t to be
S
103.23(39) kHz/(kV/cm)
2
, providing more than an order of magnitude improvement in precision
over earlier measurements of this quantity. This measurement serves as a stringent test of recently published
thallium parity nonconservation calculations.
DOI: 10.1103/PhysRevA.66.052504
PACS number s : 32.10.Dk, 32.60. i, 32.70.Jz, 32.30.Jc
I. INTRODUCTION
In recent years, atomic parity nonconservation PNC ex-
periments 1,2 have achieved precision sufcient to provide
sensitive tests of the standard electroweak model. For the
case of cesium, there has been a substantial amount of recent
theoretical work aimed at pushing the necessary wave-
function calculations in this element beyond the 1% level of
precision 3 . The current level of activity reects the impor-
tance of this standard model test, but also highlights the chal-
lenges associated with pushing such calculations to the
sub-1% level. In thallium, a new round of wave-function
calculations were also recently completed 4 . This new re-
sult now requires a variety of independent thallium atomic
structure measurements of high precision to provide cross-
checks on accuracy, and to guide the further development of
the theory. Ultimately, there would be no more satisfying test
of both PNC experiment and atomic theory than to develop
consistent standard model tests of comparable overall preci-
sion in more than one atomic system.
Recently in our group, we completed a precise measure-
ment of the electric quadrupole transition amplitude 5 as
well as hyperne splitting and isotope shift measurements
6 within the two lowest-lying transitions in thallium. Both
of these experiments made use of thallium atoms in heated
vapor cells, and the latter measurement required the devel-
opment of a frequency-doubled diode laser optical system
operating at 378 nm.
Here we report on the results of a high-precision measure-
ment of the Stark shift within the same 378-nm 6 P
1/2
-7<i>S
1/2
E</i>1 transition in thallium. For this work, we have developed
a collimated atomic beam source, and performed transverse
transmission spectroscopy in the presence of a large, pre-
cisely calibrated electric eld. The precision of our Stark
shift result represents an improvement by a factor of 15 over
earlier results 7,8 , and now substantially exceeds the preci-
sion quoted for the new thallium PNC calculation. We thus
provide a challenging test of thallium wave-function calcu-
lations. Inasmuch as our result tests the accuracy of the long-
range behavior of the wave functions, it is quite complemen-
tary to our recent hyperne splitting and isotope shift
measurements, which focus on the behavior of the wave
functions near the nucleus. Two quite different measurement
schemes were used to complete this experiment, each of
which provided results of high precision. Their sensitivity to
a variety of potential systematic errors was quite comple-
mentary, making the consistency of the results particularly
notable.
II. ATOMIC STRUCTURE DETAILS
There are two naturally occurring isotopes of thallium,
205
Tl 70.5% and
203
Tl 29.5% , each of which has nuclear
spin I
1/2, so that both the 6 P
1/2
and 7<i>S
1/2
states contain
F
0 and F
1 hyperne levels. The respective 21- and 12-
GHz hyperne splittings HFS of the ground and excited
states, and the relatively large 1.7-GHz transition isotope
shift IS
6 , yield an entirely resolved spectrum in our
atomic beam apparatus. Because we study a J
1/2
J
1/2 transition, the Stark shift of each level,
W, has only
a scalar component, producing a common shift of all sublev-
els within a given state, and yielding an experimental result
that is independent of relative laser and static electric-eld
polarization. Expressing the Stark shift of a given level as
W
1
2
0
E
2
, where
0
is the scalar polarizability, the ob-
served frequency shift of the 378-nm line can then be ex-
pressed as
S
(1/2<i>h)
0
(7<i>S
1/2
)
0
(6 P
1/2
) E
2
. The
polarizability of each level is calculable from second-order
perturbation theory. For example, in the one-electron central
eld approximation, it is straightforward to show that 9,10
0
7<i>S
1/2
2<i>e
2
9
7<i>s
1/2
, p
1/2
2
7<i>s
1/2
, p
3/2
,
0
6 P
1/2
2<i>e
2
9
6 p
1/2
,s
1/2
2
6 p
1/2
,d
3/2
,
where the s represent particular innite sums of radial in-
tegrals. For example,
*
Present address: Department of Physics, Harvard University,
Cambridge, MA 02138. Present address: Department of Electrical Engineering and Com-
puter Sciences, University of California, Berkeley, CA 94720. Present address: Department of Chemistry and Physics, NW
Missouri State University, Maryville, MO 64468.
§
Electronic address: pmajumde@williams.edu
PHYSICAL REVIEW A 66, 052504 2002
1050-2947/2002/66 5 /052504 7 /$20.00
©2002 The American Physical Society
66
052504-1 6 p
1/2
,l
J
n
0
R 6 P
1/2
rR nl
J
d
3
r
2
E
nl
J
E
6 p
1/2
.
Furthermore, due to the size of the HFS and IS compared to
the
optical
transition
frequencies
(
HFS
/
o pt
and
IS
/
o pt
are of order 10
5
and 10
6
, respectively we
expect no measurable difference in Stark-shift value among
the six isotopic and hyperne component lines, given our
level of experimental precision. Small tensor components to
the Stark shift of individual sublevels induced by higher-
order hyperne interaction effects are similarly of negligible
magnitude in our experiment 11 . The work described here
has therefore centered exclusively on the strongest F
1
F 1 transition of
205
Tl.
In this experiment, we detect the UV laser light transmit-
ted through the atomic beam, which exhibits a roughly 40%
reduction on resonance of this particular hyperne transition.
As we cannot approximate the atomic sample as optically
thin, we analyze our transmission spectra according to
T( )
exp
V( , ; ) . Anticipating that we will normal-
ize the signal to the no atoms condition, we need not
include any additional overall normalization factor. Here
0.5 is the optical depth and
V is the normalized Voigt pro-
le which characterizes our absorption line shape. The re-
sidual Doppler full width
is roughly 100 MHz, while the
Lorentzian component of the prole,
, contributes roughly
20 MHz due to the 7<i>S
1/2
-state natural lifetime.
III. APPARATUS AND EXPERIMENTAL DETAILS
A. Atomic beam system
Referring to Fig. 1, we produce our thallium thermal
atomic beam by heating roughly 300 g of thallium in a heat-
shielded stainless-steel oven to a temperature of 750800 °C
via 0.6 kW of ac power supplied to a heating element Phil-
ips Thermocoax wrapped around the oven. Atoms exit
the oven from a nozzle of overall width 2 cm. The nozzle
consists of 32 parallel vertical tunnels of width 0.25 mm,
height and depth 0.5 cm. This design allows for a favorable
combination of total throughput and beam collimation. To
avoid clogging, the nozzle assembly is heated by a second
heating element, and it maintains a temperature roughly
50 °C higher than the oven body. Nested cones are posi-
tioned immediately downstream of the oven nozzle. These
cones keep uncollimated thallium away from the path of the
beam, and allow for straightforward recycling of solidied
thallium metal back into the oven. A knife-edged aperture
centered on the downstream plate of the cone assembly,
whose dimension matches the 2 cm
0.5 cm nozzle extent,
aids in beam collimation. In this way, the vast majority of the
thallium metal exiting the oven can be recovered with mini-
mal contamination of the rest of the source chamber. The
source chamber itself is a 45-cm-diameter, 30-cm-high cylin-
drical stainless-steel structure, with vacuum ports allowing
for electrical and thermocouple feedthroughs, vacuum
gauges, and a ferrouidic rotary motion feedthrough. A
liquid-N
2
-trapped diffusion pump Varian M -6) maintains a
chamber pressure of roughly 5
10
7
torr when the oven is
hot.
In a 20-cm-diameter, 20-cm-long extension tube protrud-
ing from the source chamber, we position two pairs of razor
blades mounted on translation feedthroughs. Located 20-cm
downstream of the oven nozzle, these allow nal collimation
and denition of both the horizontal and vertical extents of
the atomic beam. We typically set the vertical blades 2-mm
apart, and the horizontal pair 1.5-cm apart. A set of three
orthogonal magnetic-eld coils limit the residual magnetic
eld in our interaction region to
10 mG in all directions.
B. High-voltage system and electric-eld calibration
Our interaction region, located 30 cm downstream of the
oven, consists of a pair of polished stainless-steel plates of
diameter 8 cm separated by four ceramic spacers. The entire
assembly is mounted on a 5-cm-diameter ceramic post at-
tached to a vacuum ange beneath the interaction region
with adjustable screws. Metric gauge blocks are used during
the assembly of the eld plates and we determine the plate
separation to be 1.0002 2 cm. Repeated measurements of
this separation at later times revealed no measurable change.
The modest temperature increase, characteristic of the down-
stream interaction region during beam operation, causes neg-
lible change in plate separation, especially given that expan-
sion of the ceramic posts and steel plates tend to oppose one
another. The UV laser beam intersects the 1.5-cm-wide
atomic beam at the center of the plate assembly. Indepen-
dently, we have performed simulations to insure that, given
our interaction region geometry, any nonidealities due to the
nite size of the plates would affect our electric eld calibra-
tion only at the level of 1 part in 10
5
or below.
A high-voltage power supply Spellman CZE2000 allow