Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from Deuterium Page: 2 of 4
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6 the angle between the polarization axis and the relative
momentum p of the two nucleons.
The spin-dependent density distribution can be probed
by quasielastic electron scattering from tensor-polarized
deuterium targets, which yields data complementary to
the elastic channel [17-19] where the total nuclear cur-
rent (i.e., nucleon and meson contributions) is probed. In
plane-wave impulse approximation (PWIA), the (e, e'p)
cross section for unpolarized electrons factorizes in a
part depending on the off-shell electron-proton cross sec-
tion and a part containing the spin-dependent momentum
distribution as shown in Eq. (1) [20]. In that case the
relative nucleon momentum p can be related to the miss-
ing momentum of the reaction, defined as pm = q - p',
with q the momentum transferred in the electron scatter-
ing process and p' the momentum of the knocked-out pro-
ton. In a cross section measurement with tensor-polarized
deuterons one can define the tensor analyzing power A:
AT = 1 o+(pm) + or(pm) - 2-o(pm)
d 2 o+(pm) + o-(pm) + oo(pm)
PWIA 2Ro(p)R2(p) + 2 R (p) do(6), (2)
Ro(p) + R (p) '
with o-o (o-) the cross section measured with mr = 0
(mz = 1) and d~o = 2 cos26 - 2. In the limit where
R2 << Ro, Ad directly relates to the ratio R2/Ro. Further-
more, in PWIA when Ro = -1 R2, then o-o = 0 and A5
is maximum with a value of + 2 for 6 = 0. Even when
FSI and all other effects are included, the cross section is
expected to be small for electron scattering from deuterons
with mz = 0. Similarly, when Ro = 2 R2, the PWIA
cross section for deuterons with mz = 1 vanishes and
Ad reaches a minimum of - 1.
The experiment was performed with a polarized gas
target [21] internal to the AmPS electron storage ring
at NIKHEF. A beam current of 120 mA was injected.
The 565 MeV electron beam had a lifetime of about
15 min. An atomic beam source was used to inject a
flux of 1.1 X 1016 atoms/s with two hyperfine states into
a T-shaped storage cell, which was cooled to 100 K in
order to further increase the target density. The data
were obtained with Teflon-coated aluminum cells (wall
thickness 25 m) with diameters of 15 or 20 mm and
a length of 400 mm. The resulting target thickness
amounted up to 2 X 1013 (2H atoms)/cm2. The tensor
polarization of the target Pzz (= 1 - 3no, with no the
fraction of deuterons with mZ = 0) was varied every
10 s between Pz = +0.488 0.014 0.03 and Pz =
-0.893 0.027 0.052, where the first (second) error
represents the statistical (systematic) uncertainty. The
tensor polarization of the deuterium atoms was measured
in situ by a polarimeter [22] that analyzes the fraction
of the target gas that has been ionized by the traversing
electron beam. Two electromagnets were used to generatea magnetic field in the interaction region that allows
one to orient the target polarization axis in the electron
scattering plane, either parallel or perpendicular to the
momentum transfer. A set of scrapers was employed to
intercept the halo of the electron beam and thus reduce the
amount of background from the cell wall.
The experimental setup has been described in detail
in Refs. [21,23], and results for elastic electron-deuteron
scattering have been presented previously [18]; here only
a brief overview is given. Electrons scattered from
the tensor-polarized deuterium gas were detected in an
electromagnetic calorimeter, consisting of six layers of
CsI(Tl) blocks covering a solid angle of 180 msr. Two
plastic scintillators, one in front of the CsI(Tl) blocks
and one positioned between the first two layers, pro-
vided the electron trigger. The total energy resolution
obtained (about 22 MeV) was sufficient to distinguish be-
tween events from quasielastic scattering and events from
pion electroproduction. Two sets of wire chambers, one
adjacent to the scattering chamber and one in front of the
first trigger scintillator, were used for track reconstruc-
tion. The central angle of the electron detector was 350
corresponding to an average transferred three momentum
of Iql 1.7 fm-1.
The ejected protons were detected in a range telescope,
consisting of 15 layers of 1 cm thick plastic scintillator
preceded by a layer of 2 mm thick plastic scintillator.
The trigger was formed by a coincidence between the
first two layers. The detector was positioned at a central
angle of 80* and covered a solid angle of nearly 300 msr.
The range telescope was preceded by two wire chambers
for track reconstruction. Protons in the range of 30-
100 MeV were detected with an energy resolution of
about 1.5 MeV.
Calibration measurements were performed with the
kinematically overdetermined reaction 1H(e, e'p). Since
the calorimeter excludes the pion-production channels,
the fivefold differential cross section can be obtained
by measuring the electron scattering angles 0e, 0 , the
angles of the ejected proton 6p, O,, and the energy
of the proton. This procedure resulted in an excellent
missing-momentum resolution, for a nonmagnetic detec-
tor setup, of 6.2 MeV/c as demonstrated in Fig. 1 (top
panel). In the bottom panel of the figure, the missing-
momentum spectrum for scattering from deuterium is
shown. The data are in reasonable agreement with the
result of a Monte Carlo calculation that includes the off-
shell electron-proton cross section of de Forest, Jr. [24],
momentum densities from Bernheim et al. [12], and a
model for the detector phase space. The shaded histogram
represents the background contribution which was deter-
mined by scattering from an empty cell. It is seen that the
background contributes significantly to the data taken for
missing momenta above 150 MeV/c.
Figure 2 shows the measured asymmetry, Ad, as a func-
tion of the angle QS between the polarization axis and688
25 JANUARY 1999
VOLUME 82, NUMBER 4
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Zhou, Z.-L.; Bouwhuis, M.; Ferro-Luzzi, M.; Passchier, E.; Alarcon, R.; Anghinolfi, M. et al. Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from Deuterium, article, January 1, 1999; Newport News, Virginia. (https://digital.library.unt.edu/ark:/67531/metadc889377/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.