The Electric Form Factor of the Neutron via
Recoil Polarimetry to Q 2 1 4 7 (GeV/cc)2
B. Plaster , R. Madey† , A. Yu. Semenov† , S. Taylor , A. Aghalaryan‡ ,
E. Crouse§ , G. MacLachlan¶, S. Tajima , W. Tireman† , Chenyu Yan† ,
A. Ahmidouch†† , B. D. Anderson† , H. Arenhövel‡‡, R. Asaturyan‡ ,
O. Baker§§, A. R. Baldwin† , H. Breuer¶¶, R. Carlini , E. Christy§§ ,
S. Churchwell , L. Cole§§, S. Danagoulian †† , D. Day , M. Elaasar††† ,
R. Ent , M. Farkhondeh , H. Fenker, J. M. Finn§ , L. Gan§§ , K. Garrow ,
P. Gueye§§ , C. Howell , B. Hu§§ , M. K. Jones , J. J. Kelly¶¶ , C. Keppel§§,
M. Khandaker‡‡‡, W.-Y. Kim§§§ , S. Kowalski , A. Lung , D. Mack ,
D. M. Manley† , P. Markowitz¶¶¶ , J. Mitchell , H. Mkrtchyan‡ ,
A. K. Opper¶ , C. Perdrisat§ , V. Punjabi‡‡‡ , B. Raue¶¶¶, T. Reichelt ,
J. Reinhold¶¶¶ , J. Roche§ , Y. Sato§§, I. A. Semenova† , W. Seo§§§,
N. Simicevic†††† , G. Smith , S. Stepanyan‡ , V. Tadevosyan‡ , L. Tang§§ ,
P. Ulmer‡‡‡‡ , W. Vulcan , J. W. Watson† , S. Wells†††† , F. Wesselmann ,
S. Wood , Chen Yan , S. Yang§§§ , L. Yuan§§ , W.-M. Zhang† , H. Zhu
and X. Zhu§§
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
†
Kent State University, Kent, Ohio 44242
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
‡
Yerevan Physics Institute, Yerevan 375036, Armenia
§
The College of William and Mary, Williamsburg, Virginia 23187
¶
Ohio University, Athens, Ohio 45701
Duke University, Durham, North Carolina 27708
††
North Carolina A&T State University, Greensboro, North Carolina 27411
‡‡
Johannes Gutenberg-Universität, D-55099 Mainz, Germany
§§
Hampton University, Hampton, Virginia, 23668
¶¶
University of Maryland, College Park, Maryland 20742
University of Virginia, Charlottesville, Virginia 22904
†††
Southern University at New Orleans, New Orleans, Louisiana 70126
‡‡‡
Norfolk State University, Norfolk, Virginia 23504
§§§
Kyungpook National University, Taegu 702-701, Korea
¶¶¶
Florida International University, Miami, Florida 33199
££££ Rheinische Friedrich-Wilhelms-Universität, D-53115 Bonn, Germany
††††
Louisiana Tech University, Ruston, Louisiana 71272
‡‡‡‡ Old Dominion University, Norfolk, Virginia 23508
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
625
Abstract. The Jefferson Laboratory E93-038 collaboration conducted measurements of the ratio of
the electric form factor to the magnetic form factor of the neutron, G nE GnM , via recoil polarimetry
from the quasielastic 2 He e¼n1 H reaction at three values of Q 2 [viz., 0.45, 1.15, and 1.47 (GeV/c) 2 ]
in Hall C of the Thomas Jefferson National Accelerator Facility. The preliminary results for G nE
at Q2 045 and 1.15 (GeV/c) 2 are consistent with the Galster parameterization; however, the
preliminary result for G nE at Q2 147 (GeV/c)2 lies slightly above the Galster parameterization.
INTRODUCTION
The electric form factor of the neutron, GnE , is a fundamental quantity needed for an
accurate description of both nucleon and nuclear structure. The Jefferson Laboratory
E93-038 collaboration conducted measurements of the ratio of the electric form factor
to the magnetic form factor of the neutron, g GnE GnM , at three values of Q2 [viz.,
0.45, 1.15, and 1.47 (GeV/c)2 ] via recoil polarimetry from the quasielastic 2 He en1 H
reaction. Data were taken in Hall C of the Thomas Jefferson National Accelerator
Facility from September 2000 to April 2001.
EXPERIMENTAL TECHNIQUE
Top Rear Array
Rear Veto/Tagger
Front Array
To HMS
e
Bottom Rear Array
Front Veto/Tagger
Lead Curtain
e
Charybdis
Target LD2, LH2
FIGURE 1. A schematic diagram of the polarimeter.
The experimental arrangement is shown in Fig. 1. A beam of longitudinally polarized
electrons scattered quasielastically from neutrons in a 15-cm liquid deuterium target.
In the plane-wave approximation, the polarization vector of the recoil neutron lies in
the scattering plane [1] and consists of two components: The longitudinal component,
PL , and the sideways component, PS , are parallel and perpendicular, respectively, to
the recoil neutron’s momentum vector. The scattered electron was detected and momentum analyzed by the Hall C High Momentum Spectrometer (HMS) in coincidence with
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the recoil neutron. A neutron polarimeter (NPOL) designed specifically for E93-038 by
Madey [2] measured the up-down scattering asymmetry from a transverse projection
of the recoil neutron’s polarization vector. A dipole magnet (Charybdis) located ahead
of the polarimeter precessed the polarization vector through an angle χ which permitted asymmetry measurements from different transverse projections of the polarization
vector.
The polarimeter consisted of 20 detectors in the front array and 12 detectors in each
of the two (upper and lower) rear arrays for a total of 44 plastic scintillation detectors.
A double layer of thin scintillators (“veto/tagger” detectors) located directly ahead of
and behind the front array detected incoming and scattered charged particles. The 100
cm 10 cm 10 cm dimensions of each detector in the front array permitted high
luminosity; in addition, a collimator shielded each detector in the rear array from the
direct flux of particles from the target. A 10-cm lead curtain located at the entrance of
the collimator attenuated the flux of electromagnetic radiation and low-energy charged
particles incident on the polarimeter. For the duration of the experiment, the polarimeter
was fixed at an angle of 46Æ relative to the incoming beam, and the mean flight path from
the target to the front array was 7 m.
The ratio of the electric form factor to the magnetic form factor of the neutron,
g GnE GnM , is
g K tan δ (1)
where K is a function of kinematic variables and tan δ PS PL [3]. After precession
through an angle χ , the transverse projection, and hence the scattering asymmetry, is
proportional to sin χ δ ; therefore g can be obtained by extracting δ from a fit of the
scattering asymmetries as a function of χ . A significant advantage of this experimental
technique is that the analyzing power of the polarimeter cancels in the ratio of PS to PL ;
the beam polarization also cancels provided the polarization is stable.
At each Q2 point, scattering asymmetry measurements were conducted with precession angles of χ 40Æ ; in addition, scattering asymmetry measurements with precession angles of χ 0Æ and 90Æ were conducted at Q2 115 and 1.47 (GeV/c)2 .
The measurements at Q2 045 and 1.47 (GeV/c)2 were associated with beam energies
of 0.884 and 3.395 GeV, respectively. The measurement at Q 2 115 (GeV/c)2 is the
weighted average of a measurement at Q2 114 (GeV/c)2 associated with a beam energy of 2.33 GeV and a measurement at Q2 117 (GeV/c)2 associated with a beam
energy of 2.42 GeV.
ANALYSIS AND PRELIMINARY RESULTS
Data were collected with an event defined to be a triple coincidence between an electron
in the HMS, a neutral particle in the front array of the polarimeter, and a neutral or
charged particle in the rear array of the polarimeter. Inelastic events were rejected via
the application of a 100 MeV/c missing momentum cut and a relative 3% to 5% bite
on the momentum of the scattered electron.
Typical time-of-flight spectra from a representative run at Q2 117 (GeV/c)2 are
shown in Fig. 2. The left panel (cTOF) is a histogram of the difference between the
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10000
4000
8000
3000
Counts
Counts
measured time-of-flight from the target to the front array of the polarimeter and the timeof-flight calculated for quasielastic scattering. The right panel (∆TOF) is a histogram
of the difference between the measured time-of-flight between a neutral event in the
front array and a neutral or charged event in either the upper or lower rear array and
the time-of-flight calculated for elastic np scattering. The secondary peak centered at
approximately 2.5 ns is the result of π 0 production in a scintillator in the front array.
The ∆TOF spectrum shown in Fig. 2 can be decomposed into four ∆TOF spectra for
scattering events to either the upper (U) or lower (D) rear array for the R () or L ()
helicity state of the incoming beam. From the yields in the four ∆TOF spectra, the cross
ratio, r, can be calculated; the cross ratio is defined to be the ratio of two geometric
means, NU ND 12 and NU ND 12 , where NU ND is the yield in the ∆TOF peak for
neutrons scattered up(down) when the beam helicity was postive(negative). The physical
scattering asymmetry is then given by r 1r 1.
6000
4000
2000
1000
2000
0
-20 -10 0 10 20
cTOF [ns]
0
-10 -5 0 5 10 15
∆TOF [ns]
FIGURE 2. Typical cTOF and ∆TOF spectra from a representative run at Q 2 117 (GeV/c)2 .
Our preliminary results for GnE are plotted as the filled squares in Fig. 3 together with
the current world data on GnE obtained via polarization measurements [4-12]. In order
to extract GnE from our measurements of g, we used the dipole parameterization for
GnM with a 5% relative uncertainty. Our preliminary results for G nE at Q2 045 and 1.15
(GeV/c)2 are consistent with the Galster [13] parameterization; however, our preliminary
result for GnE at Q2 147 (GeV/c)2 lies slightly above the Galster parameterization.
The error bars that are plotted for our preliminary results reflect statistical errors only;
however, the systematic errors are small compared to the statistical errors. Corrections
resulting from the finite acceptance of the polarimeter and final state interactions have
not yet been applied to our preliminary results for G nE ; these effects are currently under
investigation.
ACKNOWLEDGMENTS
We thank the TJNAF Hall C scientific and engineering staff for their outstanding support. This work was supported in part by the National Science Foundation, the Depart-
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FIGURE 3. The current world data on G nE versus Q2 obtained via polarization measurements. Our
preliminary data are represented by filled squares. The Galster parameterization is shown as the solid line
for Q2 07 (GeV/c)2 , and its extension to higher Q 2 is shown as the dashed line. The points on the
abscissa are projections.
ment of Energy, and the Deutsche Forschungsgemeinschaft. The Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator
Facility under the U.S. Department of Energy contract DE-AC05-84ER40150.
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