Volume 112A, number 3,4 PHYSICS LETTERS 21 October 1985

Cs I N D U C E D 129Xe N U C L E A R S P I N R E L A X A T I O N IN N 2 AND He B U F F E R G A S E S

Julia HSU, Z. WU, W. H A P P E R

Department of Physics, Princeton University, Princeton, NJ 08544, USA

Received 1 August 1985; accepted for publication 13 August 1985

The characteristic third body gas pressure Po - the third body gas pressure for which the molecular breakup rate ~'-1 is equal to the spin-rotational frequency -yN/~i - has been measured for N 2 and He in 133Cs-129Xe systems. Nitrogen, as a third body gas in the formation or breakup of Cs-Xe van der Waals molecules, is found to be 2.2 times as effective as helium. The relaxation rate of 129Xe nuclear spin in 133Cs as function of dimensionless third body gas pressure (P/Po) is described by a universal spin relaxation function.

Experimental results have shown that most of the spin transfer in the alkali-atom-noble-gas system oc- curs in the loosely bound alkali-atom-noble-gas van der Waals molecules [1 -3 ] . These van der Waals mol- ecules are formed in three-body collisions in which the third body is needed to conserve momentum and energy. Third body gases most commonly used in the spin exchange experiments are nitrogen and helium [2 -4 ] . Experiments show [4] that the spin relaxation rate o f 129Xe in Rb vapor is the same whether N 2 or He is used as the third body gas, provided that the He pressure is 1.6 times greater than the N 2 pressure. A universal theoretical formula which describes the spin relaxation as a function of the ratio (P/Po) of the third body gas pressure P to a characteristic pressure P0 was presented by Ramsey et al. [4], and a deriva- tion o f the formula can be found in ref. [5].

Since rubidium and cesium are both group IA elements (the alkali metals), one would expect the spin relaxation in the Cs-Xe system to have similar characteristics as in the R b - X e system. The first ex- perimental studies of spin relaxation of 129Xe in the Cs-Xe system were reported by Andrianov et al. [6] and by Lopatin [7]. However, their results are quali- tatively different from the extensive measurements of R b - X e spin exchange rates [4,8]. At a third body gas pressure o f 50 torr, Lopatin reported the ratio of the

H e , N 2 _ s p i n relaxation cross sections to be OCs_Xe/tTCs__Xe -

3 [7]. Since the spin relaxation rate at a fixed cesium

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number density is directly proportional to the spin relaxation cross section, their result would indicate that the Cs-Xe spin relaxation rate at a He pressure o f 50 torr would be three times that at the same N 2 pressure. However, Zeng et al. [8] have shown that the spin relaxation rate of 129Xe in Cs with 50 torr of N 2 is approximately 70% of the maximum value, which corresponds to about 25 torr o f N 2. Thus, ac- cording to Lopatin et al.'s results, the spin relaxation rate o f 129Xe in Cs with 50 tort o f He would be about 2.1 times greater than the maximum rate with N 2 as the third body gas. This would be a clear indication that the universal spin relaxation function discussed by Ramsey et al. is invalid for Cs. We have therefore repeated the experiments of Lopatin et al. on spin re- laxation of 129Xe in Cs vapor with N 2 and He as third body gases. As we describe in detail below, our experi- mental data are fitted well by the same universal spin relaxation function which works for Rb, and our data is in substantial disagreement with that o f Lopatin.

The hamiltonian representing the basic interaction in Cs-Xe systems is as follows [5]:

H = A I . S + ~/N. S + ~ K . S + gsl~BS. B . (1)

The first term in eq. (1) is the hyperfine interaction, which couples the cesium electron spin S to its own nuclear spin/. The term "yN. S is the coupling between S and the rotational angular momentum N of the Cs - Xe van der Waals molecule. The term c~K. S represents

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Volume 112A, number 3,4 PHYSICS LETTERS 21 October 1985

the Fermi contact interaction between S and the nuclear spin K of xenon. The last term is the Zeeman term. Since it has been found experimentally that the spin relaxation is dominated by the formation of Cs - Xe van der Waals molecules [3], the Cs induced Xe nuclear spin relaxation rate can be written as

1~To = PK/TK, (2)

where lIT K is the Cs-Xe molecular formation rate per Xe atom and PK is the probability of spin exchange during the molecular lifetime, ~-. Using perturbation theory one can write PK as a power series in l/x, where the Bre i t -Rabi parameter x is defined to be ~tN/oL. The value o f x has been measured to be 2.9 for 133Cs-129Xe molecules [6]. To the order of x -2 ,

one finds [5]

PK = (22/3x2) ( ¢/8)2 / [ 1 + (¢/8) 2 ]

+ ~(1 - 2/x 2) (q~/2x)2/[1 + (~/2x) 2]

+ ~-(1 - 7/2x 2) (3¢/8x)2/[1 + (3~b/Sx) 2 ]

+ ~-(1 - 6/x 2) (¢/4x)2/[1 + (¢/4x) 2 ]

+ ~-(1 - 15/2x 2) ((~/8x)2/[1 + (¢/8x) 2 ]

+ ~ (1 - 6/x2)(3¢/4x2)2/[1 + (3@/4x2) 2 ]

+ ~4(1 _ l O / x 2 ) ( 5 ¢ / 4 x 2 ) 2 / [ 1 + (5~/4x2) 21 . (3)

The phase angle,

¢ = 7Nr/h, (4)

is the product of the spin-rota t ion interaction fre- quency and the mean molecular lifetime.

Since, under the experimental conditions of this

work, the molecular lifetime r is inversely proportional to the third body gas pressure, the phase angle can be written as

4) = p o / p , (5)

where P0 is the characteristic third body gas pressure at which the molecular breakup rate r - 1 is equal to the spin-rotat ional frequency 7N/Ii. The molecular formation rate per Xe atom (~K 1) and the breakup rate of the Cs-Xe molecules ( r - 1 ) are related by

[Xe] TK 1 = [CsXe] r -1 (6)

when the system reaches equilibrium. The chemical equilibrium constant K is defined as

K = [CsXe] / [Cs] [Xe] , (7)

which is independent of the nature of the third body gas. Making use of eqs. (3) - (7) , one can rewrite eq. (2) as

1/T 0 = R0q~-lpK(~b), (8)

where R 0 = K [Cs] 7N/h. Hence from eq. (8), we ex- pect to find that the relaxation rate of 129Xe depends upon the third.body gas pressure through the universal function ¢ - l p K ( ¢ ) at a given cesium number density. (Both 7N/I~ and K are independent of the nature of the third body gas.) In this work we will compare the measured spin relaxation rates and the predicted rates [eq. (8)] at [Cs] = 1012 cm -3 fo rN 2 and He at various pressures.

The experimental apparatus is shown in fig. 1. The spherical pyrex cell is about 30 mm in diameter; it contains a small droplet of cesium metal (133Cs), 1

n-

p- _J LL

CP

h / 4

~o J

o 5

p-

, ~ O

~ 0 J OJ

0 r ' ' CHART - , - o R E C O R D E R

REFERENCE 142 KHz)

~VARIASLEOI I S'GNAL IrR,GGER I___~_r-R I

Fig. 1. Experimental arrangement.

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Volume 112A, number 3,4 PHYSICS LETTERS 21 October 1985

torr ofisotopically enriched Xe (69% 129Xe by weight), and between 20 and 200 tort of a third body gas (N 2 or He). Newly made cells have been observed to have Cs vapor pressures lower than the Cs saturation pres- sure in this and previous experiments in this labora- tory. To avoid this effect, all the cells used in this work were cured by baking them at 85°C for a week. A dc magnetic field in the direction of the optical axis (~ 4 G) defines the Larmor frequencies of 133Cs. The cell is placed inside an oven - a Pyrex cylinder with an air jacket through which hot air may flow in order to vary the temperature of the cell. The experi- ment is performed at temperatures between 40 ° and 60°C, corresponding to cesium number densities be- tween 1011 and 1012 cm -3. During the pump phase of the experiment, which lasts about 15 minutes, the Cs vapor inside the cell is optically pumped by a Cs resonance lamp using a circular polarizer (CP) and a D1 filter which transmits light of wavelength 8943 A. The optical pumping polarizes the cesium electron spin; the xenon nuclear spin is then polarized through spin exchange. During the probe phase, the circular polarizer is removed; a small amount of elliptical polarization is introduced in the unpolarized light by the repolarized Cs atoms and is measured with a photoelastic modulator, a linear polarizer, a photo- diode detector, and a lock-in amplifier. This signal is proportional to the Xe polarization signal since the repolarized Cs atoms live only for about 1 ms. Small amounts of elliptical polarization caused by the opti- cal components of the apparatus, which do not change much during the course of a run, are compensated by inserting a 5 mm × 5 mm circular polarizer at an ap- propriate location in the much larger-area probe beam. However, the baseline of the exponential decay of the xenon polarization signal could still drift slowly due

to temperature fluctuation during the data taking period. To reduce errors in the determination of the baseline, the adiabatic fast passage technique [9] is used to reverse periodically the Xe spins and thus the sign of the polarization signal. The frequency of the transverse rf field is swept from 0.3 to 9.8 kHz, passing through the Xe resonance frequency (~4.7 kHz in this case). Care is taken to make sure that the adiabatic fast passage condition is satisfied. The xenon polariza- tion signal is determined by subtracting the average signals during the four seconds before and after a flip. An Apple IIe computer controls the flip rates, acquires and analyzes the data.

The xenon polarization signal is fitted to a function of the form

A(t) = A0(1 - e) n exp(-t/Txe),

where e is the loss of polarization at each spin flip, n is the number of flips, and TXe is the 129Xe nuclear spin relaxation time. Varying the interval between consecutive spin flips allows one to determine both Txe and e. Fig. 2 is a typical decay curve. The relaxa- tion rate 1/Txe is composed of two terms,

1/rxe = 1~To + 1/Twan, where 1/T 0 = C[Cs] and 1/Twall is independent of [Cs] and is due to wall relaxation. The values of C and 1/Twa n are determined by measuring 1/Txe versus [Cs] (fig. 3). The cesium number density is deduced from measuring the cell temperature and using the semi-empirical saturation vapor pressure formula [ 10]. The effect of the third body gas is determined by measuring 1/T 0 for cells with different third body gas pressures (the filling pressure at room temperature).

At a cesium number density of 1012 cm -3 (60.6°C), the Cs induced spin relaxation rate 1/T 0 is

rain.

Fig. 2. Representative data of 129Xe nuclear spin relaxation in 133Cs vapour as observed with the apparatus of fig. 1.

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Volume 112A, number 3,4 PHYSICS LETTERS 21 October 1985

I

~ 2 ? O

r~

Z 0 7- 4

_ J

CELL No. 35t ( H E - - 5 2 TORR) I l l P I I I I I I T I I I n r I l l [ l i l T [ I I I T I I I I

Slope : 1.250 + .062 Intercept : . 9 3 + .26

i i i i i i i i I i 1 i i i t l i i i i i i i I i i i i J i l l

3 4 5 6 7 8 CESIUM DENSITY ( I O t~ C M - 3 )

Fig. 3. 129Xe nuclear spin relaxation rate versus 133Cs num- ber density.

plotted as a function of the third body gas pressure in fig. 4. The characteristic third body gas pressure of helium in the formation or breakup of the 133Cs- 129Xe molecules is

Po(He) = 384 torr,

while that of N 2 is

P0(N2) = 177 tort .

The solid lines in fig. 4 are given by eq. (8) with R 0 and P0 being the fitting parameters. The statistical uncertainty in the experimental data is about 10%. When plotted as a function of the dimensionless pres- sure (P/Po), the spin relaxation rate of 129Xe is easily seen to be described by a universal function (fig. 5).

The much larger spin relaxation rate of 129Xe in Cs with 50 torr of He as the third body gas compared

t 5

Tu 12' L.~ CO

9 i

0

6

3

o He

Nz ~

I I I I I I 40 BO 120 160 200 240

THIRD BODY GAS PRESSURE (TORR)

Fig. 4. 129Xe nuclear spin relaxation rate versus third body pressure.

~6

I U ~42 u~

0 8

o

4

r i i i i r i * i i

_ N 2

~ - H e

- - I I I I I I 1 t I I l

0.2 0.4 0.6 O8 ~O DIMENSIONLESS PRESSURE (P/Po t

Fig. 5. 129Xe nuclear spin relaxation rate as a function of dimensionless third body pressure (P/Po) is described by a universal spin relaxation function.

to 50 torr N 2 as the third body gas reported by Lopatin [7] appears to be spurious. While it is diffi- cult to comment on another experiment we mention two possible sources for this discrepancy. First, the determination o f Cs number density from temperature measurements is notoriously unreliable. In this work, every effort has been made to ensure that the Cs number density corresponds to thermal equilibrium at a well defined temperature. We also have indepen- dently checked the number density by observing the Faraday rotation of light by the vapor in a strong magnetic field (~ 1724 G). Nevertheless, uncertainties in the Cs number density are still the major source of systematic error in this work; it is estimated to be about -+15%. Secondly, we observe the longitudinal spin relaxation rate, whereas the transverse spin relax- ation rate was measured in refs. [6,7]. The transverse spin relaxation rate is sensitive to magnetic field in- homogeneities which could conceivably have affected the observed spin relaxation rate of refs. [6,7]. Field inhomogeneities do not affect our measurements.

In conclusion, the dependence upon various third body gas pressures of 129Xe spin relaxation rates in Cs vapor is similar to that already observed for 129Xe in Rb vapor, and all of the data is well described by a universal spin relaxation function.

This work was supported by the US Air Force Office o f Scientific Research under Grant No. AFOSR-81-0104-C.

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Volume 112A, number 3,4 PHYSICS LETTERS 21 October 1985

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[3] N.D. Bhaskar, W. Happer, M. Larsson and X. Zeng, Phys. Rev. Lett. 50 (1983) 105.

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[5] W. Happer, E. Miron, S. Schaefer, D. Schreiber, W.A. van Wijngaarden and X. Zeng, Phys. Rev. A29 (1984) 3092.

[6] B.A. Andrianov, V.M. Lopatin, P.S. Ovcharenko, Yu.M. Petukhov and E.M. Sychugov, Sov. Tech. Phy~ Lett. 7 (1981) 363.

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W. Happer, Phys. Rev. A31 (1985) 260. [9] C.P. Slichter, Principles of magnetic resonance

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