h at 8.0 T. These data also yield a maximum possible low-field Tt for pure xenon gas at room temperature of 5.45±0.2 h. The coupling strengths for the SR and CSA interactions that we extract are in fair agreement with estimates based both on previous experimental work and on ab initio calculations. Our results have potential implications for the production and storage of large quantities of hyperpolarized 12<JXe for use in various applications. DOI: 10.1103/PhysRevA.74.063408 PACS number(s): 33.25. + k, 32.80.Bx, 34.30.+h I. INTRODUCTION The stable spin-} isotopes 3He and ,29Xe are readily po­larized to levels exceeding 0.1 via spin-exchange optical pumping (SEOP) [1,2], making them accessible to a wide variety of magnetic resonance experiments. As the name "hyperpolarized" suggests, the relative populations of nuclear-spin sublevels in these gases are well out of thermal equilibrium; therefore an understanding of longitudinal re­laxation mechanisms (characterized by the time T{) that limit both the achievable polarization and the sample storage time is critically important. Several recently published papers [3-5], and references therein, discuss the physics and appli­cations of hyperpolarized 3He. We are concerned here spe­cifically with hyperpolarized l29Xe, which is also studied and used in a wide variety of applications, including recent ex­amples in medical imaging [6], biochemistry [7], and surface science [8]. The gas-phase relaxation mechanisms may be divided broadly into intrinsic and extrinsic categories. The former are due to the presence of the other noble-gas atoms in the sample and include, for example, the dipole-dipole mecha­nism present during 3He-3He binary collisions that limits T\ in a 1 amagat sample of 3He to =800 h [9]. (One amagat = 2.69 X 1019 cnf3, the density of 1 atm of an ideal gas at 0 °C. Unless otherwise noted, densities quoted here have been calculated from pressures measured at room tempera­ture.) In practice, T| is usually limited by extrinsic mecha­nisms, including diffusion through external magnetic-field gradients [10,11] and (more often) collisions with container (cell) walls. However, more recent work, including that pre­sented here, indicates that intrinsic mechanisms are far more important in many practical experiments involving ,29Xe than previously assumed. We thus generally describe the ,29Xe gas-phase relaxation rate Y as the sum of four terms r - r,+r„+r, + r„., (i) last two (extrinsic) terms are due to gradient and wall relax­ation, respectively. A. Xenon dimers Intrinsic gas-phase ,29Xe relaxation is related to the van der Waals forces that govern the formation of xenon dimers, and herein, we make an important distinction; transient dimers are formed in binary collisions, where the per-atom collision frequency 1/7) is proportional to the xenon density [Xe] and the collision duration rt (a few picoseconds) de­pends on the details of the Xe-Xe interatomic potential; per­sistent dimers are formed by three-body collisions and exist in a stable bound state for a molecular lifetime rp until the next collision with another atom. The possible existence of persistent dimers was suggested as early as 1959 by Bernardes and Primakoff [12], whose model can be used to estimated their concentration to be 0.5% for [Xe]=l amagat. The dimer concentration is related to the chemical equilibrium coefficient /C = [Xe2]/[Xe]2, from which we obtain the fraction of Xe atoms bound in Xe2 molecules 2[Xe2] [Xe] + 2[Xe2] '2/C[Xe], (2) where the first two (intrinsic) terms are due, respectively, to transient and persistent xenon dimers (see below), and the where the approximation is very good in the limit where [Xe2]<§[Xe]. Chann et al. [13] calculated the partition func­tion for the internal states of the Xe2 molecule to arrive at £ = 230 A3, or a 1.2% persistent dimer concentration for [Xe] = l amagat. The calculated properties of the Xe-Xe interatomic poten­tial and simple kinetic theory [14] allow reasonable estimates of the relevant kinetic parameters to be made. Here we as­sume thermal and chemical equilibrium and that Xe gas is the only constituent. The results are summarized in Table I. The velocity-averaged collision cross sections {ov)xe and (ov)x^1 are estimated as a product of relative rms speed and 1050-2947/2006/74( 6 )/063408 (9) 063408-1 ©2006 The American Physical Society BERRY-PUSEY et a I. PHYSICAL REVIEW A 74, 063408 (2006) TABLE I. Estimates of kinetic parameters [14] for transient and persistent xenon dimers in pure xenon gas in thermal and chemical equilibrium. The cross sections are calculated using the appropriate value of relative rms speed, vTmii=(SkBT/77>i)l/2, where kB is the Boltzmann constant, T is temperature, and the reduced mass jj. is 112 and 2/3 of the average (naturally abundant) Xe atomic mass for Xe-Xe and XeXe2 collisions, respectively. The transient-dimer lifetime is calculated using urms=3.08 X 104 cm/s, appropriate for Xe-Xe binary collisions. The persistent-dimer lifetime is estimated under the assumption that all collisions break up the dimers and is about two orders of magnitude longer than the transient-dimer lifetime. Quantity Symbol Formula Value at 295 K, [Xe]=1 amagat Xenon density [Xe] 2.687X1 O'9 cm"3 Xe2 equilibrium separation [15] *0 4.4 A Depth of Xe2 potential well [15] e/kB 283 K Vel.-avged. Xe-Xe cross section ((rv)xc M 1:~ 1.9X 10"10 cm3/s Vel.-avged. Xe-Xe2 cross section (ov)xc2 2TfRyUTmk 3.25 X 10"10 cm3/s Time between transient collisions T, ([Xe](cry)Xc)"l 200 ps Transient-dimer lifetime T, nl. 2.85 ps Persistent-dimer lifetime TP ([XeK<ro}Xc2r' 115 ps a classical target size. The target size is estimated as ttR\ for Xe-Xe collisions and IttRq for Xe-Xe, collisions, where /?0=4.4 A [15] is the equilibrium separation of the atoms in Xe2. The potential-well depth of -283 K [15] indicates that room-temperature collisions are likely to break up persistent dimers; hence, the corresponding breakup rate tJ} '=^[Xe] can be estimated by assuming that the breakup coefficient kXi: for persistent dimers by Xe atoms is equal to (cn;)Xts. At 295 K and [Xe]=l amagat we obtain rp- 140 ps, about two orders of magnitude longer than the transient-dimer lifetime Tr. It is this much longer lifetime that causes persistent dimers (despite their low fractional abundance) to play a dominant role in ,29Xe spin relaxation at low densities. B. Previous studies of 129Xe intrinsic relaxation in the gas phase More than 40 years ago, Hunt and Can' demonstrated that 771 for ,29Xe is linearly proportional to the xenon density [Xe] for densities above -50 amagat [16]. The dominant source of this intrinsic relaxation is fluctuations in the spin- rotation (SR) interaction, with the Hamiltonian Hsr=f/f(/?)K-N, (3) where K is the ,29Xe nuclear spin, N is the angular momen­tum of the interacting pair of Xe atoms, and cK(R) is the coupling energy at the distance R between the pair. The lin­ear density dependence suggests that the fluctuations are caused by transient dimers. In the weak-interaction limit, for which (c^N2)!^2-^: 1, the corresponding relaxation rate is [13,17] rrir= ^(DivJXe], (4) where vrmi=($kBT/tt/jl)]I2 is the relative rms speed of two interacting Xe atoms with reduced mass /jl, and crsr(D is the thermally averaged binary spin-relaxation cross section, which is a function of temperature T and of cK(R). This work was of necessity carried out at very high xenon densities (tens of amagats) using thermally generated polarization. Ex­trapolating the data down to [Xe]=l amagat yields an intrin­sic gas-phase T, for ,29Xe of -52 h. This was widely as­sumed to be the limiting value for several decades, even as SEOP made it common to work with much lower-density xenon samples. Several years ago, Moudrakovski et al. [17] essentially confirmed the results of Hunt and Carr but also found a de­pendence of the slope of 771 vs [Xe] on the square of the applied magnetic field B(j for [Xe]>20 amagat and B(j be­tween 4.7 and 9.4 T. This field dependence indicates an ad­ditional contribution to the intrinsic relaxation from fluctua­tions of the chemical shift anisotropy (CSA) interaction. The corresponding Hamiltonian may be written [18] K,u = ^(^bK-©.B0, (5) where © is the inertial tensor of an interacting pair, /xB is the Bohr magneton, and cK(R) is the same for both SR and CSA interactions. At such large values of [Xe], the fluctuations were again reasonably presumed to be due to transient dimers. The total intrinsic relaxation rate due to transient dimers is then rf=qr+r;'su, (6) where FJ'Sil can be written in a form analogous to Eq. (4) with the appropriate cross section crcsu(7') depending on By. The cross sections (and the relaxation rates FJ'Sil and Frsr) become comparable for B(j= 12.5 T. Implicit in all of the work involving transient dimers is the assumption of the fast-fluctuation limit. A more complete formulation of the cross sections <xsr(D and crcsjT) would have both multiplied by a factor 1/(1 + 02t^), where O is the Larmor frequency of the nucleus in the applied magnetic field B() [19]. (For ,29Xe, the Larmor frequency CI=2tt X 11.78 MHz/T.) The correlation time tc is on the order of the average duration of a binary collision rr, or a few pico­seconds. The fast-fluctuation limit corresponds to O2^^!, which clearly holds for any reasonable B(). As expected in 063408-2 NUCLEAR SPIN RELAXATION OF l29Xe DUE TO. PHYSICAL REVIEW A 74, 063408 (2006) this limit, no dependence on applied field was observed up to 2.5 T in the earlier work of Hunt and Carr [16], and the field dependence observed by Moudrakovski et al. [17] was due solely to the fi(2 dependence of the CSA interaction strength. A key development in understanding intrinsic gas-phase ,29Xe relaxation came with the work of Chann et al. [13], who presented strong evidence that for lower gas densities typical of SEOP, the fluctuations in the SR interaction are predominantly mediated by the formation and breakup of persistent Xe dimers. Although the fraction of such mol­ecules is small, their lifetime is about two orders of magni­tude longer than the transient-dimer lifetime. In the double limit of weak interactions and fast fluctuations, the probabil­ity of a spin transition would thus be four orders of magni­tude greater for persistent dimers. The further implications of this work are profound: in the low-field limit, the intrinsic ,29Xe T\ at low densities is independent of total gas density and depends instead only on gas composition, i.e., the rela­tive concentrations of xenon and any other gases in the mix­ture that can serve as an effective third body for the forma­tion and breakup of persistent dimers. Moreover, a maximum possible low-field T\ for pure xenon gas at room temperature was deduced from these data to be »=4 h, an order of mag­nitude smaller than the value extrapolated from the work of Hunt and Can' [16]. C. The present work The purpose of the present work is to investigate ,29Xe relaxation due to persistent dimers at high magnetic fields (8.0 T). All previous work has been carried out in the fast- fluctuation limit, for which the dimer lifetime (whether per­sistent or transient) is much shorter than the ,29Xe Larmor period. As [Xe] is reduced below «=1 amagat, an applied field of 8.0 T decouples the relaxation due to persistent dimers; we show that one obtains in this regime a depen­dence of the rate on total gas density at fixed gas composi­tion that is consistent with the theory of Chann et al. [13], including the factor 1/(1+f!27p, confirming that persistent and not transient dimers are primarily responsible for intrin­sic ,29Xe relaxation at these low gas densities. We are able to extract from our data reasonable estimates of molecular for­mation and breakup parameters, as well as the SR and CSA interaction strengths. The SR interaction strength, properly parametrized according to Ref. [13], allows us to compute for comparison a maximum possible low-field T\ for pure xenon gas at room temperature of 5.45±0.2 h, slightly larger than the result of Chann et al. [13]. We further confirm both the role of magnetic decoupling and the presence of the CSA interaction at high field with several T\ measurements for similar gas compositions and total densities in a lower 1.5 T applied field. The silicone-coated borosilicate-glass cells used in these studies had very low wall-relaxation rates, which was essen­tial in order to investigate the molecular effects with high precision. In the regime where wall relaxation dominates the contribution from persistent dimers, we have measured lon­gitudinal relaxation times >25 h at 8.0 T for ,29Xe at room temperature. II. THEORY The relaxation rate Tp of ,29Xe due to persistent xenon dimers may be written [13] rp = (2AC[Xe])(Mw + Mc")(-(7) \ 1 + ‘' 'fpl where we have slightly rearranged Eq. 2 of Ref. [13] to form the product of three factors. The first factor is the fraction of Xe atoms bound in molecules in accordance with Eq. (2); the second factor Msr+Mcsa is the sum of the SR and CSA mean- square interaction strengths (second moments) during a mo­lecular lifetime, where Mcsa^5(2; and the third factor is the power spectrum of magnetic field fluctuations [19], where rp is the correlation time for the fluctuations, assumed to be equal to the molecular lifetime. (Here Tp and rp correspond, respectively, to FvdW and tb in Ref. [13].) We note that it is immaterial whether the coherent rotation of the persistent dimers is interrupted by collisions that break up the molecule (with on average a new molecule created elsewhere by de­tailed balance) or by collisions that simply reorient its angu­lar momentum. The inverse correlation time is actually the sum of the rates for these two types of collisions; we call this total rate t~[, since it is likely that purely reorienting colli­sions are rare in such weakly bound molecules. For linear molecules, the second moments for SR [20] and CSA [21,22] are given by Mtsa=-^^(c20 i), (9) 15 fib k where &± = /jlR2 is the rotational inertia. Chann et al. [13] conducted their experiments in an ap­plied field Z?0=20.4 G (fl = 2wX 24 kHz), for which the CSA interaction is negligible and which corresponds to the fast-fluctuation (low-field) limit at all reasonable gas densi­ties, thus reducing Eq. (7) to 4/C(ciN2) Vp= 3/*2 [Xe]v (10) For a pure xenon sample in chemical equilibrium, the forma­tion and breakup rate per molecule is 1! Tp=kxJXc\, where Xe atoms serve as the third body to provide kinetic energy, and is the corresponding molecular breakup coefficient. Since [Xe]rp is a constant, Tp is independent of [Xe] in the low-field limit. However, a second gas, capable of serving as a third body in the formation and breakup of molecules, can change tp without affecting the fraction of Xe atoms bound in molecules. Chann et al. [13] found (and confirmed experi­mentally) that Tp depends on the relative gas composition but not on the total gas density at fixed composition. For applied magnetic fields on the order of 10 T (fl = 27rX 118 MHz) and gas densities on the order of 0.1 ama­gat or lower, we can no longer ignore the fl"Tj; term in the power spectrum of Eq. (7). For fixed B0, both the SR and CSA terms stay constant, and one should observe the mag­063408- 3 BERRY-PUSEY et al. PHYSICAL REVIEW A 74, 063408 (2006) netic decoupling of relaxation mediated by persistent dimers as the total gas pressure is lowered for a fixed gas composi­tion. We worked exclusively with nitrogen as a second gas and measured Fp as a function of total gas pressure for three distinct relative compositions. (An alternative to our experi­ment would be to vary the density of the second gas while holding [Xe] fixed, which would lead to a maximum in the relaxation rate for flrp=l.) We write the molecular breakup rate as - = kn[G] = kxlXe]+kN[N2], (11) Tp where kN is the Xe2 molecular breakup coefficient for nitro­gen and the total gas density [G] = [Xe] + [N2], The overall breakup coefficient k„ is given by kn = akx< + (1 - a)kN, (12) where a=[Xe]/[G] is the fractional concentration of xenon. Under our conditions, where [Xe] is small enough to ignore contributions from transient dimers and gradient relaxation is negligible (see Sec. IV), the observed ,29Xe relaxation is F = r,,+rp, where Fn, is the wall relaxation rate. Using Eqs. (7) and (11), we can write F as a function of total gas density [G] for a fixed concentration a F([G]) = rn, + 2£(M-+M-)(^[;^;). (13) III. EXPERIMENTAL PROCEDURE AND RESULTS In order to examine molecular relaxation using Eq. (13), we require stable wall-relaxation rates, where Fn, < Fp. In our early attempts, stability of Fn, was a problem. Relaxation measurements were done in the same cell that was used to polarize the Xe gas mixture. These cells are similar to those that have been fabricated and used to polarize 3He in our group [23]: They are 5.0 cm diam spheres connected via a 10 cm length of capillary tubing (0.5 mm diam) to a glass valve and side arm for refilling. A 4 cm length of 6 mm glass tubing (the stem) extends from the sphere opposite the cap­illary entrance. These cells were coated with dichlorodimeth- ylsilane [24] to inhibit wall relaxation and contained a mac­roscopic amount of Rb metal (tens of milligrams) for optical pumping. Repeated measurements of the room-temperature wall relaxation rate in these cells at 8.0 T showed fluctua­tions of a factor of two or more. The changes were observed to occur each time after a cell was pumped and polarized at 90 °C. After a cell was polarized several times, Fn, typically increased (though not necessarily monotonically) to a level comparable to Fp or even larger. We infer that at optical pumping temperatures Rb reacted with the coating in a way that ultimately degraded the cell wall lifetime. Thereafter, we switched to using two distinct types of cells: "pumping" cells and "measurement" cells. Eight dif­ferent pumping cells (as described above) were used exclu­sively to generate hyperpolarized ,29Xe. Periodically, we found it possible to rejuvenate cells with poor wall rates by removing the Rb, recoating the walls, and distilling in fresh Rb. Xenon gas was transferred from pumping cells to one of two measurement cells (designated 105B and 113B). Mea­surement cells have a similar geometry to pumping cells and are also coated, but the spherical chamber has a larger 6.7 cm diam. The smaller surface-to-volume ratio in these cells serves to further decrease the wall-relaxation rate. Mea­surement cells contained no Rb and were never heated above room temperature; they exhibited long and robust wall- relaxation times (>20 h). Our high-vacuum gas-handling system was used to mea­sure all cell volumes, as well as the ballast volumes used in gas transfer. The same system was also used to fill pumping cells with a precise amount of Xe and N2, according to the chosen value of the Xe concentration a. A known quantity of Xe atoms was first condensed into the stem of the cell, which was held at 77 K by immersing it in liquid nitrogen. Only the stem was immersed, the rest of the cell remained near room temperature (aided by a small styrofoam heat shield). While the Xe remained frozen, N2 gas was admitted into the cell at the desired final partial pressure. After filling, the cell was allowed to return completely to room temperature and a final pressure was measured with a separate solid-state gauge (GE Novasensor, Model NPC-410-015A-3L). This final pressure was generally 1-2% higher than targeted; the discrepancy was interpreted as an excess of N2 because the cell was still somewhat colder than room temperature during filling due to its proximity to the LN2. This had the effect of slightly low­ering the value of a compared to the target value and intro­ducing a small variation. We quote average values for a with an error range reflecting this variation. Once filled, the gas in a pumping cell was polarized by SEOP with a frequency-narrowed [25] 20 W diode-laser ar­ray. The cells were placed in an oven and heated to 90 °C. The oven was located in a 1.5 T superconducting magnet with a 30 cm diam horizontal bore. (The cell capillary pro­truded laterally outside of the oven so that the valve re­mained cool.) We found that the 1.5 T field generally de­creased the Fn, of the pumping cell, thus increasing final polarization, as compared to the 30 G Helmholtz arrange­ment that we initially employed. Once the Xe gas in a pumping cell was polarized, a known amount of gas was transferred from the pumping cell to a measurement cell, making use of a manifold and, in some cases, ballast volumes in order to achieve a desired total gas density [G], A vacuum pump was used to clear dead spaces and avoid contact with atmospheric oxygen. The gas transfer was performed in the fringe field (=60 G) of the 8.0 T vertical bore superconducting magnet; the measure­ment cell was then quickly placed into the NMR probe and the entire assembly secured in the magnet. The probe coil consisted of two elongated loops of wire (a few turns each) positioned on opposite sides of the stem. The coil was tuned to the ,29Xe Larmor frequency of 94.1 MHz. The NMR spectrometer incorporates a Tecmag Aries pulse programmer and digitizer with a homebuilt RF section. The longitudinal relaxation rate F was measured by the periodic acquisition of the free-induction decay (FID) following the excitation pulse. Since only spins in the relatively small volume of the stem were excited, we were able to use large flip angles while destroying a negligible amount of the total spin mag- 063408-4 NUCLEAR SPIN RELAXATION OF l2yXc DUE TO. PHYSICAL REVIEW A 74. 063408 (2006) Total Gas Density [G] (amagat) FIG. 1. Plot of l2yXc relaxation rate vs. total gas density at 8.0 T for three values of the concentration «=[Xe]/[C]; the second gas is nitrogen in all cases. The fits arc to the theory of Chann el al. [13] as parametrized in Eq. (13) and including the CSA interaction. For each value of «, the wall-relaxation rate I',,,, molecular breakup coefficient ka. and the product IK-iM*+Mcii) arc extracted from the fits (see Table II). The asymptotes at larger [C] correspond to the density-independent rates observed in Ref. [13], where &‘[G]2 Relaxation due to persistent dimers is suppressed at low den­sities, where &„[G]=0 for [C] between about 0.05 and 0.1 amagats. The data point indicated by an arrow corresponds to a measured of 25 h. netization over the course of the measurement. Either the initial height of each FID or the area of each Fourier- transform peak was plotted vs time of acquisition. The plot was fit to an exponential decay to yield F. With the gas depolarized, the solid-state pressure gauge was used again to make a precise measurement of [G]. The process of filling and polarizing a pumping cell, transferring gas to a measure­ment cell, measuring F, and measuring [G] was repeated for a range of values of [G] from about 0.02 to 0.4 amagat, to yield F vs [G] for each value of a. Plots of measured relaxation rate F at 8.0 T vs total gas pressure [G] are shown in Fig. 1 for three different values of the Xe concentration a. In each case, the data are fit to Eq. (13) with F,„ k„, and 2IC(MSI +MCSd) as free parameters. The results are summarized in Table II. Figure 2 is a plot of k„ vs a. The data are fit to Eq. (12), yielding for the molecular breakup coefficients Kxe- ■ (3.4± 0.1) X 10‘ 10 cm3/s, (14) Xenon density fraction a FIG. 2. Plot of molecular breakup coefficient ka vs fractional xenon density a. The fit is to Eq. (12) and yields molecular breakup cocfficicnts kXe and &N for xenon and nitrogen, respectively. kH = (1.9 ± 0.2) X 10-'° cm3/s. (15) The values of Fw extracted from these fits are very small, corresponding to wall-relaxation times of 20-40 h, thus al­lowing us to observe the dramatic effect of magnetic sup­pression of the molecular- relaxation. The data point for a =0.712 and total gas pressure [G]=0.0215 amagat (marked in Fig. 1 by an arrow) corresponds to a measured relaxation time of 25 h. The wall relaxation time inferred from the theory exceeds 40 h. In a separate set of measurements, relaxation data were acquired in the measurement cell 113B for a fixed value of the xenon concentration a=0.712 in applied fields of both 8.0 and 1.5 T at several additional values of the total gas density [G]. The 1.5 T data were acquired in the same way with a similar NMR spectrometer operating at (1 = 2tt X 17.6 MHz. The magnet used was the same horizontal bore imaging magnet used to perform SEOP on the pumping cells. The cell was placed on top of a tuned surface coil inside of an aluminum box for shielding. For each value of [G], the relaxation data were acquired consecutively at 1.5 T and then 8.0 T with the same gas, except for the lowest density [G]=4.9X 10-3 amagat, for which only data at 1.5 T could be acquired. The results are shown in Fig. 3. The theoretical TABLE II. Free parameters cxtractcd from the fits of the data in Fig. 1 to Eq. (13) for three values of the Xc concentration a. Errors arc given in parentheses for the least significant figurc(s). The near constancy of 2K.(M" +MC*A) is cvidcncc for the validity of the pcrsistcnt-dimcr theory of Chann el al. [13], Measurement ccll a 2k'AM" + M'") (10-14 cm3/s2) ka (10-10 cm3/s) r„ do-5 s-1) 113B 0.546(4) 2.43(23) 2.76(8) 0.76(5) 113B 0.712(13) 2.66(15) 2.86(5) 0.64(3) 105B 0.823(8) 2.37(8) 3.14(5) 1.25(3) 063408-5 BERRY-PUSEY et al. PHYSICAL REVIEW A 74, 063408 (2006) Total Gas Density [G] (amagat) FIG. 3. Plot of l2yXe relaxation rate vs. total gas density at two different applied magnetic fields and a fixed value of the xenon concentration a=0.712. All data were acquired using the measure­ment cell 113B, for which the wall-relaxation rate (intercept of both curves) is taken as 7.0X 10"6 s"1. For each value of [C], the data were acquired consecutively at 1.5 T and then 8.0 T with the same gas, except for the lowest density point, for which only data at 1.5 T could be acquired. The curves are not tits to the data but rather are predictions derived entirely from the separate and inde­pendent data taken and displayed in Fig. 1 and Table II. High-tield suppression of the relaxation rate due to persistent dimers is stron­ger at 8.0 T for low densities, but the larger contribution to relax­ation from the CSA interaction at 8.0 T eventually causes the curves to cross near [G]=0.1 amagat, where the 1.5 T curve is already well into the limit H2f <t 1. The data point indicated by an arrow corresponds to a measured Tt of 27.0±1.3h, the longest gas-phase Tt ever reported for l2yXe. curves show the dependence of the rate on [G] for both B() = 1.5 T and B() = 8.0 T derived exclusively from the analysis of the separate 8.0 T data presented in Fig. 1; the method for arriving at these curves is discussed below. IV. DISCUSSION The present work provides strong confirmation of the theory presented by Chann et al. [13] for relaxation of gas- phase ,29Xe at low densities, particularly through the dem­onstration of the critical role played by persistent xenon dimers in setting an intrinsic lower bound to the relaxation rate and of high-field suppression of the molecular mecha­nism, as shown in Fig. 1. The role of transient dimers in our experiments was negligible: our largest xenon density was [XeJ^O.25 amagat, for which the contribution to relaxation from transient dimers for B(J = 8.0T is F( = 1.7 X 10"6 s'"1 [17], four to eight times smaller than the wall-relaxation rates extracted from our fits. The product of the chemical equilibrium coefficient 1C and the total second moment A/sr + A/csa (third column of Table II) is dependent strictly on the physics of persistent-dimer formation and of the spin- relaxation interactions, respectively. They cannot be sepa­rated experimentally, but the fact that the product remains nearly constant for the three values of Xe concentration a is further evidence for the validity of the persistent-dimer theory. In further analysis below, we will make use of the weighted average 2= (2.44±0.03) X 10"14 cm3/s2. (16) The 1.5 T vs 8.0 T data in Fig. 3 appear to demonstrate the correct dependence of Tp on B(), accounting for the dif­ferent (and somewhat competing) degrees of both high-field suppression and contribution from the CSA interaction. If we make the reasonable assumption that the ratio A/sl/A/cs:i is the same for persistent as for transient dimers (still in the weak- interaction limit in all cases), then we can use Ref. [17] to calculate the fraction/ of the total interaction strength that is due to SR to be f= Ajsr ..M = (71.0± 2.7) % at 8.0 T, (17) M + M whereas /= 1 at B()= 1.5 T. The theoretical curves in Fig. 3 have the form of Eq. (13). The intercept for both curves corresponds to FH.=7.0X 10"6 s""1, which is the average of the two extracted values for Flv, from the two fits in Fig. 1 involving the same measurement cell 113B (see Table II). We used Eqs. (14) and (15) to calculate k„ for a=0.712 and the weighted average in Eq. (16), where in the case of 50=1.5 T, 2/C(/V/sr+/V/csa) was multiplied by /(8.0 T)//(1.5 T)=/(8.0 T) to account for the much weaker CSA interaction at the lower field. The larger magnelic-field suppression combined with the presence of the CSA interac­tion for Z?0 = 8.0 T causes the curves to cross near [G]=0.1 amagat. Near this crossing point, we measured almost iden­tical T\ values for the two applied fields of about 6 h. Com­pared to this value, at the lower density [G]=0.017 amagat T| increases by about 25% at 1.5 T but by more than a factor of four at 8.0 T, due to the stronger magnetic suppression. The latter data point (marked with an arrow in Fig. 3) corre­sponds to a measured T\ of 27.0±1.3h, which is to our knowledge the longest gas-phase relaxation time ever re­ported for ,29Xe. We have assumed in Fig. 3 that the wall relaxation rate F,.,., is independent of B(h at least for the two values of B() we investigated. The assumption is physically plausible because interactions due to wall collisions should be in the fast- fluctuation limit for all reasonable values of B(), although the possibility of xenon dissolving into the surface coating [24] potentially complicates this picture. The assumption is also supported by how well the data fall on the curves, which we emphasize are not fits to these data but were derived exclu­sively from the independent 8.0 T data shown in Fig. 1 and Table II. Finally, even allowing for some field dependence to Fit is clear from the very low pressure 1.5 T data point ([G]=4.9 X 10"3 amagat), where T\ is over 12 h, that the difference in relaxation rates for [G] = 0.017 amagat could not be explained by a difference in F,.,., alone. 063408-6 NUCLEAR SPIN RELAXATION OF l29Xe DUE TO. PHYSICAL REVIEW A 74, 063408 (2006) Using Eqs. (16) and (17), and the value /C = 230 A3 cal­culated in Ref. [13], we can make an estimate of the SR interaction strength Msr=3.77x 107 s""2. Using Eq. (8), we obtain Itdw^xe = 2/C(Msr + Mcsa)/(8.0 T). \/<c‘KN2) = h X 1200 Hz. (18) This value falls between two estimates made by Chann et al. [13], one of 820 Hz based on their measurement of the low- field pure-xenon relaxation rate [see Eq. (22) below] and the relationship between the SR coupling and the Xe-Xe chemi­cal shift [26-28], and the other of 1400 Hz based on the measured spin-relaxation rate due to transient dimers in the applied-field regime where the CSA interaction is negligible [16,17]. These estimates and our result imply a value for cK(RQ)/h (where R0 is the equilibrium separation) of between 20 and 40 Hz, consistent with ab initio results of «=30 Hz [15]. Using a similar argument and the fraction 1 -/of the total interaction strength that is due to CSA, along with Eq. (9), we estimate \I(ciR4) = hx 240 Hz A2, (19) which is consistent with c^R^/h^ 10 Hz. We note that the CSA interaction is related to the anisotropic chemical shift Act of the xenon dimer by [22] Acr= (Xi, - tr. where y is the 129Xe gyromagnetic ratio. However, the ex­tremely short correlation times in the gas phase do not readily permit direct NMR measurements of <jj| and . Our values for kXe and kn are quite reasonable compared to the estimates based on kinetic theory. In fact, our esti­mated velocity-averaged cross section for collisions between xenon dimers and xenon atoms is within 20% of the value of kXe in Eq. (14) (see Table I), supporting our assumption that most collisions result in the breakup of the weakly bound persistent dimers. We find nitrogen as a third body to be only about half as efficient as Xe, somewhat in disagreement with the results of Chann et al. [13], who measured the ratio kn/kxe to be close to unity and deduced a breakup rate kXe = 1.2x 10"10 cm3/s, where the latter number is based on the calculated 820 Hz estimate for yj(c2KN2)lh discussed above. We can make a further comparison to the results of Chann et al. [13] by considering the low-field limit (fl2<s£2[G]2) of Eq. (13). Ignoring the CSA interaction and using Eq. (8), we obtain p, Be i ck(r) yh} (20) r([c]) = r„ + 4lC(c2KN2)a 3 h2k„ (21) In the limit where a= 1 and ka=kXe, we obtain what is called F*dew in Ref. [13], the low-field pure-xenon relaxation rate due to persistent dimers ~"Xe k - vdW*Xe - 4 IC(c2kN2) 3ft2 ' (22) We can write an equivalent expression that is appropriate for our data using Eq. (17) to account for our 8.0 T applied field (23) Using our values for kXe and/(8.0 T) in Eqs. (14) and (17), and the weighted average of 2/C(Msr+Mcsa) in Eq. (16), we find -^Xe - vdW ' : (5.1 ±0.2) X 10-5 S- (24) which corresponds to a limiting low-field relaxation time for pure xenon of 5.45±0.2 h, slightly larger than Chann et al.'s value [13] of 4.1 ±0.1 h. Relaxation due to diffusion of 129Xe through magnetic- field gradients in Eq. (1) should be negligible in our experi­ments. We confirmed this by displacing the entire cell and probe vertically by as much as 4 cm and recording the change in NMR frequency. We estimated a gradient of «=3G/cm in the 8.0 T magnet. (The relative gradients were even smaller in the 1.5 T magnet.) In the regime where the diffusion time across the cell is much longer than the Larmor period [10], gradient relaxation is given by D JVfi, Bl (25) where VB j is the transverse magnetic field gradient and D is the Xe diffusion coefficient. Even in the fastest-diffusion case of a cell containing 0.01 amagat of pure xenon, Eq. (25) predicts T{> 108 s from this mechanism alone. It is possible that there are contributions to our measured relaxation rates from persistent Xe-N2 dimers [29], produc­ing another molecular term in Eq. (13) with a different chemical-equilibrium coefficient, interaction strength, and molecular lifetime. These molecules are somewhat more weakly bound, having well depth e/kB between 200 and 250 K [29]. In addition to the quality of our fits to a model involving only Xe2 dimers, we rely on the results and con­clusions of Chann et al. [13], where the asymptotic relax­ation rate at high second-gas densities approached a common value (the wall-relaxation rate for the one cell employed) for Ar, N2, and He gases. This result is relevant because the well depth for Xe-He is exceedingly small at «=30 K; the asymptotic rates should have been different for the different second gases had the corresponding dimers played a signifi­cant role in relaxation. They were thus lead to conclude that Xe-N2 dimers are not contributing significantly to the mea­sured relaxation rates, and there is no reason to expect this to change at higher applied fields. It is likely that in some earlier work [17,30] at lower xenon densities, F„. was inadvertently overestimated due to a significant contribution from the molecular mechanism. For example. Breeze et al, [30] measured F""1 «=3 h in cells con­taining «=1 amagat of xenon and a relatively small amount of nitrogen, attributing virtually all of this relaxation to wall interactions. For this density and their applied field of 4.7 T, we would predict F"1=4.4 h; the actual wall relaxation time (F-Tp)-1 would then be almost 10 h. Variations in the applied field B0 and/or the total gas den­sity [G] at fixed xenon concentration a thus lead to changes in two distinct aspects of the relaxation due to persistent dimers: the rate of fluctuations compared to fl, and the rela- 063408-7 BERRY-PUSEY et al. PHYSICAL REVIEW A 74, 063408 (2006) tive strengths of the CSA and SR interactions. In the regime where B0 is below several tesla, the fast-fluctuation limit 1 (low field and high density, as in Ref. [13]) leads to an intrinsic relaxation that is independent of both [G] and B0. In the opposite limit of slow fluctuations (high field but still SR-dominated, and low density) the intrinsic relaxation is proportional both to [G]2 and to 1//?q. In the regime where /?0 >10 T, the CSA interaction begins to dominate, and re­laxation in the fast-fluctuation limit, while still density inde­pendent, is now proportional to Bq. In the limit of slow fluc­tuations, the relaxation still depends on [G]2 but becomes independent of B0 as the effects of the CSA interaction and slow fluctuations cancel each other. We note that (according to our value for kXi.) firp=1 for /^/[G]^ 120 T/amagat for pure xenon, so that the fast-fluctuation limit is readily at­tained for densities =1 amagat, even for very large labora­tory magnetic fields, and the fast-fluctuation limit always holds for Bq at or below =0.1 T, where the gas densities otherwise start to become too low to be detectable by NMR (even when hyperpolarized). Our data straddle both the tran­sition from near-zero to moderate CSA interaction strength and the transition from the slow- to the fast-fluctuation limit. Finally, for completeness we note that the contribution to relaxation from transient dimers (always in the fast- fluctuation limit and linearly dependent on [Xe]) becomes equal to that from persistent dimers for [XeJ^IO amagats, with a dependence coming in at the largest applied fields. The extraordinarily long T, values for gas-phase " Xe measured here have potential implications for accumulating and storing large quantities of hyperpolarized xenon. We have fabricated cells with sufficiently low wall-relaxation rates (<1/20 h"') that the maximum T, = 5 h due to the mo- [1] T. G. Walker and W. Happcr, Rev. Mod. Phys. 69, 629 (1997). [2] S. Appclt, A. B. Baranga, C. J. Erickson, M. V. Romalis, A. R. Young, and W. Happcr, Phys. Rev. A 58, 1412 (1998). [3] E. Babcock, B. Chann, T. G. Walker, W. C. Chen, and T. R. Gentile, Phys. Rev. Lett. 96, 083003 (2006). [4] M. S. Conradi, B. T. Saam, D. A. Yablonskiy, and J. C. Woods, Prog. Nucl. Magn. Rcson. Spcctrosc. 48, 63 (2006). [5] H. E. Mollcr, X. J. Chen, B. Saam, K. D. Hagspicl, G. A. Johnson, T. A. Altcs, E. E. dc Lange, and H.-U. Kauczor, Magn. Rcson. Med. 47, 1029 (2002). [6] K. Ruppcrt, J. F. Mata, J. R. Brookcman, K. D. Hagspicl, and J. P. Mugler III, Magn. Rcson. Med. 51, 676 (2004). [7] M. M. Spence, E. J. Ruiz, S. M. Rubin, T. J. Lowery, N. Winssingcr, P. G. Schultz, D. E. Wcmmcr, and A. Pines, J. Am. Chem. Soc. 126, 15287 (2004). [8] H. J. Jiinsch, P. Gerhard, and M. Koch, Proc. Natl. Acad. Sci. U.S.A. 101, 13715 (2004). [9] N. R. Newbury, A. S. Barton, G. D. Cates, W. Happcr, and H. Middleton, Phys. Rev. A 48, 4411 (1993). [10] G. D. Cates, S. R. Schaefer, and W. Happcr, Phys. Rev. A 37, 2877 (1988). [11] L. D. Shearer and G. K. Walters, Phys. Rev. 139, A1398 (1965). lecular mechanism for pure xenon samples can be realized in practice. Many designs for accumulation are based on storing hyperpolarized Xe frozen at 77 K [31,32], where T} of the solid is only 2.5 h [33], and one must adequately address potential polarization losses due to the freeze-thaw cycle. The use of an 8.0 T magnet in a practical device is clearly cumbersome, but there is strong evidence that the wall- relaxation rates in our cells do not increase by much for B0 as low as 1.5 T. Much longer T, values are possible, although these are currently realized only for gas compositions that are lean in Xe and/or have total gas densities =s0.1 amagat. However, given that the Xe2 potential-well depth elkB is so close to room temperature, increasing the temperature by even a few tens of degrees Celsius may significantly de­crease the limiting relaxation rates due to persistent dimers and greatly improve prospects for a room-temperature accu­mulator at xenon densities approaching 1 amagat. Additional experiments to look for the Bq dependence at relatively high applied magnetic fields would better sort out the contribu­tions from the spin-rotation and chemical-shift-anisotropy in­teractions, as well as any variable wall-relaxation rate, in order to find the optimal field in which to operate a practical device. A CKNOWLEDGMENTS We are grateful to D. C. Ailion for the use of equipment and helpful discussions, to M. S. Conradi and C. J. Jameson for helpful comments and discussions, and to K. Teaford for assistance with cell fabrication. This work was supported by the National Science Foundation Grant No. PHY-0134980. [12] N. Bcmardcs and H. Primakoff, J. Chem. Phys. 30, 691 (1959). [13] B. Chann, I. A. Nelson, L. W. Anderson, B. Drichuys, and T. G. Walker, Phys. Rev. Lett. 88, 113201 (2002). [14] F. Rcif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965). [15] M. Hanni, P. Lantto, N. Runcbcrg, J. Jokisaari, and J. Vaara, J. Chem. Phys. 121, 5908 (2004). [16] E. R. Hunt and H. Y. Carr, Phys. Rev. 130, 2302 (1963). [17] I. L. Moudrakovski, S. R. Breeze, B. Simard, C. I. Rateliffc, J. A. Ripmccstcr, T. Scidcman, and J. S. Tsc, J. Chem. Phys. 114, 2173 (2001). [18] N. N. Kuzma, D. Babich, and W. Happcr, Phys. Rev. B 65, 134301 (2002). [19] N. Blocmbcrgcn, E. M. Purcell, and R. V. Pound, Phys. Rev. 73, 679-712 (1948). [20] P. S. Hubbard, Phys. Rev. 131, 1155 (1963). [21] H. M. McConnell and C. H. Holm, J. Chem. Phys. 25, 1289 (1956). [22] H. W. Spicss, D. Schwcizcr, U. Hacbcrlcn, and K. H. Hausscr, J. Magn. Rcson. (1969-1992) 5, 101 (1971). [23] R. E. Jacob, S. W. Morgan, and B. Saam, J. Appl. Phys. 92, 1588 (2002). 063408-8 NUCLEAR SPIN RELAXATION OF l29Xe DUE TO. PHYSICAL REVIEW A 74. 063408 (2006) [24] B. Driehuys. G. D. Cates, and W. Happer. Phys. Rev. Lett. 74. 4943 (1995). [25] B. Chann. I. Nelson, and T. G. Walker. Opt. Lett. 25. 1352 (2000). [26] N. F. Ramsey. Phys. Rev. 78. 699 (1950). [27] H. C. Torrey. Phys. Rev. 130. 2306 (1963). [28] C. J. Jameson. A. K. Jameson, and S. M. Cohen. J. Chem. Phys. 62.4224 (1975). [29] A. C. de Dios and C. J. Jameson. J. Chem. Phys. 107. 4253 (1997). [30] S. R. Bree/e. S. Lang. I. Moudrakovski. C. I. Ratcliffe. J. A. Ripmeester. G. Santyr. B. Simard. and I. Zuger. J. Appl. Phys. 87. 8013 (2000). [31] B. Driehuys. G. D. Cates. E. Miron. K. Sauer. D. K. Walter, and W. Happer. Appl. Phys. Lett. 69. 1668 (1996). [32] I. C. Ruset. S. Ketel. and F. W. Hersman. Phys. Rev. Lett. 96. 053002 (2006). [33] M. Gatzke. G. D. Cates. B. Driehuys. D. Fox. W. Happer. and B. Saam. Phys. Rev. Lett. 70. 690 (1993). 063408-9