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Spin effects in medium-energy electron-3He scattering
NUCLEAR INSTRUMENTS 81METHODS IN PHYSICS RESEARCH Nuclear Instruments and Methods in Physics Research A 402 (1998) 268-276
ELSEVIER
Spin effects in medium-energy
electron-3He
Section A
scattering
J.F.J. van den Branda, b. *, R. Alarconc, Th. Bauerd, D. Boersmad, T. Bottob, H.J. Bulterf, L. van Buurena, R. Ent”, M. Ferro-Luzzib, D. Geurt9, M. Harvey”, P. Heimberg”, D. Highinbothamf, C.W. de Jagerb, B. Norumf, I. Passchierb, H.R. Poolmanb, M. van der Putteb, E. Six”, J. Steijgerb, D. Szczerbaa, H. de Vriesb aDepartment
ofPh.vsicsand
Astronomy, Vrije Umiversiteit, 1081 HV Amsterdam, The Netherlands bNIKHEF, 1009 DB Amsterdam, The Netherlands ‘Department of Physics, Arizona State University, Tempe, AZ 85287, USA ‘Department ofPhysics, Rijks Universiteit Utrecht, The Netherlands “TJNAF, Newport News, VA 23606, and Department of Physics, Hampton University, Hampton, l44 23668, USA ‘Department of Physics, University of Virginia, Charlottesville, VA 22901, USA
Abstract New physics can be accessed by scattering polarized electrons from a polarized 3He internQas target. It is discussed how the asymmetries for the reactions 3Hk@, e’), 3Hk@, e’p) G@, e’n) GE, e’d) and 3He@, e’pn) may provide precise information on the S’ and the D-wave parts of the 3He ground-state wave function, the neutron form factors, and the role of spin-dependent reaction mechanism effects. The experiment uses up to 900 MeV (polarized) electrons from the AmPS storage ring in Amsterdam, Netherlands, in combination with large acceptance electron and hadron detectors.
1. Introduction The 3He nucleus is the subject of considerable current interest. It is a calculable nuclear system where our understanding of nuclear structure can be precisely compared with data. In addition, it is generally thought that polarized 3He can serve as
*Correspondence address: Department of Physics and Astronomy, Vrije Universiteit, 1081 HV Amsterdam, The Netherlands. 016%9002/98/$19.00 0 1998 Elsevier PII SO168-9002(97)00848-6
Science B.V. All rights reserved
an effective polarized neutron target for experiments in nuclear [l] and particle [2] physics. Fundamental properties of the neutron such as its charge and spin distributions remain largely unconstrained experimentally. Thus, many experiments using polarized 3He targets are underway world-wide in large part motivated by measurement of neutron elastic form factors [3-51 and deep inelastic structure functions [S-S]. It is imperative to understand the ground state spin structure of the 3He nucleus to extract information on neutron structure from these measurements.
JF.J.
uan den Brand et al. INucl. Ins@. and Meth. in Phys. Rex A 402 (1998) 268-276
The nuclear structure information of the 3He ground state is contained in the spin-dependent spectral function [9] $(E,p) defined as the probability density of finding a nucleon N with separation energy E,momentum p and spin along (opposite) the 3He spin indicated by 6 = + (-). spin-dependent electron-induced Quasielastic knockout of the constituent nucleons of 3He offers the most direct experimental approach to constrain the spectral function. We will show that exclusive and semi-inclusive scattering of polarized electrons from polarized 3He using the reactions ($ e’p) and p, e’d) offers a powerful tool to disentangle the S, S’ and D-state components of the ground-state wave function. In the non-relativistic approximation using Faddeev techniques, the S-state contribution to the spectral function is found to be dominant at low initial nucleon momenta 11,101. Motivated by this we will measure the sideways target asymmetry, A:,in the reactions (Z, e’), and @, e’n) to constrain the neutron charge form factor. Our method of simultaneously surveying several reactions over a wide range of kinematics is central in our approach to disentangle nucleon and nuclear structure from reaction mechanism effects such as final-state interactions (FSI) and meson-exchange currents (MEC). In addition, we intend to measure induced asymmetries as an additional means to isolate the FSI and MEC contributions. 2. Physics motivation Exact non-relativistic calculations based on realistic nucleonnucleon (NN) potentials can be performed for the three-body system. This allows for a meaningful meeting place between theory and experiment. It turns out that even the static observables, such as binding energy and charge radius, are not in agreement with the results of such calculations (see e.g. Ref. [ 111). This has led to speculations that relativistic effects and/or three-body forces should be accounted for. The analysis of dynamic observables, such as the elastic electron scattering form factors, show the importance of virtual Delta components in the ground-state wave function of 3He. Their probability is estimated [12,13] to be about 2%. Finally, T,, measured
269
in capture reactions indicates the presence of the D-state components in the wave function. The dominant component of the 3He wave function is the spatially symmetric S-wave. Here, the proton spins are in the singlet state and the 3He spin is solely carried by the neutron. This picture is supported by the near equality of the 3He and neutron magnetic moments (,uL,~~= - 2.12 nm and ,u~ = - 1.91 nm). In this model polarized 3He would serve as an effective neutron target. Several experiments based on this concept have been proposed/approved and carried out with the goal to study the structure of the neutron (for example experiments El42 and El54 at SLAC, and HERMES at DESY). Furthermore, experiments are in preparation at MIT-Bates, Mainz and CEBAF to measure the charge form factor of the neutron. However, it is clear that there are corrections to this naive picture. It is expected that the protons in 3He are partly polarized due to the presence of the S’ and D-state components in the nuclear wave function, which have small probabilities of Psfz 1.5% and PD z 8%, respectively. In addition, one should be aware that Fermi motion, virtual Delta’s, mesons, three-body forces, etc., can complicate the interpretation. Finally, one has to understand the spin dependence of the reactionmechanism effects such as final-state interactions and meson-exchange currents. The S’ state is a mixed symmetry S-wave configuration of the nucleons which indicates the deviation from symmetry due to the isospin-space correlations in the nuclear interaction. Results of a multitude of three-body calculations [14] show that its probability is strongly correlated with the The S/-state is binding energy as PsrszEg2.1. an intriguing quantity: it obviously does not exist for “H, for the three-body isospin doublet one has whereas for 4He and heavier nuclei PS Al-1.5%, it is expected to be strongly suppressed (P,. < 0.1 “A) due to the higher binding energies. The S’-state is an important quantity that deserves experimental investigation. For example, it is thought to be largely responsible for the difference in the charge radius between 3He and 3H. However, an important question is how one should go about in making precise measurements sensitive to such a small quantity.
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Besides the dominant S-waves, the 3He groundstate wave function contains P and D-states. P-state probabilities are believed to be extremely small (~0.01%) and I will not discuss them. The tensor part of the NN force induces various D-state components with a total probability estimated [1,12] at PD z 8%. For the D-state contribution the orbital angular momentum L = 2 couples with the total spin S = $ to the nuclear spin J = 4. Therefore, the spins of the nucleons are all dominantly oriented opposite to the nuclear spin. There are significant effects of including the S’ and D-states on the calculated momentum distribution of a neutron with spin opposite to the nuclear spin. Contrary to the S-waves, the D-wave contribution to the momentum distribution is highly dependent on the angle t between the nucleon momentum and the nuclear spin vectors. More than a factor of two variation in the momentum density is predicted at momentum values p z 100 MeV/c. The NIKHEF storage ring in combination with a polarized 3He internal gas target will allow for high-quality measurements of asymmetries in the quasi-free scattering region. Fig. 1 shows the asymmetries calculated in the model of Laget [15] for an incident electron beam of energy 880 MeV and a three-momentum transfer q of 400 MeV/c as a function of missing momentum pm (which is the momentum of the recoiling nuclear system. In plane-wave impulse approximation (PWIA), one has pm = -pi, with pi the initial momentum of the proton inside the nucleus). It is seen that the asymmetries are of the order of 0.05-0.1. The calculations show that the effects of FSI and MEC are important. Experimental information on these reaction-mechanism contributions will be obtained by orienting the nuclear spin normal to the electron scattering plane. One then measures the asymmetry At, which equals zero in PWIA and therefore is entirely due to reaction-mechanism effects like FSI and MEC. The figure also shows the statistical accuracy projected for 500 h of running time with a beam polarization of 0.7 and target polarization of 0.5. The luminosity is assumed to be 8 x. 1O32 atomscm-2 s- ‘. It is seen that at zero recoil momentum the asymmetries are significant and can be measured to high precision. Here, only
the S-states contribute, and therefore such a measurement will provide unique information about this important partial-wave channel. At non-zero recoil momentum the D-state and also contributes and may be separated from the S/-state contribution by taking advantage of the dependence on the angle t. In Fig. 2 we show the asymmetries for the (e, e’n) channel as a function of momentum transfer, as calculated by Laget [15]. Furthermore, we show the world data (figure from Ref. [16]) of Gg obtained from elastic scattering off the deuteron. The curves indicate the uncertainty on Gg, due to the choice of NN-potential in the analysis. Exclusive data yield an absolute normalization of G& provided that the description of the reaction mechanism is under control.
3. The experiment We intend to measure the spin-dependent spectral function. The transverse asymmetry A,” and the sideways and longitudinal spin-correlation parameters A!! and A: will be measured for elastic scattering and for quasi-elastic (e, e’p), (e, e’n) and (e, e’d) scattering with large-acceptance detectors up to missing momenta of 400 MeV/c. We will perform measurements at values of momentum transfer Q2 of 0.15,0.3, and 0.5 GeV2. A consistent set of measurements of these different asymmetries will provide the means to disentangle different aspects of the reaction mechanism. The asymmetry A,” is identical to 0 in plane-wave impulse approximation; its measurement will isolate the effects of final-state interactions and meson-exchange currents. The measurements of A: and A: in the (e, e’) and (e, e’n) reaction channels will constrain Gi and G&. The spin-correlation parameters in the (e, e’p) channel are sensitive to the S-state at low and D-state at high missing momentum. The experiment will be performed at the internal target hall at NIKHEF. Polarized electrons of energies up to 900 MeV will be scattered from a 3He target [17]. Recently, we accelerated polarized electrons with currents up to 150 mA. The polarization of the beam as measured by laser Compton backscattering is shown in Fig. 3. The data show
J.F.J. van den Brand et al.lNucl.
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Instr. and Meth. in Phys. Rex A 402 (1998) 268-276
MeV/cl
P,
[MeV/cl
Fig. 1. The transverse-induced asymmetry A,” and the sideways and longitudinal spin-correlation parameters AX and Al for the reaction 3He(Z, e’p). Left panel: the exclusive reaction 3He(e, e’p)d. The dotted and dashed curves correspond to PWIA when only the S-wave, and the S-wave and D-wave contributions are taken into account, respectively. The dot-dashed curves include FSI, while the solid curve also include MEC effects. Right panel: the semi-inclusive reaction 3He(e, e’p)pn. The dotted, dot-dashed, and dashed curves correspond to PWIA when only the iSO, the ISO and the %SO.and the S- and D-wave contributions are taken into account, respectively. The solid curves also include FSI and MEC effects. The markers indicate the projected accuracy that can be obtained in this experiment.
that the injected polarization is maintained in the ring. The polarization at the injector was 0.5. Due to the fact that the spin rotator was not calibrated yet, the expected initial polarization injected into the ring was 0.34. Since the measured polarization lifetimes z, were greater than 2000 s, and the beam lifetime with full gas load is of the order of 200 s, depolarization of the beam will be negligible during the experiment.
We apply the metastability optical pumping technique. 3He gas is flown into a Pyrex pumping cell. A discharge is created by two RF-coils, driven by a 20 MHz generator. The discharge populates the 23S1 triplet state. Circularly polarized laser light with a wavelength of 1.083 urn impinges on the pumping cell, and induces transitions between the 23S1 and 23P0 states. The resulting polarization of the 3He nuclei can be reversed by inverting the
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helicity of the laser light. The target polarization can be determined by analyzing the circular polarization of the 667 nm Balmer line in the fluorescence spectrum [lS]. The external magnetic field that is used to direct the spin of the 3He nucleus is supplied by three mutually perpendicular sets of Helmholtz coils, that allow for rotation of the spin to any given direction. We obtain slightly more than 40% of polarization at a flow of 1017 at/s (see Fig. 4). The T-shaped storage cell is cooled to 20 K in order to further
3He(e,e’n)pp I
-0.1
0.0
I
I
I
0.2
0.4
I
0.6
increase the atomic density of the target. The cryogenic target is shown in Fig. 5. The coldhead contains ferromagnetic materials; therefore it is located outside the Helmholtz coils, far away from the pumping cell. In order to suppress heating of the cell due to the RF field of the beam, wake field suppressors were installed between the storage cell and the beam pipe. Fig. 6 shows the experimental setup. Scattered electrons are detected by a magnetic spectrometer with a solid angle of 100 msr and a momentum acceptance of 300-1000 MeV/c. The angular resolution of this detector is dominated by multiple scattering (a few mrad), the momentum resolution is expected to be Ap/p N 5 x 10-3. Protons are detected in a range telescope, which contains two wire chambers (with planes at O”, 45”, and 90”) for tracking, followed by a 30 strips wide hodoscope and 15 layers of 10 mm thick plastic scintillators. The range telescope has a solid angle of - 200 msr and an energy resolution of -3 MeV. Behind the range telescope, at 3 m from the interaction point, a neutron detector is positioned, covering about the same solid angle. This neutron detector contains 8 scintillator bars of 0.2 x 0.2 x 1.6 m. Each bar is preceded by two veto scintillators of 4 and 10 mm thickness. Silicon detectors are located inside the vacuum to enable detection of recoiling
-0.6 -0.8 -
-0.6t
0.0
-I
0.2
Q2 [GeV2]
0.4
0.6
or0
I
I
5
IO Q’
I5
20
[fin-‘1
Fig. 2. The asymmetry A: and the spin-correlation parameters A: and AZ as a function of Q2_ The dashed and solid curves represent the calculations of Laget [15] for PWIA and including FSI and MEC effects, respectively. Right: World data [18] on G; as a function of Q*. The solid markers represent the expected accuracy of the present experiment. The open circle at Qz = 8 fm-* represents the datum from Ref. [4], which is obtained with the 3He(e, e’n) reaction.
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I
I
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+
0.32 ‘,+
0.24 0.16 0.08 0.00
0
‘inject
=
4o
InA
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[sl
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‘inject = 120
InA
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t [sl
Fig. 3. Polarization in the ring as measured with Compton backscattering, for an injected current of 40 mA (left panel) and 120 mA (right panel).
800 time
1000
(set)
+
Fig. 4. Polarization for the ‘He target as a function of time. At t - 850 s, the laser light is blocked
protons and deuterons. Since the energy resolution of the electron and proton detector is not good enough to unambiguously separate the two- and three-body break-up channel in the (e, e’p) reaction, this separation has to be obtained in another manner. We will follow three strategies to assess the physics related to these different break-up channels: (a) we simultaneously perform measurements for the (e, e’d) reaction channel; (b) we will explore the (e, e’p) asymmetries as a function of missing energy by applying cuts to the low- and high-energy side of the missingenergy peak corresponding to two-body breakup; (c) we will analyze triple coincidences, in which a recoiling proton or deuteron is detected in the silicon detectors. Obviously, the latter approach
will only allow separation of two- and three-body breakup for a limited part of the (e, e’p) phase space. Fig. 7 shows, that with the silicon detectors we can cleanly separate elastically scattered 3He particles from background. Since the spin-spin correlation for elastic scattering from 3He can be calculated from the electromagnetic form factors for 3He, which are well-known in the range of Q2, this coincidence reaction provides us with an alternative way to determine the product of target and beam polarization. The experiment has been approved for 1000 h of beam time. First data taking has been scheduled for 1997. The expected accuracy for the asymmetries has been indicated in Figs. 1 and 2.
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Fig. 5. Overview of the cryogenic bends to the storage cell.
target. The coldhead
is located
4. Summary In summary, with the advent of CW polarized electron beams, polarized 3He internal targets, and a large acceptance detector, a vivid future for the
outside the Helmholtz
coils and is connected
via a heat pipe with two
study of spin observables in the 3He system is upcoming. We have shown that precise determination of the small components of the 3He groundstate wave function is possible within a reasonable time frame.
J.F.J. van den Brand et al./Nucl.
Fig. 6. Overview detector.
of the experimental
Ins@. and Meth. in Phys. Rex A 402 (1998) 268-276
area. Part of the beam line is shown, as well as the target chamber,
Helmholtz
coils and electron
Acknowledgements
120 100
This work was supported in part by the Stichting voor Fundamenteel Onderzoek der Materie (FOM).
80 60 40 20 0
IO
20 E,, (h4eV)
50
40 30 20 10 0
0 'O" ezay(M
0
’
-100 t3He-teLc fa.df
Fig. 7. Coincident events between the electron detector and the silicon detector. Top left panel: correlation of the deposited energies in the first and second silicon layers. One can clearly distinguish bands for recoiling protons, deuterons, tritons, 3He and 4He nuclei. The area that yields recoiling %e nuclei is indicated. Top right: timing difference between the events in the electron and recoil detector. The shaded area corresponds to the 3He nuclei in the top left panel. Bottom left: energy spectrum of the electron detector. The shaded area corresponds to the 3He nuclei in the top left panel. Bottom right: correlation in out-ofplane angles for the 3He events. For elastic scattering, these events should be coplanar.
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References [l] B. Blankleider, R.W. Woloshyn, Phys. Rev. C 29 (1984) 538. PI R.G. Milner,in: R.W. Dunford, F.P. Calaprice (Eds.), Proc. Workshop on Polarized “He Beams and Targets, AIP 131, New York, 1984, p. 186. c31 H. Gao et al., Phys. Rev. C 50 (1994) R546. t41 M. Meyerhoff et al., Phys. Lett. B 327 (1994) 201. c51 Bates Large Acceptance Spectrometer Toroid (BLAST) proposal, MIT-BATES, 1992. C61 P.L. Anthony et al., Phys. Rev. Lett. 71 (1993) 959. c71 HERMES experiment at DESY, DESY Rep. No. DESYPRC-93-06, 1993, unpublished. PI Experiment E-154; spokesperson R. Hughes.
[9] S. Frullani, J. Mougey, Adv. Nucl. Phys. 14 (1984).
[lo] [ll] [12] [13] [14] [15] [16] [17]
[18]
R.W. Schulze, P.U. Sauer, Phys. Rev. C 48 (1993) 38. B.F. Gibson, Nucl. Phys. A 543 (1992) lc. W. Strueve et al., Nucl. Phys. A 465 (1987) 651. A. Picklesimer, R.A. Rice, R. Brandenbirg, Phys. Rev. c 44 (1991) 1359. J.L. Friar et al., Phys. Lett. B 161 (1985) 241. J.M. Laget, Phys. Lett. B 276 (1992) 398. S. Platchkov et al., Nucl. Phys. A 510 (1990) 740. H.R. Poolman, in: H. Paetz gen. Schick, L. Sydow (Eds.), Proc. Internat. Workshop on Polarized Beams and Polarized Gas Targets, Cologne, 6-9 June, World Scientific, Singapore, 1995. W. Lorenzon et al., Phys. Rev. A 47 (1993) 468.
ELSEVIER
Spin effects in medium-energy
electron-3He
Section A
scattering
J.F.J. van den Branda, b. *, R. Alarconc, Th. Bauerd, D. Boersmad, T. Bottob, H.J. Bulterf, L. van Buurena, R. Ent”, M. Ferro-Luzzib, D. Geurt9, M. Harvey”, P. Heimberg”, D. Highinbothamf, C.W. de Jagerb, B. Norumf, I. Passchierb, H.R. Poolmanb, M. van der Putteb, E. Six”, J. Steijgerb, D. Szczerbaa, H. de Vriesb aDepartment
ofPh.vsicsand
Astronomy, Vrije Umiversiteit, 1081 HV Amsterdam, The Netherlands bNIKHEF, 1009 DB Amsterdam, The Netherlands ‘Department of Physics, Arizona State University, Tempe, AZ 85287, USA ‘Department ofPhysics, Rijks Universiteit Utrecht, The Netherlands “TJNAF, Newport News, VA 23606, and Department of Physics, Hampton University, Hampton, l44 23668, USA ‘Department of Physics, University of Virginia, Charlottesville, VA 22901, USA
Abstract New physics can be accessed by scattering polarized electrons from a polarized 3He internQas target. It is discussed how the asymmetries for the reactions 3Hk@, e’), 3Hk@, e’p) G@, e’n) GE, e’d) and 3He@, e’pn) may provide precise information on the S’ and the D-wave parts of the 3He ground-state wave function, the neutron form factors, and the role of spin-dependent reaction mechanism effects. The experiment uses up to 900 MeV (polarized) electrons from the AmPS storage ring in Amsterdam, Netherlands, in combination with large acceptance electron and hadron detectors.
1. Introduction The 3He nucleus is the subject of considerable current interest. It is a calculable nuclear system where our understanding of nuclear structure can be precisely compared with data. In addition, it is generally thought that polarized 3He can serve as
*Correspondence address: Department of Physics and Astronomy, Vrije Universiteit, 1081 HV Amsterdam, The Netherlands. 016%9002/98/$19.00 0 1998 Elsevier PII SO168-9002(97)00848-6
Science B.V. All rights reserved
an effective polarized neutron target for experiments in nuclear [l] and particle [2] physics. Fundamental properties of the neutron such as its charge and spin distributions remain largely unconstrained experimentally. Thus, many experiments using polarized 3He targets are underway world-wide in large part motivated by measurement of neutron elastic form factors [3-51 and deep inelastic structure functions [S-S]. It is imperative to understand the ground state spin structure of the 3He nucleus to extract information on neutron structure from these measurements.
JF.J.
uan den Brand et al. INucl. Ins@. and Meth. in Phys. Rex A 402 (1998) 268-276
The nuclear structure information of the 3He ground state is contained in the spin-dependent spectral function [9] $(E,p) defined as the probability density of finding a nucleon N with separation energy E,momentum p and spin along (opposite) the 3He spin indicated by 6 = + (-). spin-dependent electron-induced Quasielastic knockout of the constituent nucleons of 3He offers the most direct experimental approach to constrain the spectral function. We will show that exclusive and semi-inclusive scattering of polarized electrons from polarized 3He using the reactions ($ e’p) and p, e’d) offers a powerful tool to disentangle the S, S’ and D-state components of the ground-state wave function. In the non-relativistic approximation using Faddeev techniques, the S-state contribution to the spectral function is found to be dominant at low initial nucleon momenta 11,101. Motivated by this we will measure the sideways target asymmetry, A:,in the reactions (Z, e’), and @, e’n) to constrain the neutron charge form factor. Our method of simultaneously surveying several reactions over a wide range of kinematics is central in our approach to disentangle nucleon and nuclear structure from reaction mechanism effects such as final-state interactions (FSI) and meson-exchange currents (MEC). In addition, we intend to measure induced asymmetries as an additional means to isolate the FSI and MEC contributions. 2. Physics motivation Exact non-relativistic calculations based on realistic nucleonnucleon (NN) potentials can be performed for the three-body system. This allows for a meaningful meeting place between theory and experiment. It turns out that even the static observables, such as binding energy and charge radius, are not in agreement with the results of such calculations (see e.g. Ref. [ 111). This has led to speculations that relativistic effects and/or three-body forces should be accounted for. The analysis of dynamic observables, such as the elastic electron scattering form factors, show the importance of virtual Delta components in the ground-state wave function of 3He. Their probability is estimated [12,13] to be about 2%. Finally, T,, measured
269
in capture reactions indicates the presence of the D-state components in the wave function. The dominant component of the 3He wave function is the spatially symmetric S-wave. Here, the proton spins are in the singlet state and the 3He spin is solely carried by the neutron. This picture is supported by the near equality of the 3He and neutron magnetic moments (,uL,~~= - 2.12 nm and ,u~ = - 1.91 nm). In this model polarized 3He would serve as an effective neutron target. Several experiments based on this concept have been proposed/approved and carried out with the goal to study the structure of the neutron (for example experiments El42 and El54 at SLAC, and HERMES at DESY). Furthermore, experiments are in preparation at MIT-Bates, Mainz and CEBAF to measure the charge form factor of the neutron. However, it is clear that there are corrections to this naive picture. It is expected that the protons in 3He are partly polarized due to the presence of the S’ and D-state components in the nuclear wave function, which have small probabilities of Psfz 1.5% and PD z 8%, respectively. In addition, one should be aware that Fermi motion, virtual Delta’s, mesons, three-body forces, etc., can complicate the interpretation. Finally, one has to understand the spin dependence of the reactionmechanism effects such as final-state interactions and meson-exchange currents. The S’ state is a mixed symmetry S-wave configuration of the nucleons which indicates the deviation from symmetry due to the isospin-space correlations in the nuclear interaction. Results of a multitude of three-body calculations [14] show that its probability is strongly correlated with the The S/-state is binding energy as PsrszEg2.1. an intriguing quantity: it obviously does not exist for “H, for the three-body isospin doublet one has whereas for 4He and heavier nuclei PS Al-1.5%, it is expected to be strongly suppressed (P,. < 0.1 “A) due to the higher binding energies. The S’-state is an important quantity that deserves experimental investigation. For example, it is thought to be largely responsible for the difference in the charge radius between 3He and 3H. However, an important question is how one should go about in making precise measurements sensitive to such a small quantity.
II. SPIN STRUCTURE
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Besides the dominant S-waves, the 3He groundstate wave function contains P and D-states. P-state probabilities are believed to be extremely small (~0.01%) and I will not discuss them. The tensor part of the NN force induces various D-state components with a total probability estimated [1,12] at PD z 8%. For the D-state contribution the orbital angular momentum L = 2 couples with the total spin S = $ to the nuclear spin J = 4. Therefore, the spins of the nucleons are all dominantly oriented opposite to the nuclear spin. There are significant effects of including the S’ and D-states on the calculated momentum distribution of a neutron with spin opposite to the nuclear spin. Contrary to the S-waves, the D-wave contribution to the momentum distribution is highly dependent on the angle t between the nucleon momentum and the nuclear spin vectors. More than a factor of two variation in the momentum density is predicted at momentum values p z 100 MeV/c. The NIKHEF storage ring in combination with a polarized 3He internal gas target will allow for high-quality measurements of asymmetries in the quasi-free scattering region. Fig. 1 shows the asymmetries calculated in the model of Laget [15] for an incident electron beam of energy 880 MeV and a three-momentum transfer q of 400 MeV/c as a function of missing momentum pm (which is the momentum of the recoiling nuclear system. In plane-wave impulse approximation (PWIA), one has pm = -pi, with pi the initial momentum of the proton inside the nucleus). It is seen that the asymmetries are of the order of 0.05-0.1. The calculations show that the effects of FSI and MEC are important. Experimental information on these reaction-mechanism contributions will be obtained by orienting the nuclear spin normal to the electron scattering plane. One then measures the asymmetry At, which equals zero in PWIA and therefore is entirely due to reaction-mechanism effects like FSI and MEC. The figure also shows the statistical accuracy projected for 500 h of running time with a beam polarization of 0.7 and target polarization of 0.5. The luminosity is assumed to be 8 x. 1O32 atomscm-2 s- ‘. It is seen that at zero recoil momentum the asymmetries are significant and can be measured to high precision. Here, only
the S-states contribute, and therefore such a measurement will provide unique information about this important partial-wave channel. At non-zero recoil momentum the D-state and also contributes and may be separated from the S/-state contribution by taking advantage of the dependence on the angle t. In Fig. 2 we show the asymmetries for the (e, e’n) channel as a function of momentum transfer, as calculated by Laget [15]. Furthermore, we show the world data (figure from Ref. [16]) of Gg obtained from elastic scattering off the deuteron. The curves indicate the uncertainty on Gg, due to the choice of NN-potential in the analysis. Exclusive data yield an absolute normalization of G& provided that the description of the reaction mechanism is under control.
3. The experiment We intend to measure the spin-dependent spectral function. The transverse asymmetry A,” and the sideways and longitudinal spin-correlation parameters A!! and A: will be measured for elastic scattering and for quasi-elastic (e, e’p), (e, e’n) and (e, e’d) scattering with large-acceptance detectors up to missing momenta of 400 MeV/c. We will perform measurements at values of momentum transfer Q2 of 0.15,0.3, and 0.5 GeV2. A consistent set of measurements of these different asymmetries will provide the means to disentangle different aspects of the reaction mechanism. The asymmetry A,” is identical to 0 in plane-wave impulse approximation; its measurement will isolate the effects of final-state interactions and meson-exchange currents. The measurements of A: and A: in the (e, e’) and (e, e’n) reaction channels will constrain Gi and G&. The spin-correlation parameters in the (e, e’p) channel are sensitive to the S-state at low and D-state at high missing momentum. The experiment will be performed at the internal target hall at NIKHEF. Polarized electrons of energies up to 900 MeV will be scattered from a 3He target [17]. Recently, we accelerated polarized electrons with currents up to 150 mA. The polarization of the beam as measured by laser Compton backscattering is shown in Fig. 3. The data show
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Fig. 1. The transverse-induced asymmetry A,” and the sideways and longitudinal spin-correlation parameters AX and Al for the reaction 3He(Z, e’p). Left panel: the exclusive reaction 3He(e, e’p)d. The dotted and dashed curves correspond to PWIA when only the S-wave, and the S-wave and D-wave contributions are taken into account, respectively. The dot-dashed curves include FSI, while the solid curve also include MEC effects. Right panel: the semi-inclusive reaction 3He(e, e’p)pn. The dotted, dot-dashed, and dashed curves correspond to PWIA when only the iSO, the ISO and the %SO.and the S- and D-wave contributions are taken into account, respectively. The solid curves also include FSI and MEC effects. The markers indicate the projected accuracy that can be obtained in this experiment.
that the injected polarization is maintained in the ring. The polarization at the injector was 0.5. Due to the fact that the spin rotator was not calibrated yet, the expected initial polarization injected into the ring was 0.34. Since the measured polarization lifetimes z, were greater than 2000 s, and the beam lifetime with full gas load is of the order of 200 s, depolarization of the beam will be negligible during the experiment.
We apply the metastability optical pumping technique. 3He gas is flown into a Pyrex pumping cell. A discharge is created by two RF-coils, driven by a 20 MHz generator. The discharge populates the 23S1 triplet state. Circularly polarized laser light with a wavelength of 1.083 urn impinges on the pumping cell, and induces transitions between the 23S1 and 23P0 states. The resulting polarization of the 3He nuclei can be reversed by inverting the
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helicity of the laser light. The target polarization can be determined by analyzing the circular polarization of the 667 nm Balmer line in the fluorescence spectrum [lS]. The external magnetic field that is used to direct the spin of the 3He nucleus is supplied by three mutually perpendicular sets of Helmholtz coils, that allow for rotation of the spin to any given direction. We obtain slightly more than 40% of polarization at a flow of 1017 at/s (see Fig. 4). The T-shaped storage cell is cooled to 20 K in order to further
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increase the atomic density of the target. The cryogenic target is shown in Fig. 5. The coldhead contains ferromagnetic materials; therefore it is located outside the Helmholtz coils, far away from the pumping cell. In order to suppress heating of the cell due to the RF field of the beam, wake field suppressors were installed between the storage cell and the beam pipe. Fig. 6 shows the experimental setup. Scattered electrons are detected by a magnetic spectrometer with a solid angle of 100 msr and a momentum acceptance of 300-1000 MeV/c. The angular resolution of this detector is dominated by multiple scattering (a few mrad), the momentum resolution is expected to be Ap/p N 5 x 10-3. Protons are detected in a range telescope, which contains two wire chambers (with planes at O”, 45”, and 90”) for tracking, followed by a 30 strips wide hodoscope and 15 layers of 10 mm thick plastic scintillators. The range telescope has a solid angle of - 200 msr and an energy resolution of -3 MeV. Behind the range telescope, at 3 m from the interaction point, a neutron detector is positioned, covering about the same solid angle. This neutron detector contains 8 scintillator bars of 0.2 x 0.2 x 1.6 m. Each bar is preceded by two veto scintillators of 4 and 10 mm thickness. Silicon detectors are located inside the vacuum to enable detection of recoiling
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Fig. 2. The asymmetry A: and the spin-correlation parameters A: and AZ as a function of Q2_ The dashed and solid curves represent the calculations of Laget [15] for PWIA and including FSI and MEC effects, respectively. Right: World data [18] on G; as a function of Q*. The solid markers represent the expected accuracy of the present experiment. The open circle at Qz = 8 fm-* represents the datum from Ref. [4], which is obtained with the 3He(e, e’n) reaction.
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Fig. 3. Polarization in the ring as measured with Compton backscattering, for an injected current of 40 mA (left panel) and 120 mA (right panel).
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Fig. 4. Polarization for the ‘He target as a function of time. At t - 850 s, the laser light is blocked
protons and deuterons. Since the energy resolution of the electron and proton detector is not good enough to unambiguously separate the two- and three-body break-up channel in the (e, e’p) reaction, this separation has to be obtained in another manner. We will follow three strategies to assess the physics related to these different break-up channels: (a) we simultaneously perform measurements for the (e, e’d) reaction channel; (b) we will explore the (e, e’p) asymmetries as a function of missing energy by applying cuts to the low- and high-energy side of the missingenergy peak corresponding to two-body breakup; (c) we will analyze triple coincidences, in which a recoiling proton or deuteron is detected in the silicon detectors. Obviously, the latter approach
will only allow separation of two- and three-body breakup for a limited part of the (e, e’p) phase space. Fig. 7 shows, that with the silicon detectors we can cleanly separate elastically scattered 3He particles from background. Since the spin-spin correlation for elastic scattering from 3He can be calculated from the electromagnetic form factors for 3He, which are well-known in the range of Q2, this coincidence reaction provides us with an alternative way to determine the product of target and beam polarization. The experiment has been approved for 1000 h of beam time. First data taking has been scheduled for 1997. The expected accuracy for the asymmetries has been indicated in Figs. 1 and 2.
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Fig. 5. Overview of the cryogenic bends to the storage cell.
target. The coldhead
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4. Summary In summary, with the advent of CW polarized electron beams, polarized 3He internal targets, and a large acceptance detector, a vivid future for the
outside the Helmholtz
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study of spin observables in the 3He system is upcoming. We have shown that precise determination of the small components of the 3He groundstate wave function is possible within a reasonable time frame.
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Fig. 6. Overview detector.
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area. Part of the beam line is shown, as well as the target chamber,
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Acknowledgements
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This work was supported in part by the Stichting voor Fundamenteel Onderzoek der Materie (FOM).
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Fig. 7. Coincident events between the electron detector and the silicon detector. Top left panel: correlation of the deposited energies in the first and second silicon layers. One can clearly distinguish bands for recoiling protons, deuterons, tritons, 3He and 4He nuclei. The area that yields recoiling %e nuclei is indicated. Top right: timing difference between the events in the electron and recoil detector. The shaded area corresponds to the 3He nuclei in the top left panel. Bottom left: energy spectrum of the electron detector. The shaded area corresponds to the 3He nuclei in the top left panel. Bottom right: correlation in out-ofplane angles for the 3He events. For elastic scattering, these events should be coplanar.
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References [l] B. Blankleider, R.W. Woloshyn, Phys. Rev. C 29 (1984) 538. PI R.G. Milner,in: R.W. Dunford, F.P. Calaprice (Eds.), Proc. Workshop on Polarized “He Beams and Targets, AIP 131, New York, 1984, p. 186. c31 H. Gao et al., Phys. Rev. C 50 (1994) R546. t41 M. Meyerhoff et al., Phys. Lett. B 327 (1994) 201. c51 Bates Large Acceptance Spectrometer Toroid (BLAST) proposal, MIT-BATES, 1992. C61 P.L. Anthony et al., Phys. Rev. Lett. 71 (1993) 959. c71 HERMES experiment at DESY, DESY Rep. No. DESYPRC-93-06, 1993, unpublished. PI Experiment E-154; spokesperson R. Hughes.
[9] S. Frullani, J. Mougey, Adv. Nucl. Phys. 14 (1984).
[lo] [ll] [12] [13] [14] [15] [16] [17]
[18]
R.W. Schulze, P.U. Sauer, Phys. Rev. C 48 (1993) 38. B.F. Gibson, Nucl. Phys. A 543 (1992) lc. W. Strueve et al., Nucl. Phys. A 465 (1987) 651. A. Picklesimer, R.A. Rice, R. Brandenbirg, Phys. Rev. c 44 (1991) 1359. J.L. Friar et al., Phys. Lett. B 161 (1985) 241. J.M. Laget, Phys. Lett. B 276 (1992) 398. S. Platchkov et al., Nucl. Phys. A 510 (1990) 740. H.R. Poolman, in: H. Paetz gen. Schick, L. Sydow (Eds.), Proc. Internat. Workshop on Polarized Beams and Polarized Gas Targets, Cologne, 6-9 June, World Scientific, Singapore, 1995. W. Lorenzon et al., Phys. Rev. A 47 (1993) 468.