Measurement of the Electric Form Factor of the
Neutron at MAMI
Michael Seimetz, for the A1 collaboration
Johannes Gutenberg–Universität, Institut für Kernphysik, Becherweg 45, 55099 Mainz, Germany
Abstract.
A new De e¼n p experiment has been performed at Mainz University to measure the electric
form factor of the neutron, G E n . To this purpose a neutron polarimeter, optimized to withstand high
electromagnetic background rates, was built for the Three Spectrometer Hall of the A1 collaboration. We present the experimental setup and the status of our data analysis.
MOTIVATION
The elastic form factors parametrize the nucleon’s ability to absorb momentum transfer
in a scattering reaction without excitation or production of further particles. They are
related to the charge and magnetization distributions, and thereby reflect the inner
structure of the nucleon. Precise measurements of GE and GM offer insight into the
basic constituents of matter, being a crucial test for every nucleon model. Furthermore,
precise values of the nucleon electromagnetic form factors are needed as input for many
other experiments in nuclear and hadron physics.
Among the four Sachs form factors, GE n is the least precisely known, for various
experimental reasons. First of all, light nuclei D 3 He are commonly used due to
the lack of a free neutron target, which in general implies model dependencies of the
GE n results on nuclear binding effects. In GE n measurements based on elastic e D
scattering [1] these uncertainties amount to more than 50%. Secondly, results on G E n
obtained from experiments based on the Rosenbluth separation technique are compatible
with zero because in the cross section, GE n is dominated by the much larger magnetic
form factor, GMn . Thirdly, absolute neutron cross sections are hard to measure because
they require a calibration of the neutron detection efficiency. An alternative approach,
developed during the last decade, is offered by double polarization experiments, which
provide results with small systematic and model errors for the ratio G E n GMn .
e e n pp experiments
The published data points from De e n p, De e n p, and 3 He
are shown in Figure 1. The first neutron recoil polarization experiment on Deuterium
was performed at MIT-Bates [2] (open circle), albeit with large systematic errors. Two
data points using the same reaction were obtained at Mainz (A3) [3] (full circles). In this
experiment a neutron spin precession technique [4] was used for the first time with which
the systematic errors were reduced significantly. Furthermore, the model uncertainties
could be minimized by including calculations of nuclear binding effects, such as final
state interactions (FSI) and meson exchange currents (MEC), as published by Arenhövel
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
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GE,n Polarisation Measurements
0.1
GE,n
0.08
0.06
0.04
Galster
0.02
0
0
0.5
Q2 / (GeV/c)2
1
FIGURE 1. GE n data points from double polarisation experiments. References are given in the text.
and coworkers [5, 6].
Two further data points were obtained at MAMI using polarized 3 He targets [7, 8]
(squares). For the lower-lying one preliminary calculations of FSI effects [9] exist, introducing a significant shift of GE n towards the value expected from the experiments
with deuteron target. Another two points were acquired using polarized deuterium targets at NIKHEF [10] (open triangle) and JLab [11] (full triangle). All these experimental
results agree (within their error range) with the GE n parametrization originally given by
Galster [12], a fact which, from a theoretical point of view, has to be regarded as fortuitous.
In the new A1 experiment, three additional data points at central four-momentum
transfers Q2 03 06 and 08 GeVc2 are acquired, allowing an independent check
of the former results and an extension to higher Q 2 values.
EXPERIMENTAL METHOD
In the A1 experiment GE n is determined from the quasielastic De en p reaction. It is
based on the spin transfer in the elastic scattering of polarized electrons on unpolarized
nucleons [13]. The recoil nucleon carries nonvanishing polarization components, Px and
Pz, which are proportional to the form factor products G E GM and G2M , respectively. The
coordinate system is spanned by ẑ, the direction of momentum transfer, and x̂ lying in
the electron scattering plane. Then the polarization ratio
RP Px
Pz
1
τ τ 1 τ tan2 ϑ2e
621
G
GE n
M n
(1)
Rear wall
Top view
Front wall
n
e’
x
P
By
P
z
χ0
e
Θn , Φn
FIGURE 2. Sketch of the A1 neutron polarimeter setup (top view).
with τ Q2 4Mn2 determined by the kinematics of the scattering reaction. Together
with the known value of GMn ([14] and references therein), R p gives the desired value
of GE n . The measurement of R p requires the use of a neutron polarimeter, which will
be illustrated in the following, together with the other components of the experimental
setup.
The De en p experiment is performed in the A1 Three Spectrometer Hall [15]
at Mainz. A beam of polarized electrons, provided by the MAMI accelerator with
Pe 80%, hits a 5 cm long liquid deuterium target cell. The momentum of the scattered
electrons is analyzed with high resolution in a magnetic spectrometer. The outgoing neutrons are detected in the neutron polarimeter (Figure 2) at forward angles between 27Æ
and 47Æ . Their scattering angles and time of flight are measured in a highly segmented
wall of plastic scintillators.
At the same time, the neutron polarization is determined using the scintillators as
active scattering target: The strong n p and n C scattering reactions in the first
scintillator wall carry analyzing power. A transverse polarization, Pt , of the outgoing
neutron results in an asymmetry in the azimuthal angle Φ n ,
A Pe Aeff Pt sinΦn (2)
which can be measured as up-down asymmetry in the neutron distribution on a second
wall of scintillators. Pe is the polarization of the incident electron beam and A eff the
effective analyzing power.
This method is sensitive only to the transverse polarization component, which initially
is Px . However, by precessing the neutron spin in a magnetic dipole field perpendicular
to the x z plane both Px and Pz become accessible. At a certain precession angle χ0 Pt ,
and with it the asymmetry (2), vanish. At this angle the effective analyzing power and
the absolute electron beam polarization cancel out. Thereby systematic uncertainties are
minimized.
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Massive concrete shielding protects the large-area scintillators from electromagnetic
background. Furthermore, a 5 cm thick lead brick wall is built up inside the magnet gap
in front of the 1st wall, which in turn is highly segmented in order to keep the single
paddle rates as low as possible. Systematic errors due to charge exchange effects in the
lead shielding were investigated during the data taking using a LH 2 target. The rear wall
is divided into two parts above and below the beam without direct target view, but in
a way that neutrons scattered in the front wall can be detected in the rear wall with
angles corresponding to high analyzing power. By these means luminosities of up to
5 cm LD2 15 µ A beam current could be used during data taking.
We chose three central four-momentum transfers, Q2 03 06 and 08 GeVc2 .
The energy of the electron beam was 698, 855 and 883 MeV, respectively. A Møller
polarimeter was used to monitor the electron beam polarization.
DATA ANALYSIS
The reconstruction of the kinematics of the quasielastic De e n p reaction is based
on five independent observables. The energy, Ee , and scattering angles, ϑe ϕe , of the
outgoing electron are determined in a magnetic spectrometer. The neutron scattering
angles, ϑn ϕn , are measured in the neutron polarimeter. In addition, the neutron Time
of Flight is obtained allowing cross checks. This requires a good calibration of all
scintillators, which is performed in one-arm measurements using minimally ionizing
particles, and in the elastic He e p reaction. Thereby a timing resolution around 300 ps
is achieved for the first wall scintillators.
The identification of quasielastically scattered neutrons and their separation from
charged and uncharged background is a major task of the data analysis. In the A1 experiment various methods are applied. Veto paddles on both scintillator walls of the neutron
polarimeter, partly implemented in the hardware trigger, filter out charged particles. Additional veto conditions between each neutron detector and its neighbours refine this
separation in the offline analysis. Protons can be discriminated against neutrons since
they lose part of their kinetic energy in the lead shielding. Even if they are not stopped,
their time of flight is significantly larger than the one of the neutrons. In addition, the
energy deposition of the neutrons in elastic pn n p and quasielastic 12Cn n p11 B reactions is kinematically related to the scattering angles in the front wall, a fact which
can be used to enrich the analyzing power.
The azimuthal scattering angles Φn in the front wall are combined to the asymmetry
AΦn N Φ
N Φ
n N Φn π n N Φn π N Φ
N Φ
n π N Φn n π N Φn (3)
It shows the sine-like dependence on Φn given in Equation (2). The amplitude of the
sine depends on the transverse neutron polarization, Pt , and thus on the spin precession
angle in the dipole magnet. Data were taken for seven different values of χ , permitting
a precise determination of the precession angle χ0 at vanishing Pt . An example for such
a fit is shown in Figure 3.
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Asymmetry vs. Precession Angle
VERY PRELIMINARY
NOT FOR QUOTATION
FIGURE 3. Variation of the asymmetry with the spin precession angle χ (example).
The GE n data taking was completed in August 2002. The analysis is in progress,
and first results seem to confirm that GE n is significantly larger than assumed from
former unpolarized experiments. We aim to achieve a relative error of our data points of
∆GE n GE n 10%.
ACKNOWLEDGMENTS
This work has been supported by SFB 443 of the Deutsche Forschungsgemeinschaft
(DFG) and the Federal State of Rhineland-Palatinate.
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