RMP Colloquia

Spin-exchange optical pumping of noble-gas nuclei

Thad G. Walker
Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706

William Happer
Department of Physics, Princeton University, Princeton, New Jersey 08544

Spin-exchange optical pumping of mixtures of alkali-metal vapors and noble gases can be used to
efficiently polarize the nuclei of the noble-gas atoms. Liters of noble gases at standard temperature
and pressure and with nuclear spin polarizations of several tens of percent are now used in many
applications. The authors describe the basic phenomena that govern the spin-exchange process and
review the physics of angular momentum transfer and loss in optical pumping and spin-exchange
collisions. [S0034-6861(97)00802-7]

CONTENTS sions between the alkali-metal atoms and noble gas at-
oms transfer some of the electron-spin polarization to
I. Introduction 629 the nuclei of the noble gas.
II. Overview of Spin-Exchange Optical Pumping 630 Many applications use spin-exchange optical pumping
III. Optical Pumping 630 for producing large numbers of spin-polarized nuclei.
A. Interaction of alkali-metal atoms with circularly Some examples are the first determination of the neu-
polarized light 630
tron spin-structure function, measured by scattering po-
B. Collisions between alkali-metal atoms 631
C. Light propagation 632
larized, high-energy electrons from highly polarized tar-
IV. Spin-Exchange 634 gets of 3 He (Anthony et al., 1993); magnetic resonance
A. Rate equations 634 imaging of lungs and other organs of the human body
B. Photon efficiency 635 with the gases 3 He and 129Xe (Albert et al., 1994;
V. Spin-Dependent Interactions 635 Middleton et al., 1995); studies of surface interactions
A. Wave functions 636 (Wu et al., 1990; Raftery et al., 1991); studies of funda-
B. Hyperfine interactions 637 mental symmetries (Newbury et al., 1991; Chupp et al.,
1. Isotropic 638 1994); neutron polarizers and polarimeters (Thompson
2. Anisotropic 638 et al., 1992). Recently developed high-power diode-laser
C. Spin-rotation interaction 639
arrays, which can provide tens to hundreds of watts of
1. Alkali-metal core 639
2. Noble-gas core 639
pumping light, have greatly decreased the cost and im-
VI. Other Relaxation Processes 640 proved the performance of spin-exchange optical pump-
A. Relaxation in alkali-metal collisions 640 ing, and so its use seems likely to grow. An in vivo image
B. ¹B relaxation 640 of a human lung, obtained using 3 He gas that was polar-
C. Wall relaxation 640 ized by spin-exchange optical pumping, is shown in
D. Noble-gas self-relaxation 640 Fig. 1.
VII. Summary 641 Laser technology is progressing so rapidly that the de-
Acknowledgments 641 tails of spin-exchange optical pumping systems are con-
References 641 tinually changing. Familiarity with the basic physics of
spin-exchange optical pumping will make the exploita-
tion of new technology much more efficient, and one
goal of this colloquium is to provide a convenient sum-
I. INTRODUCTION mary of the current state of knowledge. We shall also
point out important gaps in our understanding and areas
In spin-exchange optical pumping, circularly polarized where further research would have important payoffs.
resonance light is absorbed by a saturated vapor of After a brief overview in Sec. II, the interchange of an-
alkali-metal atoms contained in a glass cell. The cell also gular momentum between a light beam and alkali-metal
includes a much larger quantity of noble-gas atoms. In atoms is discussed in Sec. III. The interchange of spin
well-designed systems, nearly half of the spin angular between alkali-metal atoms and the nuclei of noble-gas
momentum of the absorbed photons is transferred to the atoms is discussed in Sec. IV. The fundamental origin of
alkali-metal atoms, thereby spin-polarizing the valence the spin-dependent interactions between alkali-metal at-
electrons of the alkali-metal atoms. Subsequent colli- oms and noble-gas atoms is discussed in Sec. V. Since

Reviews of Modern Physics, Vol. 69, No. 2, April 1997 0034-6861/97/69(2)/629(14)/$12.10 © 1997 The American Physical Society 629
630 T. G. Walker and W. Happer: Spin-exchange optical pumping . . .

nitrogen. Although any of the alkali metals are suitable,

rubidium is often chosen. The high vapor pressure of
rubidium allows operation at modest temperatures
where chemical attack on the glass container is not a
problem. The 7947 Å resonance line lies in a region of
the spectrum where intense, tunable light sources such
as dye lasers, titanium sapphire lasers, and gallium alu-
minum arsenide injection lasers exist. A simple oven
keeps the cell at a constant temperature, usually in the
range between 80 °C and 130 °C. This ensures an ad-
equate saturated vapor pressure (typically 1011 to 1014
cm 23 ) from a few droplets of Rb metal in the cell. A
few to many tens of watts of circularly polarized laser
light spin-polarizes the alkali-metal atoms via optical
pumping. The nitrogen, which is chemically inert, sup-
presses reradiation of light by quenching the excited at-
oms. The pressure of the noble gas which is to be polar-
ized by spin-exchange is usually in the range of 10 Torr
to 10 atmospheres. During binary collisions, the hyper-
fine interaction between the alkali-metal electron and
the noble-gas nucleus partially transfers spin polariza-
tion from the alkali-metal atoms to the noble-gas atoms.
Repeated collisions increase the nuclear-spin polariza-
tion to several tens of percent, typically five orders of
FIG. 1. Image of a human lung using spin-exchange-polarized magnitude larger than the thermal polarization obtain-
3
He (MacFall et al., 1996). able in even the largest laboratory magnetic fields.
The buildup of the nuclear polarization of the noble
the physics of these interactions is subtle, Sec. V is gas is most conveniently monitored by nuclear magnetic
rather detailed. The most important parasitic spin-loss resonance (NMR). The nuclear polarization is so large
mechanisms of alkali-metal atoms and noble-gas atoms that almost any continuous or pulsed NMR method will
are discussed in Sec. VI. work. Indeed, masing of the highly polarized spins can
easily occur if high-Q NMR coils are used (Chupp et al.,
1994). The polarization can be absolutely calibrated by
II. OVERVIEW OF SPIN-EXCHANGE OPTICAL PUMPING comparison with the NMR signal from a water sample in
a cell with the same shape (Bhaskar et al., 1982). One
Figure 2 shows a typical experimental arrangement can also measure the absolute noble-gas nuclear polar-
for spin-exchange optical pumping. A glass cell of a few ization by observing the resulting shift of the electron-
cm 3 volume, carefully prepared to remove paramagnetic paramagnetic-resonance (EPR) frequencies of the
impurities from the walls (Newbury, Barton, Cates, alkali-metal atoms (Newbury, Barton, Bogorad, et al.,
Happer, and Middleton, 1993), contains the gases of in- 1993). The EPR shifts result from the hyperfine interac-
terest, namely, alkali-metal vapor and a noble gas, plus tion and are typically a few kilohertz for situations of
practical interest. As is well known, frequency measure-
ments can be relatively free of systematic errors. It is
also possible to monitor optically the small electron-spin
polarization induced in a non-optically-pumped alkali-
metal vapor by the nuclear-spin polarization of the
noble gas (Bhaskar et al., 1983; Zeng et al., 1983).

III. OPTICAL PUMPING

A. Interaction of alkali-metal atoms with circularly

polarized light

Optical pumping uses light to spin-polarize both the

electron spin S and the nuclear spin I a of the alkali-
metal atoms1 (Happer, 1972). The atoms are subject to a

FIG. 2. Experimental arrangement for spin-exchange optical 1

Here and later, the subscripts a and b refer to alkali-metal
pumping. and noble-gas atoms, respectively.

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

 T. G. Walker and W. Happer: Spin-exchange optical pumping . . . 631

FIG. 3. The interaction of alkali-metal atoms with left-

circularly ( s 1 ) polarized light.

magnetic field applied along the z axis of a coordinate

system, so the Hamiltonian for the alkali-metal atoms is FIG. 4. Singlet and triplet potential energies as a function of
the internuclear separation R between a pair of cesium atoms
ma (Krauss and Stevens, 1990).
H a 5A a Ia •S1g s m B S z B 0 2 I B . (1)
I a az 0
amagat or more (Happer, 1972).
The first term is the hyperfine interaction, while the re- (d) As a result of (b) and (c), the nuclear-spin polar-
maining terms give the interaction of the electron and ization of the atom is conserved in the time interval be-
nuclear moments with the external applied field. In low tween excitation by a pumping photon and deexcitation
fields, used for most spin-exchange optical pumping ex- by a quenching collision (Bhaskar et al., 1981).
periments, the hyperfine interaction dominates over the Under these assumptions, the light spin-polarizes the
Zeeman interactions, so the eigenstates of H a are also alkali-metal electrons as shown in Fig. 3. Left-circularly
eigenstates of the total angular momentum F5S1Ia and polarized resonance light excites atoms from the spin-
its projection F z along the external field. We shall be down (m S 521/2) sublevel of the 2 S 1/2 state into the
interested mainly in the observables S z , I az , and spin-up sublevel (m J 51/2) of the 2 P 1/2 state. Collisions
F z 5S z 1I az . In general we describe the states of the with noble-gas atoms rapidly equalize the sublevel popu-
alkali-metal atoms with a density matrix r a whose diag- lations of the excited state. Then quenching collisions
onal elements give the probability of finding the atom in with N 2 molecules repopulate both ground-state sublev-
a given state. els with nearly equal probability. Since the atoms have
Optical pumping can be quite complex in the most 21/2 units of electron-spin angular momentum before
general case, especially at low gas pressures where the absorbing the photons and 0 units of electron-spin an-
hyperfine structure of the absorption lines is well re- gular momentum after being quenched from the excited
solved (Happer, 1972). However, in almost all applica- state, on the average each absorbed photon deposits
tions of spin-exchange optical pumping the following 1/2 unit of spin angular momentum in the vapor, the
simplifying conditions prevail: remainder being lost to translational motion.
(a) Circularly polarized light is used, resonant with the The mean photon absorption rate per atom is
transition from the 2 S 1/2 ground state of the alkali-metal
atom to the lowest 2 P 1/2 excited state. ^ d G & 5 ~ 122 ^ S z & ! R p (2)
(b) Pressure broadening of the absorption line makes where R p , the absorption rate for unpolarized atoms,
the alkali-metal hyperfine structure unresolved. For depends on the spectral profiles of the light and the tran-
most applications of spin-exchange optical pumping the sition line shape. In practice, both ^ S z & and R p are func-
total noble-gas and nitrogen densities exceed one tions of position in the pumping cell. Since each photon
amagat,2 giving absorption linewidths of typically 30 adds on the average \/2 of angular momentum, the total
GHz or more. For comparison, the largest alkali-metal alkali-metal atomic spin ^ F z & grows with time as

S D
ground-state hyperfine interval, that of 133Cs, is only 9
d ^ F z& 1
GHz. 5R p 2 ^ S z & . (3)
(c) The quenching gas eliminates radiation trapping as dt 2
a source of relaxation. This requires N 2 densities of 0.1
B. Collisions between alkali-metal atoms

2 Spin-exchange collisions between pairs of optically

The density of an ideal gas at STP is 1 amagat
5 2.6931019 cm 23 . pumped alkali-metal atoms strongly affect the optical

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

632 T. G. Walker and W. Happer: Spin-exchange optical pumping . . .

FIG. 5. Alkali metal spin exchange. (a) Example of a spin-exchange collision between two alkali-metal atoms. The total spin of the
alkali-metal atoms is rigorously conserved, but the level populations are redistributed by the collisions. (b) Spin-temperature
distribution of the spin sublevels, arrived at after many spin-exchange collisions.

pumping process by transferring polarization between is called the paramagnetic coefficient.3 The rate at which
the electron spin and the nuclear spin. The alkali-metal- the system approaches the spin-temperature distribution
dimer interaction potential, sketched in Fig. 4, has sin- depends on the magnetic-field strength (Walker and
glet and triplet components. The large splitting of the Anderson, 1993a, 1993b).
singlet and triplet potentials causes the electron spins to Under the conditions of spin-exchange optical pump-
rotate about each other many times during a single col- ing, the rate of electron-spin exchange collisions is typi-
lision. The spin-exchange cross sections are therefore cally between 104 and 106 sec 21 , which is much greater
quite large, typically 2310214 cm 2 . This efficient process than other collisional relaxation rates and comparable to
was first identified by Purcell and Field (1956) to explain or greater than R p , so the alkali-metal atoms are well
the intensity of the 21-cm line radiation in radio as- described by the spin-temperature distribution. The spin
tronomy.
parameter b a depends on position in the vapor because
Spin-exchange collisions conserve the total spin angu-
of spatial variation of pumping light intensity, and b a
lar momentum of the colliding atoms, but redistribute
may also change with time as the atomic-spin polariza-
the angular momentum between the ground-state sub-
levels [Fig. 5(a)]. During a spin-exchange collision the tion evolves under the influence of optical pumping and
hyperfine interaction has little effect, but between colli- relaxation mechanisms. Even when the rate of spin-
sions it transfers angular momentum internally between exchange collisions is small compared to the optical
the nuclear and electron spins of each alkali-metal atom. pumping rate, the equilibrium state of the atoms will be
Successive collisions like those of Fig. 5(a) lead to the well-described by a spin-temperature if the conditions
‘‘spin-temperature’’ distribution (Anderson et al., 1960) (a)–(c) prevail and if the collisions are of sufficiently
illustrated in Fig. 5(b): short duration that the resulting spin relaxation is well
described as ‘‘electron randomization.’’
e baSz e b a I az
r a5 . (4)
Z ~ S, b a ! Z ~ I a , b a ! C. Light propagation

The spin partition function for arbitrary spin K is Light radiated by the alkali-metal atoms is nearly un-
sinh@ b ~ K11/2!# polarized and can be reabsorbed by the Rb atoms,
Z ~ K, b ! 5 . (5) thereby optically depumping the atoms. High Rb vapor
sinh@ b /2#
pressures are necessary for spin-exchange optical pump-
The spin-temperature parameter b uniquely determines ing experiments, in order to keep spin-exchange rates
the population distribution for the spin sublevels, so all large enough to attain high polarizations. Thus the cell is
observables can be expressed in terms of b . In particu- usually many optical depths thick, and a single photon
lar, the mean value of K z is can be scattered several times and thus depolarize sev-
e ~ K, b ! b
^ K z& 5 tanh , (6)
2 2 3
Explicitly, e (K, b ) 5 (2K 1 1)coth( b /2)coth( b @ K 1 1/2 # )
where 2 coth2 ( b /2). This decreases from 4K(K 1 1)/3 at small po-
larization (b!1) to 2K for large polarization (b@1); for K
e ~ K, b ! 52 ^ K ~ K11 ! 2K 2z & (7) 5 1/2, e(1/2,b)=1.

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

 T. G. Walker and W. Happer: Spin-exchange optical pumping . . . 633

FIG. 7. Attenuation of light as a function of distance through

the cell, for (a) low and (b) high incident intensities. l n is the
attenuation length for unpolarized atoms.

FIG. 6. Polarization as a function of position near the cell wall, The diffusing alkali-metal atoms (density n a ) carry a
where diffusion losses reduce the polarization of the alkali- spin flux
metal atoms. For I a .1/2, S z increases more slowly than F z
] 1
because at low polarizations the angular momentum is prima- j a 52n a D a ^ F & ' n a AR p D a ~ 2I a 11 ! (9)
rily contained in the nuclear spin. ]z z 2
to the wall of the cell through which the pumping light
eral atoms before escaping from the cell (Tupa et al., enters. The diffusion skin thus attenuates the photon
1986, 1987). The N 2 quenching gas removes this damag- flux by an amount DJ52j a . For efficient spin-exchange
ing depolarization mechanism so that intense circularly optical pumping, this flux must be much smaller than the
polarized laser light can still penetrate and illuminate flux J(0) incident on the cell. In spin-exchange pumping
most of the optically thick cell (Bhaskar et al., 1979), as of 3 He, small alkali-metal/He spin-exchange cross sec-
indicated in Fig. 2. In the illuminated part of the cell the tions necessitate high alkali-metal number densities,
spin polarization is nearly 100%. In the dark volume possibly violating the condition of negligible spin flux to
where little light penetrates, the spin polarization is the wall. Tuning the laser somewhat off resonance to
nearly zero. The boundary between the illuminated and decrease the absorption cross section s minimizes wall
dark volumes of the cell is about one optical depth thick. losses while permitting absorption of most of the pump-
In a well-designed system, matching of the gas composi- ing light (Wagshul and Chupp, 1994; Larson et al., 1991).
tion, the cell temperature, and the spatial profile of the Inside the bulk of the cell, absorption by the nearly
laser intensity allows most of the cell to be illuminated. fully polarized alkali-metal atoms attenuates the laser
Diffusion losses are negligible within the bulk of the beam:
cell at the high pressures of these experiments, but dif- dJ
fusion does produce a thin layer near the cell walls 52n a ^ d G & 52n a ~ 122 ^ S z & ! R p . (10)
dz
where the polarization drops from nearly 100% to zero.
The walls are usually bare glass or are coated with vari- Collisional spin relaxation and spin exchange make the
ous silicone derivatives. The residence time of an ad- factor 122 ^ S z & 'Ḡ /R p , where Ḡ is the alkali-metal re-
sorbed alkali-metal atom on such a wall is sufficiently laxation rate. For pumping light with a much narrower
long that interactions at the wall completely depolarize spectral width than that of the optical absorption cross
both electron and nuclear spins. Thus at the walls section, R p } J, giving
^ F z & 50, while far away from the wall ^ F z & 'I11/2. In
steady-state, optical pumping [Eq. (3)] balances the dif- J ~ z ! 5J ~ 0 ! 2DJ2Ḡ n a z. (11)
fusion losses, so near the cell walls This linear attenuation changes to exponential attenua-

2D a
d ^ F z&
2

dz 2 5R p
1
2 S
2 ^ S z& , D (8)
tion when the photon flux cannot maintain high spin
polarization of the alkali-metal atoms, that is, when
J<Ḡ / s (see Fig. 7).
where D a is the alkali-metal atom diffusion coefficient. For broadband pumping sources like diode laser ar-
Assuming spin-temperature equilibrium, Fig. 6 shows a rays, no well-defined mean free path for the pumping
numerical integration of Eq. (8). Defining a diffusion photons exists, so the division of the absorption cell into
length l D 5 A2D a /R p , we see that S z is very close to the illuminated regions with high spin polarization of the
bulk value within a few diffusion lengths. alkali-metal atoms and dark regions with negligible spin

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

634 T. G. Walker and W. Happer: Spin-exchange optical pumping . . .

Most of the residual molecular contribution has the

same selection rules as binary collisions—that is, both
DF50 and DF561 transitions are permitted, so the
resulting relaxation is nearly indistinguishable from that
due to binary collisions. Since we are interested in spin
exchange at high gas pressures, we shall henceforth treat
the relaxation as if it were all due to binary collisions.
Spin-dependent interactions, denoted V 1 (R), produce
the spin transfer and relaxation in collisions. For spin-
exchange optical pumping, evidence suggests that the
spin-rotation interaction between S and the rotational
angular momentum N and the isotropic hyperfine inter-
action between S and the noble-gas nuclear spin Ib
dominate the spin-exchange process:
V 1 ~ R! 5 g ~ R ! N•S1A b ~ R ! Ib •S. (12)
FIG. 8. Polarization transfer processes. (a) Formation and We discuss these interactions in some detail in Sec. V,
breakup of an alkali-metal/noble-gas van der Waals molecule. but, simply stated, the spin-rotation interaction arises
(b) Binary collision between an alkali-metal atom and a noble- from magnetic fields produced by the relative motion of
gas atom. the charges of the colliding atoms, while the isotropic
hyperfine interaction arises from the magnetic field in-
polarization is blurred. The broad laser linewidth wastes side the nucleus of the noble-gas atom. V 1 depends
photons, since photons with frequencies too far from the strongly on interatomic separation R.
peak optical absorption frequency pass through the cell
unattenuated. However, this waste is more than com- A. Rate equations
pensated for by the cost savings of inexpensive diode
laser arrays as compared to Ti:Sapphire lasers or dye The spin-dependent interaction [Eq. (12)] causes tran-
lasers. sitions between various spin states. The spin-rotation in-
teraction produces relaxation of the alkali-metal elec-
tron spins, while the isotropic hyperfine interaction
IV. SPIN-EXCHANGE transfers angular momentum back and forth between
the alkali-metal electron spins and the noble-gas nuclear
The key process in spin-exchange optical pumping is
spins. In the spin-temperature limit for the alkali-metal
collisional transfer of polarization between optically
atoms, the following two rate equations describe the
pumped alkali-metal atoms and the nuclei of the noble-
gas atoms. As indicated in Fig. 8, the transfer of angular evolution of angular momentum as a result of collisions
momentum occurs either while the atoms are bound in between the alkali-metal atoms and the noble-gas atoms
van der Waals molecules or in simple binary collisions under the influence of V 1 :
between the atoms. For 3 He, binary collisions dominate d ^ F z&
the spin relaxation, and the contribution from van der 52G a ~ g ! ^ S z & 2G a ~ A b !@ e ~ I b , b b ! ^ S z & 2 ^ I bz & #
dt
Waals molecules is negligible. The time for a binary col-
(13)
lision (;10212 sec) is so short that the collision can in-
duce both DF561 and DF50 transitions between the d ^ I bz &
hyperfine sublevels of the alkali-metal atom. For heavier 5G b ~ A b !@ e ~ I b , b b ! ^ S z & 2 ^ I bz & # . (14)
dt
noble gases like 129Xe at total gas pressures of a few tens
of Torr, the contributions of van der Waals molecules to Detailed balance requires that n b G b (A b )5n a G a (A b ),
the spin relaxation can greatly exceed the contribution where n k is the density of species k. For the important
of binary collisions. At such low pressures, the collision- noble gases 3 He and 129Xe with I b 51/2, Eq. (14) sim-
ally limited lifetime of the van der Waals molecules is plifies to
long enough (>1029 sec) that the total spin angular mo- d ^ I bz &
mentum F5I a 61/2 of the alkali-metal atoms is a good 52G b ~ A b !@ ^ I bz & 2 ^ S z & # . (15)
dt
quantum number and the molecules induce relaxation
through DF50 transitions. A magnetic field of a few Thus, in steady-state, if all other relaxation mechanisms
hundred Gauss is sufficient to suppress the relaxation are neglected, the noble-gas nuclear-spin polarization
due to van der Waals molecules at these low pressures equilibrates to the same value as the alkali-metal
(Happer et al., 1984). At the multiatmosphere pressures electron-spin polarization.
of interest for practical spin-exchange optical pumping, The characteristic rates G may be estimated from
the collisionally limited lifetimes of the van der Waals time-dependent perturbation theory (Walker, 1989). For
molecules are so short that their contribution to the re- example, given A b (R) (Sec. V.B), the spin-exchange
laxation are small compared to that of binary collisions. rate is

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

 T. G. Walker and W. Happer: Spin-exchange optical pumping . . . 635

where R 0 is the distance of closest approach, w̄ is the

thermal speed, and t is the collision time. Spin-exchange
and relaxation cross sections obtained from the rates us-
ing the relation G5n s w̄ are shown in Figs. 9 and 10.
These figures show that, for most atom pairs, the spin-
relaxation cross sections exceed the spin-exchange cross
sections.

B. Photon efficiency

The efficiency of transfer of angular momentum in the

spin-exchange process is critical for applications, such as
magnetic resonance imaging and polarized targets, that
require large numbers of highly polarized noble-gas nu-
clei. The spin-rotation interaction represents a funda-
mental limit on the efficiency, but other relaxation
mechanisms contribute as well. As pointed out above
(Sec. III.C), in well-optimized systems, relaxation in the
FIG. 9. Spin-exchange cross sections for alkali-metal/noble-gas bulk dominates over spin relaxation of the alkali-metal
atom pairs: open symbols, theoretical estimates (Walker, atoms at the walls. Then bulk relaxation mechanisms
1989); filled symbols, measurements for Na-He (Soboll, 1972), limit the photon-to-polarization conversion efficiency.
Rb-He (Coulter, 1989), Rb-Ne (Chupp and Coulter, 1985), and For small noble-gas polarizations, the angular mo-
Rb-Kr (Schaefer et al., 1990). mentum of the noble-gas nuclei increases at a rate found
from Eq. (14):

G b ~ A b ! 5n a Ep
2 0
`
dbb E
0
`
d 3 wf ~ w! w n bV
d
^ I & 5n b VG b ~ A b ! e ~ I b ,0! ^ S z &
dt bz
(18)

3 UE `

2`
dtA b ~ R ~ t !! /\ , U 2
(16)
where V is the cell volume, assumed to be fully illumi-
nated. Equations (3) and (13) give the rate at which pho-
tons are deposited in the cell as
which is an average over the impact parameter b, the
velocity distribution f(w), and the classical collision tra- n a VR p ~ 122 ^ S z & ! 52n a V @ Ḡ 1G a ~ A b ! e ~ I b ,0!# ^ S z & ,
jectory R(t). An order-of-magnitude estimate is (19)
A b~ R 0 ! 2t 2 where Ḡ includes relaxation arising from the spin-
G b ~ A b ! 'n a w̄ p R 20 , (17) rotation interaction in collisions with noble-gas atoms
4\ 2
and other processes such as spin relaxation in collisions
between alkali-metal atoms or alkali-metal–N 2 colli-
sions.
The ratio of Eq. (18) to Eq. (19) determines the trans-
fer efficiency (Bhaskar, Happer, and McClelland, 1982):
G a ~ A b ! e ~ I b ,0!
h5 . (20)
2 @ Ḡ 1G a ~ A b ! e ~ I b ,0!#
Estimates of the fundamental limiting efficiencies, where
Ḡ 5G a ( g ), range from 0.04 for Rb-Xe to 0.38 for K-He.

V. SPIN-DEPENDENT INTERACTIONS

In this section we describe the current understanding

of the physical origins of the spin-dependent forces that
are so important for spin-exchange optical pumping. An
alkali-metal atom and a noble-gas atom interact via both
FIG. 10. Spin-relaxation cross sections for alkali-metal/noble- a large spin-independent interaction V 0 (R) and the
gas atom pairs: open symbols, theoretical estimates (Walker, much smaller, spin-dependent part V 1 (R). V 0 can be
1989; Walker et al., 1995); filled symbols, measurements for used to calculate distorted partial waves for subsequent
Na-He (Soboll, 1972), Rb-He (Wagshul and Chupp, 1994), distorted-wave Born approximations of the spin-
K-Ar (Martin and Anderson, 1995), Rb-Ar,Kr,Xe (Bouchiat dependent effects of V 1 (Newbury, Barton, Bogorad,
et al., 1972), Cs-Kr (Beverini et al., 1973), and Na-Xe et al., 1993). Equivalently, at the high temperatures of
(Bhaskar, Hou, Ligare, Suleman, and Happer, 1980). interest, V 0 determines classical collision trajectories,

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

636 T. G. Walker and W. Happer: Spin-exchange optical pumping . . .

FIG. 12. Geometry used for description of the valence-

electron wave function in the presence of a noble-gas atom.
The rotational angular momentum of the atom pair is labeled
N.

1
f ki [ f knlm ~ rk ! 5 P ~ r !Y ~ u ,f !, (22)
r k knlm k lm k k
FIG. 11. Spin-independent interaction potentials V 0 between
noble-gas and alkali-metal atoms, as calculated by Pascale where P knlm (r k ) is a radial wave function of the dis-
(1983) and Pascale and Vandeplanque (1974). placement r k of the valence electron from the nucleus of
the atom k, and Y lm ( u k , f k ) is a spherical harmonic of
the angular coordinates u k , f k . Convenient radial wave
along which V 1 acts as a small perturbation (Walker, functions for core orbitals are available in tabular form
1989). The best V 0 (R) available use pseudopotential (Clementi and Roetti, 1974; McLean and McLean,
methods constrained by scattering experiments (Buck 1981).
and Pauly, 1968; Pascale and Vandeplanque, 1974; Pas- The mixing coefficients c ai inside the alkali-metal core
cale, 1983), with examples shown in Fig. 11. can be estimated using the Fermi pseudopotential
(Fermi, 1934; Roueff, 1970),
2 p \ 2a
V F ~ R! 5 d ~ ra 2R! , (23)
A. Wave functions m
to describe the effective interaction between the valence
Understanding the small spin-dependent interactions electron and the noble-gas atom in terms of the electron
requires realistic wave functions for the valence electron mass m and the s wave scattering length a. This was first
in the presence of the noble-gas atom. In principle, these derived to explain the pressure shift of alkali-metal
wave functions could be supplied by ab initio theory, but Rydberg states but has since been used for a variety of
such wave functions have been calculated for only a few problems including neutron scattering (Kittel, 1963) and
cases, making it necessary to develop other methods. interactions in degenerate Bose gases (Huang, 1987).
These methods have generally been quite successful at Table I gives values for a. First-order perturbation
predicting the strengths of the various interactions and
often have simple physical interpretations.
The spin-dependent phenomena generally arise from TABLE I. Some important noble-gas characteristics for spin-
the electric and magnetic fields generated well inside the exchange optical pumping. S wave scattering lengths (a) for
cores of either the alkali-metal atom or the noble-gas electrons scattering from noble-gas atoms (From O’Malley
atom. It is convenient to split the electron wave function 1963). Orthogonalized wave values of the enhancement factor
c into separate parts. Inside each core, the wave func- h , representing the ratio of the electron wave function at the
noble-gas nucleus to that of the wave function in the absence
tion is represented as
of the noble-gas atom. (From Walker et al., 1987). The factor
G is a measure of the strength of the spin-orbit interaction in
c k ~ rk ! 5 f 0 ~ rk ! 1 ( c ki f ki ~ rk ! , (21) the core of the noble-gas atom.
i

where f 0 is the ground-state wave function of the alkali- Atom a (Å) h G (ev Å 5 )
metal electron in the absence of the noble-gas atom, and He 0.63 -9.5 0.00093
the sum extends over the excited orbitals of the alkali- Ne 0.13 15 0.24
metal atom for k5a, and over the occupied core orbitals Ar -0.90 -21 1.9
of the noble-gas atom for k5b. Figure 12 shows the Kr -1.96 35 12
geometry. Xe -3.4 -50 39
The free-atom orbitals have the form

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

 T. G. Walker and W. Happer: Spin-exchange optical pumping . . . 637

theory predicts
2 p \ 2a
c ai 52 f ~ R! f 0 ~ R! , (24)
mE ai ai
where E ai is the excitation energy of state i. These co-
efficients allow estimates of the alkali-metal isotropic
hyperfine shift, the alkali-metal anisotropic hyperfine in-
teraction, and the contribution to the spin-rotation inter-
action from the core of the alkali-metal atom. For each
of these cases either the s or p states dominate, so, ne-
glecting orbitals of larger l,

c a ~ ra ! 5 f 0 ~ ra ! 1 ( @ c ans f ans ~ ra ! 1c anp R̂• fanp ~ R!# .

n
(25)
FIG. 13. The valence-electron wave function c of Rb-He and
Here we use the vector p orbital defined by Rb-Xe as a function of position along the internuclear axis.
fknp 5 f knpx x̂1 f knpy ŷ1 f knpz ẑ
fails for the p wave inside the helium atom, so integra-
5 (m ~ 21 ! m f kn1m û2m , (26) tion of the Schrödinger equation is necessary (Walker
et al., 1987). Representative wave functions are shown in
depending on whether Cartesian or spherical basis unit Fig. 13.
vectors (û61 57(x̂6iŷ)/ A2, û0 5ẑ) are used.
A useful approximation for c b , the wave function in- B. Hyperfine interactions
side the noble-gas core, results from orthogonalizing the
undistorted wave function f 0 to the occupied core orbit- The spin-dependent interaction potential V 1 (R), in-
als. The orthogonalized wave (OW) approximation cluding terms neglected in Eq. (12), can be written as a
(Wu, Walker, and Happer, 1985) is analogous to the power series in the rotational angular momentum N and
well-established orthogonalized plane-wave approxima- the spin operators S, Ia , and Ib of the atomic pair, mul-
tion in solids (Cohen and Heine, 1961) and gives tiplied by coupling coefficients that are functions of the
c b ~ rb! 5 f 0 ~ R1rb! internuclear separation R:

2 (i f bi~ rb ! E d 3 rb8 f bi* ~ rb8 ! f 0~ R1rb8 ! . (27) V 1 ~ R! 5 g N•S1 (k A k~ R ! Ik •S

The sum extends over all occupied core orbitals of the
noble-gas atom.
1 (k B k~ R ! Ik • ~ 3RR21! •S
The unperturbed wave function varies slowly over the
volume of the noble-gas atom, so we represent it with
the first two terms (s wave and p wave) of a Taylor
1 (k C k~ R ! Ik • ~ 3RR21! •Ik . (31)
series in rb . With this simplification, Eq. (27) becomes

F
c b ~ rb ! 5 f 0 ~ R! 12 ( Q bns f bns ~ rb !
n
G
F
1¹f 0 ~ R! • rb 2R̂ (n Q bnp R̂• fbnp~ rb ! G (28)

where the s and p orbital moments are

Q bns 5 Ef bns ~ rb ! d
3
rb (29)

Q bnp 5
1
3
E rb • fbnp ~ rb ! d 3 rb . (30)

The first terms in each bracket of Eq. (28), the incident

wave in the scattering picture, are normally much
smaller than the others generated by the Coulomb po-
tential of the noble-gas atom. Since the ground-state he- FIG. 14. Spin-dependent interaction strengths as a function of
lium atom has no occupied p orbitals, the OW method interatomic separation.

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

638 T. G. Walker and W. Happer: Spin-exchange optical pumping . . .

Here g is the coefficient of the spin-rotation interaction, noble gas, and are hardly affected by d A a . However,
which will be discussed in Sec. V.C. The coupling coef- d A a causes the pressure shift of the frequency of opti-
ficients for the hyperfine interactions include the follow- cally pumped gas-cell clocks, like those used on the GPS
ing: A k , for the isotropic magnetic-dipole hyperfine in- satellite system (Riley 1981; Vanier, 1989).
teraction of the nucleus k; B k , for the anisotropic
magnetic-dipole hyperfine interaction; and C k for the
electric quadrupole interaction. Of these coupling coef- 2. Anisotropic
ficients, only A a remains finite when the atomic pair is Although quite a bit is known experimentally and
well separated. Figure 14 shows representative R depen- theoretically about the isotropic coupling coefficients
dences of each of the coupling coefficients. A k (R), little consideration has been given to the aniso-
tropic and quadrupole couplings B k (R) and C k (R).
1. Isotropic Based on precise experimental measurements (Childs
et al., 1982) of the hyperfine coupling in molecules like
The isotropic hyperfine interactions A a and A b origi- CaCl, which is isoelectronic to the van der Waals mol-
nate from the Fermi-contact magnetic fields produced ecule KAr, Happer et al. (1984) argued that only a small
by the two nuclei. The term A b is responsible for spin percentage of the spin exchange can be due to the an-
exchange and is given by (Herman, 1965) isotropic hyperfine interaction.
8 p g sm Bm b The noble-gas anisotropic coupling coefficient from
A b~ R ! 5 u c b~ 0 !u 2 Eq. (31) is
3I b

5
8 p g sm Bm b
3I b
u h f 0~ R !u 2, (32)
B b~ R ! 5
g Sm Bm b
Ib
E d 3r
u c ~ r! u 2
2r 5
@ 3r•R̂R̂•r2r 2 # . (34)

At large interatomic separations, this interaction gives

where the enhancement factor h 512 ( n Q bns f bns (0) the dipole-dipole interaction, averaged over the wave
represents the ratio of the perturbed wave function at function of the alkali-metal atom: B b (R)
the noble-gas nucleus to what it would be in the absence 5g S m B m b /I b R 3 . For heavy noble gases at smaller inter-
of the noble-gas atom. Note that h depends only on the atomic separations, penetration of the alkali-metal elec-
properties of the noble-gas atom. Estimates for h are tron into the core is the dominant contribution to B b .
given in Table I, and spin-exchange cross sections in Using the wave function of Eq. (28), we find
Fig. 9.
The isotropic hyperfine interaction also produces a 2g S m B m b
B b~ R ! 5 u ¹f 0 ~ R! u 2
frequency shift of the magnetic resonance lines of both 5I b

E F( G
the alkali-metal and the noble-gas atoms (Schaefer et al., 2 dr
`
1989). The frequency shift is characterized by an en- b
3 Q bnp P bnp ~ r b ! . (35)
hancement factor k , being the ratio of the shift actually 0 n r 3b
experienced by the alkali-metal electron due to the po-
larized noble-gas nuclei to that which would be pro- Numerical estimates are shown in Fig. 14. We see that
duced by the magnetic field of a noble gas of the same the anisotropic interaction is probably negligible com-
density and polarization contained in a spherical cell. At pared to A b .
high pressures the frequency-shift enhancement factor is The isotropic magnetic-dipole coupling (proportional
to A b ) polarizes the noble-gas nuclei parallel to the
k 05 E 4 p R 2 dR u h f 0 ~ R ! u 2 e 2V 0 ~ R ! /kT . (33)
electron-spin polarization, while the anisotropic
magnetic-dipole coupling polarizes in the opposite direc-
tion, to compensate for the excess angular momentum
For a nonspherical cell, long-range dipole-dipole inter-
lost to ^ N z & . For example, for the important spin-1/2
actions between the polarized nuclei also affect the fre-
noble gases 3 He and 129Xe, the rate of change of ^ I bz &
quency shift, thereby allowing k to be measured without
including anisotropic coupling is
accurate density, magnetic field, or polarization mea-
surements. In this way Barton et al. (1994) measured d ^ I bz &
k 0 for Rb-He to 62.5% accuracy, making measure- 52G b ~ A b !@ ^ I bz & 2 ^ S z & # 2G b ~ B b !
dt

F G
ments of frequency shifts attractive for absolute polar-
imetry. ^ S z&
3 ^ I bz & 1 , (36)
The isotropic hyperfine interaction with the alkali- 2
metal nucleus A a S•Ia produces a pressure shift
d A a (R)5A a (R)2A a (`) of the alkali-metal hyperfine where the anisotropic coupling rate is G b (B b ). The
steady-state solution is
splitting. d A results from a change in the unpaired elec-
tron density at the alkali-metal nucleus due to the pres- ^ I bz & 2G b ~ A b ! 2G b ~ B b ! A 2b 2B 2b
ence of the noble-gas atom, as described by Eqs. (24) 5 ' 2 . (37)
^ S z & 2 @ G b ~ A b ! 1G b ~ B b !# A b 12B 2b
and (25). Most experiments on spin-exchange optical
pumping make measurements using magnetic resonance Spin-exchange optical pumping produces large polariza-
spectroscopy of the Zeeman levels of the alkali-metal or tions of the noble-gas nuclei only if A 2b @B 2b .

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

 T. G. Walker and W. Happer: Spin-exchange optical pumping . . . 639

Similar estimates of the strengths of the anisotropic 4\ 2 E SO c 2ap ~ R !

hyperfine interaction in the alkali-metal core, as well as g a~ R ! 5 . (42)
3E p M R2
the quadrupole interactions, are shown in Fig. 14. The-
oretical estimates indicate these interactions are small This is proportional to the spin-orbit splitting of the
compared to A b and B b . alkali-metal atom and therefore decreases strongly from
Cs (E SO 5555 cm 21 ) to Na (E SO 517 cm 21 ). In the
C. Spin-rotation interaction Fermi approximation, it is proportional to the square of
the noble-gas scattering length and is therefore smallest
The spin-rotation interaction g (R)S•N transfers po- for Ne.
larization from the electron spin to the translational de-
grees of freedom of the atoms, thus limiting the spin-
transfer efficiency. The spin-rotation interaction arises 2. Noble-gas core
from precession of the electron spin about motionally
In order to estimate the spin-rotation coupling that
produced magnetic fields inside the core of either the
originates in the noble-gas core, we modify the orthogo-
alkali-metal atom or the noble-gas atom. We discuss the
nalized wave approximation of Eq. (27) to account for
two cases separately. For the heavy noble gases, the
the transverse motion w5 v3R of the atoms. The mo-
spin-rotation interaction arises mostly from the noble-
tion adds translational phase factors to the alkali-metal
gas core, while for He the dominant source is inside the
and noble-gas orbitals, changing the wave function to
alkali-metal core. Estimates of the two contributions,
g b and g a , respectively, are shown in Fig. 14, while pre- m
dicted and observed relaxation rates are shown in Fig. C b ~ rb! 5 c b ~ rb! 2i
MR 2 (n Q bnp f 0~ R! R3N• fbnp ,
10. (43)
1. Alkali-metal core which is quite similar in form to Eq. (40).
The expectation value of the spin-orbit interaction
The spin-rotation interaction g S•N is inherently
gives (Wu et al., 1985)
nonadiabatic in origin. The pair of atoms rotate about
each other at a frequency mG d u f 0 u 2
g b ~ R ! 52 , (44)
\N MR dR
v5 , (38)
MR 2 where the parameter
where M is the reduced mass. To account for this rota-
tion, it is useful to transform to a rotating coordinate
system (Van Vleck, 1951), in which the electron experi-
G5 S D E F(
1 \
2 mc
2

0
`

n
Q bnp P bnp ~ r b ! G 2 1 dV
dr
r b dr b b
(45)

ences a Coriolis interaction, reflects the strength of the spin-orbit interaction in the
noble-gas core. Equation (44) naturally separates into
V v 52\ v•L. (39) the factor G that depends only on the noble-gas atom
Since this interaction involves the angular momentum and the factor d u f 0 u 2 /dR that depends on the alkali-
L of the electron, it would vanish to first order were it metal atom. Table I shows estimated values of G, which
not for the small admixture of p state into the adiabatic increase by orders of magnitude from He to Xe due to
wave function [Eq. (25)] caused by the scattering of the the increased strength of the spin-orbit interaction and
valence electron on the noble-gas atom. the increased penetration of the valence electron into
When we use first-order perturbation theory, the the noble-gas core for the heavy atoms.
wave function including the Coriolis interaction be- The two formulas, Eqs. (42) and (44), explain the
comes principal features of Fig. 10. For He, G is so small that
g a is the dominant contribution to g . The strong
\ 2c scattering-length dependence of g a accounts for the
C a ~ ra ! 5 c a ~ ra ! 2i (n MR 2 Eanpanp R̂3N• fanp. (40)
large spread of cross sections for different alkali-metal
atoms. For Ar, Kr, and Xe, g b @ g a , so the dependence
The expectation value of the spin-orbit interaction
on the alkali-metal atom is slight, while the rates vary
V SO 5 j (r a )S•L is then, using the identity
over orders of magnitude due to the wide range of val-
LA• fnp 5iA3 fnp ,
ues of G.
^ C a u V SO u C a & 5 (
nn 8 MR 2 S
\ 2 c anp c an 8 p 1
1
1
E anp E an 8 p D Spin relaxation can also occur in collisions with the
nitrogen quenching gas. For Rb-N 2 , the cross section
has been recently measured to be 1.2310222 cm 2 (Wag-
3 ^ f anp u j ~ r a ! u f an 8 p & S•N shul, 1994), not significantly larger than the spin-
rotation-induced cross sections predicted for Rb-Ne
5 g a S•N. (41)
from Fig. 10. The coupling of the electron spin to the
The dominant contribution to the sum comes from the rotational angular momentum of the N 2 molecule is an
first excited p state for which the spin-orbit splitting is additional potential relaxation mechanism, but this has
E SO 53 ^ f p u j (r a ) u f p & /2, which makes not been studied.

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

640 T. G. Walker and W. Happer: Spin-exchange optical pumping . . .

TABLE II. Measured spin destruction cross sections for time T w . T w can be expressed in terms of the cell ge-
alkali-metal pairs (Bhaskar et al., 1980; Knize, 1989). ometry and the probability a of spin destruction in a
Atom pair s (cm 2 ) single wall collision. The spin flux into the cell wall is
j I 5n b w̄ ^ I bz & /4, so the rate at which spin polarization is
Cs-Cs 2.03310216 lost at the walls is n b V/T w ^ I bz & 5 a j I A, where A is the
Rb-Rb 1.6310217 surface area of the cell. The wall relaxation time is
K-K 2.4310218 therefore T w 54V/ a w̄ A. The detailed physical mecha-
nisms of wall relaxation are poorly understood at
present.
VI. OTHER RELAXATION PROCESSES For the case of 129Xe, silicone coatings are known to
A. Relaxation in alkali-metal collisions
extend wall relaxation times substantially, from tens of
seconds to tens of minutes (Zeng et al., 1983). Recent
With the high alkali-metal vapor pressures used in work (Driehuys et al., 1995) showed that the relaxation
spin-exchange experiments, relaxation in collisions be- is dominated by absorption of the Xe by the coating for
tween spin-polarized alkali-metal atoms becomes impor- times as long as several microseconds. Spin transfer
tant. The cross sections vary significantly from Cs-Cs to from the 129Xe to the protons in the coating reduces the
K-K, as shown in Table II. The relaxation is thought to spin-relaxation time of the Xe, but under optimum con-
arise from a tensor interaction B SS (R)S•(3RR21)•S, ditions can cause orders-of-magnitude increases in pro-
where in this case S5S1 1S2 is the total electronic spin ton polarizations and allow NMR studies of surfaces.
of the colliding alkali-metal pair. The large Cs-Cs cross For 3 He, relaxation times in well-prepared cells can be
section requires B SS to be of the order of 1 cm 21 at a tens of hours, increasing to over 100 hours for a Cs film
typical turning point of 5 Å. The origin of this extremely surface (Heil et al., 1995).
large coupling is not currently understood.

B. ¹B relaxation
D. Noble-gas self-relaxation
For relaxation due to magnetic-field inhomogeneities,
two different regimes can be identified (Cates et al., The three most intensely studied nuclei for spin-
1988) depending on the parameter w 5 v t D , where v is exchange optical pumping are 3 He, 129Xe, and 131Xe.
the Larmor frequency for the nuclei and t D 'R 2 /D is Gas-phase relaxation due to self-collisions of these at-
the characteristic diffusion time for a cell of size R. Let- oms is dominated by three different mechanisms, the
ting V' be the Larmor precession frequency due to the nuclear magnetic-dipole-magnetic-dipole interaction for
transverse portion of the magnetic-field inhomogeneity, 3
He, the nuclear spin-rotation interaction for 129Xe, and
at high pressures ( w @1) the relaxation rate for the spin the electric-quadrupole interaction for 131Xe.
polarization approaches (Schearer and Walters, 1965) For 3 He, the dipole-dipole interaction dominates the
u ¹V' u 2 D bulk relaxation in the gas phase (Mullin et al., 1990;
G ¹B 5 , (46) Newbury, Barton, Cates, Happer, and Middleton, 1993).
v2
With careful wall preparation, it is possible to achieve
which is inversely proportional to the pressure, since the samples for which bulk relaxation dominates. At high
diffusion coefficient is inversely proportional to pres- temperatures, many partial waves contribute to the spin-
sure. This condition is usually well satisfied for spin- flip scattering and the relaxation time increases with in-
exchange optical pumping experiments. At high pres- creasing temperature. At temperatures of a few K, the
sures, the atoms nearly adiabatically follow the local smaller partial waves dominate and the rate reaches a
direction of the magnetic field. The correlation time is minimum before increasing again at lower temperatures.
roughly the mean time t 5l/ v between collisions, and For 129Xe, gas-phase relaxation arises from the spin-
between collisions the atoms see a field rotating at rotation interaction in collisions between Xe atoms
roughly a frequency x ; v ¹V' / v . The relaxation rate is (Hunt and Carr, 1963; Torrey 1963). The dipole-dipole
therefore approximately G ¹B ; x 2 t 5 v l u ¹V' u 2 / v 2 , interaction is negligible. The observed relaxation times
which corresponds to Eq. (46). are given by T 1 n b 523105 s-amagat and are in good
agreement with theory.
C. Wall relaxation For all the stable noble-gas nuclei other than 129Xe
and 3 He, the electric quadrupole interaction dominates
In spin-exchange optical pumping experiments, the the gas-phase relaxation. During binary collisions, the
cell walls are normally prepared with sufficient care that interaction between the induced electric-field gradients
the relaxation due to the wall takes at least tens of min- and the nuclear quadrupole moments produce torques
utes and can be as long as days. Under these conditions, on the spins, thus causing relaxation. These interactions
the noble-gas polarization is essentially uniform are well understood. For 131Xe, for example, the mea-
throughout the cell, so the very slow loss of spin polar- sured rate T 1 n b 525.3 s-amagat (Brinkman et al., 1962)
ization to the walls can be described by a wall relaxation is in excellent agreement with theory (Staub, 1956).

Rev. Mod. Phys., Vol. 69, No. 2, April 1997

 T. G. Walker and W. Happer: Spin-exchange optical pumping . . . 641

VII. SUMMARY Bhaskar, N. D., W. Happer, and T. McClelland, 1982, Phys.

Rev. Lett. 49, 25.
Spin-exchange optical pumping of noble gases like Bhaskar, N. D., M. Hou, M. Ligare, B. Suleman, and W. Hap-
3
He and 129Xe involves a wide range of atomic, molecu- per, 1980, Phys. Rev. A 22, 2710.
lar, and optical physics. In this review we have focused Bhaskar, N. D., M. Hou, B. Suleman, and W. Happer, 1979,
on the fundamental spin interactions between alkali- Phys. Rev. Lett. 43, 519.
metal atoms and noble-gas atoms. The key physics of Bhaskar, N. D., J. Pietras, J. Camparo, W. Happer, and J. Ki-
these interactions is summarized in Fig. 9 and Fig. 10, ran, 1980, Phys. Rev. Lett. 44, 930.
which show theoretical and experimental cross sections Bouchiat, M. A., J. Brossel, and L. C. L. Pottier, 1972, J.
for spin exchange and spin destruction rates. Both cross Chem. Phys. 56, 3703.
sections increase rapidly with the atomic number of the Brinkman, D., E. Brun, and H. H. Staub, 1962, Helv. Phys.
noble-gas atom. The cross sections also increase with Acta 35, 431.
atomic number of the alkali-metal atom, a dependence Buck, U., and H. Pauly, 1968, Z. Phys. 208, 390.
which is particularly pronounced in the spin-relaxation Cates, G. D., S. R. Schaefer, and W. Happer, 1988, Phys. Rev.
cross sections of 3 He. Thus, if lasers were equally prac- A 37, 2877.
tical for all D 1 lines (Na—590 nm; K—770 nm; Rb—795 Childs, W. J., D. R. Cok, and L. S. Goodman, 1982, J. Chem.
nm; Cs—894 nm), and if one could ignore issues like the Phys. 76, 3993.
need for higher-temperature operation for the lighter Chupp, T. E., and K. P. Coulter, 1985, Phys. Rev. Lett. 55,
alkali atoms and the need to limit the gas pressure to 1074.
keep the D 1 and D 2 lines well resolved, it would be best Chupp, T. E., R. J. Hoare, R. L. Walsworth, and Bo Wu, 1994,
to use Na or K for spin-exchange pumping of 3 He and Phys. Rev. Lett. 72, 2363.
best to use Cs or Rb for spin-exchange pumping of Clementi, E., and C. Roetti, 1974, At. Data Nucl. Data Tables
129 14, 177.
Xe, since these choices would maximize the spin
Cohen, M. H., and V. Heine, 1961, Phys. Rev. 122, 1821.
transfer rates from the alkali-metal atoms to the noble-
Coulter, K. P., 1989, Ph. D. thesis (Princeton University).
gas atoms while minimizing the spin destruction rates. Driehuys, B., G. D. Cates, and W. Happer, 1995, Phys. Rev.
Careful, systematic measurements of the spin destruc- Lett. 74, 4943.
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Experimental measurements show that, at very high Happer, W., 1972, Rev. Mod. Phys. 44, 169.
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alkali-metal atoms. If these rates are due to collisions of Heil, W., H. Humblot, E. Otten, M. Schafer, R. Sarkau, and M.
alkali-metal atoms with each other, there is a serious Leduc, 1995, Phys. Lett. A 201, 337.
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ACKNOWLEDGMENTS
Krauss, M., and W. J. Stevens, 1990, J. Chem. Phys. 93, 4236.
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with Mr. D. K. Walter. This work was supported by the Thiessen, 1991, Phys. Rev. A 44, 3108.
National Science Foundation (NSF), the David and Lu- Martin, C., and L. W. Anderson, 1996, Phys. Rev. A 53, 921.
cile Packard Foundation, the US Air Force Office of McLean, A. D., and R. S. McLean, 1981, At. Data Nucl. Data
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Scientific Research (AFOSR), and the Defense Ad-
MacFall, J.R., 1996, Radiology 200, 553.
vanced Research Project Agency (DARPA).
Middleton, H., R. D. Black, B. Saam, G. D. Cates, G. P. Cofer,
R. Guenther, W. Happer, L. W. Hedlund, G. A. Johnson, K.
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