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Measurement of T20 in Elastic Electron-Deuterium Scattering
Bouwhuis, M.; Botto, T.; van den Brand, J.F.J.; Bulten, H.J.; Ferro Luzzi, M.M.E.;
Passchier, M.; Poolman, H.R.
published in
Physical Review Letters
1999
DOI (link to publisher)
10.1103/PhysRevLett.82.3755
document version
Publisher's PDF, also known as Version of record
Link to publication in VU Research Portal
citation for published version (APA)
Bouwhuis, M., Botto, T., van den Brand, J. F. J., Bulten, H. J., Ferro Luzzi, M. M. E., Passchier, M., & Poolman,
H. R. (1999). Measurement of T20 in Elastic Electron-Deuterium Scattering. Physical Review Letters, 82, 3755-
3758. https://doi.org/10.1103/PhysRevLett.82.3755
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VOLUME
82, NUMBER 19 PHYSICAL REVIEW LETTERS 10M
AY
1999
Measurement of T
20
in Elastic Electron-Deuteron Scattering
M. Bouwhuis,
1
R. Alarcon,
2
T. Botto,
1
J.F.J. van den Brand,
1,3
H.J. Bulten,
3
S. Dolfini,
2
R. Ent,
5,6
M. Ferro-Luzzi,
1
D.W. Higinbotham,
8
C. W. de Jager,
1,5,8
J. Lang,
7
D.J.J. de Lange,
1
N. Papadakis,
1
I. Passchier,
1
H. R. Poolman,
1
E. Six,
2
J.J.M. Steijger,
1
N. Vodinas,
1
H. de Vries,
1
and Z.-L. Zhou
4
1
Nationaal Instituut voor Kernfysica en Hoge-Energie Fysica, P.O. Box 41882, 1009 DB Amsterdam, The Netherlands
2
Department of Physics, Arizona State University, Tempe, Arizona 85287
3
Department of Physics and Astronomy, Vrije Universiteit, 1081 HV Amsterdam, The Netherlands
4
Department of Physics, University of Wisconsin, Madison, Wisconsin 53706
5
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
6
Department of Physics, Hampton University, Hampton, Virginia 23668
7
Institute für Teilchenphysik, Eidgenössische Technische Hochschule, CH-8093 Zürich, Switzerland
8
Department of Physics, University of Virginia, Charlottesville, Virginia 22901
(
Received 5 October 1998)
We report on a measurement of the tensor analyzing power T
20
in elastic electron-deuteron scattering
in the range of four-momentum transfer from 1.8 to 3.2 fm
21
. Electrons of 704 MeV were scattered
from a polarized deuterium internal target. The tensor polarization of the deuterium nuclei was
determined with an ion-extraction system, allowing an absolute measurement of T
20
. The data are
described well by a nonrelativistic calculation that includes the effects of meson-exchange currents.
[S0031-9007(99)09127-9]
PACS numbers: 25.30.Bf, 13.40.Gp, 21.45.+v, 24.70.+s
The deuteron, as the simplest nucleus, serves as a sen-
sitive testing ground for a variety of nuclear models (non-
relativistic [1,2], fully covariant [3,4]). The charge and
current distributions inside the nucleus can be probed with
elastic electron scattering at intermediate energies. Elastic
electron scattering off the spin-1 deuteron is completely
described in terms of three electromagnetic form factors:
the charge monopole G
C
, the magnetic dipole G
M
, and the
charge quadrupole G
Q
. Measurements of the unpolarized
cross section yield the structure functions AsG
C
, G
M
, G
Q
d
and BsG
M
d. All three form factors can be separated,
when either the tensor analyzing power T
20
or the re-
coil deuteron tensor polarization t
20
is also determined
[5]. The observables T
20
and t
20
contain an interference
between G
C
and G
Q
and are thus sensitive to the effects
of short-range and tensor correlations in the ground-state
wave function of the deuteron. A large body of data is
available for A and B for values of the four-momentum
transfer Q of up to 12 fm
21
, while T
20
has been measured
up to 3.6 fm
21
[6], albeit with limited accuracy, and t
20
up to 4.6 fm
21
[7]. In this paper absolute measurements
with a small systematic error are presented on the ana-
lyzing power T
20
in the
2
$
Hse, e
0
dd reaction for Q values
between 1.8 and 3.2 fm
21
.
The cross section for elastic electron-deuteron scatter-
ing with unpolarized electrons and tensor-polarized deu-
terium nuclei can be expressed as [5]
s s
0
"
1 1
A
T
d
P
zz
p
2
#
, with A
T
d
2
X
i0
d
2i
T
2i
and
d
20
3 cos
2
u
p
2 1
2
, d
21
2
s
3
2
sin2u
p
cosf
p
, d
22
s
3
2
sin
2
u
p
cos2f
p
,
(1)
with s
0
the unpolarized cross section, T
2i
the tensor ana-
lyzing powers, and P
zz
the degree of tensor polarization.
The polarization axis of the deuteron is defined by the an-
gles u
p
and f
p
in the frame where the z axis is along the
direction of the three-momentum transfer
$
q and the x axis
is perpendicular to z in the scattering plane.
The experiment was performed using a 704 MeV
electron beam in the AmPS storage ring [8] and a
tensor-polarized deuterium internal target [9] at NIKHEF
(Amsterdam). By stacking several pulses of electrons,
produced by the medium-energy accelerator, circulating
currents of up to 150 mA were stored in the ring. A beam
lifetime in excess of 2000 s was obtained by compensating
synchrotron radiation losses with a 476 MHz cavity.
Nuclear-polarized deuterium gas was provided by an
atomic beam source. Deuterium atoms are produced by
means of an rf dissociator. Atoms with their electron
spin up are focused into the target-cell feed tube by two
sextupole magnets, whereas those with spin down are
defocused. A medium- and a strong-field rf unit induce
transitions between the hyperfine states, resulting in a
tensor polarization P
2
zz
sP
1
zz
d of ideally 22 s11d with
zero vector polarization. The tensor polarization was
flipped every 20 s between P
2
zz
and P
1
zz
. The atomic
0031-9007y99y 82(19)y3755(4)$15.00 © 1999 The American Physical Society 3755
VOLUME
82, NUMBER 19 PHYSICAL REVIEW LETTERS 10M
AY
1999
beam is fed into an open-ended T-shaped dwell cell
with a diameter of 15 mm and a length of 400 mm.
The cell was cooled to approximately 150 K. With
a flux of 1.3 3 10
16
atomsys in two hyperfine states
into the cell an integrated target density was obtained
of 2 3 10
13
atomsycm
2
. The direction of the deuteron
polarization axis was defined by a magnetic holding
field sB 23 mTd and chosen to be on average parallel
to the three-momentum transfer (at ø62
±
to the beam
direction).
Two polarimeters were available to study the polar-
ization in the dwell cell. A small sample (10%) of the
atomic beam was continuously analyzed by a Breit-Rabi
polarimeter. The nuclear polarization of the atoms and
the composition of the gas in the dwell cell was mea-
sured with an ion-extraction system [10]. Ions, produced
by the circulating electrons, were extracted from the beam
line and transported through a Wien filter (an E 3 B ve-
locity selector). Since molecular and atomic deuterium
ions have different velocities, measuring the ion current
as a function of the Wien filter B field allows determina-
tion of the atomic fraction averaged over the target cell.
The nuclear polarization can be determined by acceler-
ating the ions onto a tritium target and using the well-
known analyzing power [11] of the low-energy reaction
3
Hs
2
$
H, nda. We measured the polarization of molecules,
originating from recombination in the cell, in a dedi-
cated experiment [12]. Combining these measurements
the effective target polarization was determined to be
DP
zz
P
1
zz
2 P
2
zz
1.175 6 0.057.
The scattered electrons were detected in an electromag-
netic calorimeter [13] consisting of 6 layers of CsI(Tl)
crystals with a total depth of 19 radiation lengths. The
first layer of CsI(Tl) was sandwiched between two plas-
tic scintillators. The second of these, shielded from low-
energy Møller electrons, provided the trigger. A pair of
wire chambers provides tracking information of the de-
tected electrons. The calorimeter, with an acceptance of
approximately 150 msr, was positioned at a central angle
u
e
of 45
±
.
The ejected or recoiling hadrons were detected in
coincidence in a so-called range telescope (RT) [14],
consisting of 16 layers of plastic scintillator. The first
layer had a thickness of 2 mm, all following layers were
10 mm thick. This detector was also preceded by two
wire chambers, and was positioned at a central angle of
62.3
±
. The kinetic energy of the recoiling deuterons was
kinematically limited to 120 MeV.
Event selection was based on coincidence timing be-
tween the two arms, the response of the RT scintillators
and on tracking information. The coincidence time was
corrected for effects from walk, time of flight, and impact
position on the trigger scintillators.
Particle identification was performed by comparing
the response of the RT scintillators to the energy loss,
calculated using the formula of Bethe and Bloch [15]. A
particle identification parameter P
id
was defined as
P
id
1
N
N
X
i1
L
meas
L
calc
(2)
with N the number of active RT scintillators and L
meas
sL
calc
d the actual (calculated) response in the ith scintil-
lator. P
id
will display a peak around 1 for deuterons, and
a peak at smaller values for protons and electrons.
For the kinematically overdetermined elastic scattering
reaction, requiring correlations between the scattering
angles of the electron and the hadron reduces the number
of protons even further.
Figure 1 shows the distribution of P
id
and the coinci-
dence timing t
p
between the scattered electron and the
recoiling hadron. To obtain this distribution 62.5s cuts
were applied on their angular correlations. A clear sepa-
ration is observed between protons and deuterons. The
proton contamination was estimated to be 4.6%. Analysis
of a proton sample has shown that these have an analyzing
power much lower than that of the deuterons. Scattering
from the cell walls was observed to be negligibly small in
runs without gas flowing into the cell.
In the event selection additional 62.5s cuts were ap-
plied on the coincidence time and on P
id
. An asymmetry
A
T
d
was formed for events that fall within a 0.5 fm
21
wide
Q bin, using the expression
A
T
d
p
2
N
1
2 N
2
P
1
zz
N
2
2 P
2
zz
N
1
(3)
with N
1
sN
2
d the number of events in the Q bin
considered when the target polarization was positive
(negative). To correct for the fact that the direction of the
holding field—and thus the spin orientation—varies over
the length of the cell with respect to
$
q the uncorrected
tensor asymmetry A
T
d
is weighted with d
20
from Eq. (1).
Note from Eq. (1) that A
T
d
contains small contributions
from T
21
and T
22
. Since A
T
d
can be expressed as a func-
tion of T
20
, A and B, one can derive T
20
from A
T
d
using
the world data set for the unpolarized structure functions
FIG. 1. Particle identification parameter P
id
(defined in the
text) versus coincidence time t
p
.
3756
VOLUME
82, NUMBER 19 PHYSICAL REVIEW LETTERS 10M
AY
1999
TABLE I. Result on A
T
d
, T
20
s70
±
d, and G
C
with statistical and systematic uncertainties,
extracted from our T
20
measurements and the world data on A and B.
Q ffm
21
g
A
T
d
T
20
s70
±
d (stat.)
(syst.) G
C
(stat.) (syst.)
2.03 20.683
20.713s0.082d
(0.036) 0.163(0.003) (0.014)
2.35 20.891
20.897s0.081d
(0.045) 0.100(0.003) (0.009)
2.79 21.383
21.334s0.223d
(0.066) 0.035(0.015) (0.005)
A and B (see [7] for an overview). To investigate the
sensitivity of the extraction procedure to the uncertainty
in the input parameters (i.e., Q, u
e
, d
2i
, A
T
d
, A, and B),
these were varied independently within their error and the
extraction repeated. The total error was taken to be the
quadratic sum of the separate errors. Note that the main
contribution to the systematic error in A
T
d
comes from the
systematic uncertainty in the polarization.
The observables A, B, and T
20
provide three different
combinations of the form factors G
C
, G
Q
, and G
M
, from
which these can be extracted. The result for T
20
was
recalculated at u
e
70
±
, to allow a direct comparison
with the results of other experiments. The extracted
values for T
20
and G
C
are shown in Table I and in Fig. 2.
The new data on T
20
are each at least one s below the
predictions of nonrelativistic [1,2] and relativistic models
[3,4]. This confirms the findings of the previous NIKHEF
experiment [16].
To evaluate the model sensitivity of the T
20
and t
20
data sets a x
2
analysis was performed, for which the data
measured most recently at Bates [7], using a calibrated
recoil parameter, and those from the NIKHEF experiments
were selected. The data from BINP have poor accuracy at
low Q [17] and poor discriminating power in the Q range
from 1 to 3 fm
21
[18], since the T
20
values were extracted
by normalizing one datum to a selected model prediction.
The selected data sets are compared to the calculations
of Wiringa [1], Mosconi [2], Hummel [3], Van Orden
[4], and Buchmann [20]. The first two calculations, both
using the nonrelativistic impulse approximation, differ in
the NN potential used (Argonne-y
18
for Wiringa and
Paris for Mosconi) and in the implementation of meson-
exchange contributions. The Buchmann calculation used
a nonrelativistic cluster model of constituent quarks and
mesons in a limited parameter space, but fails to reproduce
the data on A and B with great accuracy. The first two
columns of Table II give the x
2
values when only the T
20
data of either experiment are considered. In addition, both
these experiments yielded data on other tensor analyzing
powers: in the 95 data run of NIKHEF [16] T
22
was also
determined, and the Bates experiment determined all tensor
moments simultaneously. The last two columns of the
table give the results when all data are taken into account.
The two data sets lead to different conclusions about
the quality of the models. The NIKHEF set shows a
preference for nonrelativistic calculations with realistic
NN potentials, when only the T
20
data are considered, and
this conclusion remains unaltered when the datum on T
22
is included in the fit. The Bates data set, on the other
hand, shows a preference for the relativistic calculations,
but loses most of its discriminating power when all data on
t
2i
are taken into account, mainly due to an inconsistency
in one value of t
22
. The then available data on T
20
and t
20
led Henning et al. [21] to point out an inconsistency in the
location of the minimum of the charge form factor of two-
and three-nucleon systems.
Stringent constraints are imposed on models by the
extensive data for the unpolarized structure functions A
and B, in addition to the polarized data. In Table III
the result of a x
2
-analysis is given for A and for B,
FIG. 2. Extracted values (solid triangles) of T
20
s70
±
d (top)
and G
C
(bottom) as a function of Q compared to the world
data and selected calculations. Data: solid triangles (present
experiment), open squares [7], solid square [16], open diamond
[17], open triangles [18], open circles [19], and open cross [6].
Curves: short-dashed [1], dash-dotted [2], full [3], long-dashed
[4], dotted [20]. The shaded area indicates the size of the
systematic errors from the present experiment.
3757
VOLUME
82, NUMBER 19 PHYSICAL REVIEW LETTERS 10M
AY
1999
TABLE II. x
2
yN analysis for NIKHEF sN95 1 N96d: [16] and present results) T
2i
and
Bates (B90: [7]) t
2i
data, against various model predictions. N is the number of data points
used in the analysis.
T
20
sN95 1 96d t
20
sB90d T
2i
sN95 1 96d t
2i
sB90d
N 4 N 3 N 5 N 9
Wiringa 1.14 2.40 1.37 3.35
Mosconi 1.31 0.30 1.48 2.46
Hummel 2.80 0.89 2.68 2.54
Van Orden 2.28 0.29 2.27 2.52
Buchmann 0.16 5.15 0.57 3.32
together with the overall x
2
. Data [7] for A and B in
the Q range of 0.5 to 6.0 fm
21
were taken into account.
The normalization of each data set was varied within the
quoted systematic uncertainty until a minimum value for
the x
2
was obtained. The best description is given by the
nonrelativistic calculation of Ref. [1] that includes the
relevant corrections to the impulse approximation, which
conforms to the conclusions from the NIKHEF data. It
should be noted that especially the inclusion of meson-
exchange currents is of great importance, in describing
both the unpolarized and the polarized data.
In conclusion, absolute measurements of the tensor
analyzing power T
20
were performed in a Q range from
1.8 to 3.2 fm
21
. This new data set, together with that
of a previous measurement at NIKHEF, has provided
additional stringent constraints on the deuteron form
factors. Recently, an experiment [22] has been completed
at Jefferson Laboratory, which will provide accurate data
on t
20
in a Q range from 4 to 6.5 fm
21
, thus covering
the expected position [21] of the minimum in G
C
. Future
measurements of T
20
are to be expected with the BLAST
[23] detector at MIT-Bates in a Q range of 0.2 to
4.6 fm
21
.
This work was supported in part by the Stichting voor
Fundamenteel Onderzoek der Materie (FOM), which
is financially supported by the Nederlandse Organisatie
voor Wetenschappelijk Onderzoek (NWO), the Swiss
National Foundation, the National Science Foundation
under Grants No. PHY-9316221 (Wisconsin), No. PHY-
9200435 (Arizona State), and No. HRD-9154080
(Hampton), NWO Grant No. 713-119, and HCM Grants
No. ERBCHBICT-930606 and No. ERB4001GT931472.
TABLE III. x
2
yN analysis of the A and B world data set.
ABA1B
Model N 81 N 34 N 115
Wiringa 5.6 5.9 5.7
Mosconi 11.0 1.8 8.3
Hummel 16.5 4.9 13.1
Van Orden 72.7 2.7 52.0
Buchmann 50.8 6.9 37.8
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3758
![TABLE II. x2yN analysis for NIKHEF sN95 1 N96d: [16] and present results)T2i and Bates (B90: [7])t2i data, against various model predictions.N is the number of data points used in the analysis.](/figures/table-ii-x2yn-analysis-for-nikhef-sn95-1-n96d-16-and-present-3ehxqisl.webp)
