BLED WORKSHOPS
IN PHYSICS
VOL. 13, NO. 1
p. 84
Proceedings of the Mini-Workshop
Hadronic Resonances
Bled, Slovenia, July 1 - 8, 2012
Approaching the spin structure of 3He
by polarization observables
S. Šircaa,b
a Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000
Ljubljana, Slovenia
b Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
Abstract. The E05-102 experiment at Jefferson Laboratory (TJNAF) was devised to study
the double-polarization asymmetries in electron-induced deuteron, proton, and neutron
knockout from polarized 3He at low momentum transfers, in a wide range of missing
momenta. With this advanced experimental technique, we strive to obtain a much clearer
insight into the ground-state structure of 3He, the cornerstone nucleus widely used as the
effective neutron target. An order of magnitude improvement in the statistical uncertain-
ties with respect to existing measurements is anticipated. We report on the status of the
ongoing data analysis.
1 Physics motivation
The primary motivation to study electron-induced processes involving the 3He
nucleus (see [1] and references therein) is to understand the ground-state struc-
ture of this nucleus. This structure is not only interesting by itself; it is also impor-
tant to study it in order to be able to interpret all data “on the neutron” for which
3He acts as an effective target to a very good approximation. Contrary to com-
mon belief, there is no widely adopted consensus about the exact level at which
this approximation can be treated as “good” or “good enough”.
A precise understanding of the transition between the experimental data
acquired on 3He targets and the observables corresponding to the neutron has
become a burning issue since the statistical precision of recently performed (or
future) experiments is so large that the systematical uncertainties of this compu-
tational transition procedure have become comparable to it. Some of the most
interesting observables fall into this category, like e.g. the neutron elastic form-
factors
GnE , G
n
M ,
and the polarized quark structure functions corresponding to the neutron,
GnE , G
n
M , A
n
1 , g
n
1 , g
n
2 ,
as well as the studies of the GDH sum rule.
Approaching the spin structure of 3He by polarization observables 85
One of the main complications, of course, is that the protons in 3He partly
polarized due to the presence of S ′- and D-state components of the ground-state
wave-function. (The ground-state configuration of 3He is intimately connected
to another open question of differences in RMS-radii, 〈r2〉1/2, of 3H as opposed
to 3He, a matter largely unresolved due to an almost complete lack of measure-
ments on tritium.) The manifestations of the distribution of spin, orbital angular
momentum and isospin within 3He appear to be most prominent and unambigu-
ous in double-polarization asymmetries for electron-induced deuteron, proton,
and neutron knockout from polarized 3He. Numerous discrepancies among the
state-of-the-art theories persist for these observables.
In short, understanding the role of D and S ′ states as the two most relevant
sub-leading components of the 3He wave-function, and of the spin- and isospin-
dependence of reaction mechanisms on 3He is one of the key issues in the “Stan-
dard Model” of few-body theory.
2 The measurements
The exclusive cross-section for electron-induced deuteron knockout (with both
the beam and the target polarized) has the form
dσ(h,S)
dΩe dEe dΩd dpd
=
dσ0
dΩe dEe dΩd dpd
[
1+ S ·A0 + h(Ae + S ·A)
]
.
In the experiment described in this contribution, we measured two components
of A (or linear combinations thereof), which correspond to the transverse and
longitudinal double-polarization asymmetries
Ax,z =
[dσ++ + dσ−− ] − [dσ+− + dσ−+ ]
[dσ++ + dσ−− ] + [dσ+− + dσ−+ ]
,
where the subscript signs denote the helicities of the electron beam and the ori-
entation of the target spin. The target was polarized along the beam-line and per-
pendicular to it (in both sideways directions). Similarly, the asymmetries for ex-
clusive processes in which the proton and the neutron were knocked out (with
obvious modifications to the above formulas) have been measured.
Since the transverse and longitudinal asymmetries in each channel have very
distinct sensitivities to the dominant S and the sub-dominant D and S ′ compo-
nent of the 3He as functions of missing momentum, our experiment carries an im-
mense resolving power for testing theories mentioned below. The fact that several
exclusive channels were measured at the same time at approximately the same
four-momentum transfer of about 0.2 to 0.3 (GeV/c)2, in a large range of missing
momenta, and with excellent statistical and systematical uncertainties, is another
landmark feature of this experiment.
The resulting asymmetries will be compared to state-of-the-art theories of the
3He nucleus. We exploit the calculations of the Bochum/Krakow group [4] that
86 S. Širca
apply a full Faddeev approach with the AV18 NN-potential and the Urbana IX
three-nucleon force, together with a complete treatment of final-state interactions
(FSI) and meson-exchange currents (MEC).
Also available to use are the calculations of the Hannover/Lisbon group [5]
that are also full Faddeev, but with a coupled-channel extension and refit of the
CD-Bonn NN-potential. They also incorporate FSI and MEC, while the effective
three-nucleon force and two-body currents are provided by inclusion of the ∆ as
an active degree-of-freedom. Coulomb interaction for outgoing charged baryons
is also included.
The group from Pisa has also provided us with their calculations based on
the AV18 potential and the Urbana IX force in which the FSI are included by
means of the variational pair-hyperspherical harmonics expansion, and MEC are
also accounted for. This is not a Faddeev-type calcuation, but its accuracy is as-
sumed to be completely equivalent to it [6]. All three predictions (full calculations
only) are presented in comparison to the anticipated experimental uncertainties
in Fig. 1.
Fig. 1. The predictions for the asymmetries Ax and Ay in the quasi-elastic
3He(e, e ′d)
process. The anticipated experimental uncertainties and three calculations by the
Bochum/Krakow, Hannover/Lisbon and Pisa groups are shown.
3 Status of data analysis
The polarizations of the electron beam and the target have been established, and
the beam and target monitoring apparatus have been calibrated. The magneto-
optical properties of the BigBite spectrometer that was used to detect the charged
hadrons have been determined [3], and the tracking and PID detectors have been
calibrated, along with the neutron detector and the spectrometer used to detect
the electrons. Presently the analysis work is focused on the correct averaging of
Approaching the spin structure of 3He by polarization observables 87
the theoretical asymmetries over the relatively large experimental acceptance. To
this purpose, we have obtained the calculations of the asymmetries on a rather
dense grid of points in the (Ee, θe) plane that covers the majority of our accep-
tance, as shown in Fig. 2. The additional dimension in which averaging is per-
formed is the deuteron (or proton) emission angle with respect to the virtual
photon.
 [deg]eθ
10 11 12 13 14 15 16 17
E
’ [
G
eV
]
2.15
2.20
2.25
2.30
2.35
2.40
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31
32
33 34 35
Fig. 2. The grid in (Ee, θe) plane on which the theoretical calculations will be performed,
thus covering the most relevant parts of the experimental acceptance in the 3He(e, e ′d)
channel. The high density of points is needed for reliable acceptance averaging because
the asymmetries have a strong dependence on the energy transfer Ee − E
′
e (vertical axis).
The statistics of the data is sufficient to achieve a precision better than 2% on
the asymmetries in each 20MeV/c bin in missing momentum, ranging to about
200MeV/c in the deuteron channel and about 300MeV/c in the proton channels.
Similar accuracy will be achieved in the neutron channel, and an even better one
in the inclusive channels, which are a “bonus” of our experiment.
References
1. S. Širca, Few-Body Systems 47 (2010) 39.
2. S. Širca, S. Gilad, D. W. Higinbotham, W. Korsch, B. E. Norum (spokespersons),Mea-
surement ofAx andAz asymmetries in the quasi-elastic
3He (e, e ′d), JLab Experiment E05-
102, June 2005.
3. M. Mihovilovič et al. (Hall A Collaboration), Nucl. Instr. Meth. A 686 (2012) 20.
4. J. Golak, R. Skibiński, H. Witała, W. Glöckle, A. Nogga, H. Kamada, Phys. Reports 415
(2005) 89.
5. A. Deltuva et al., Phys. Rev. C 70 (2004) 034004.
6. L. E. Marcucci, M. Viviani, R. Schiavilla, A. Kievsky, S. Rosati, Phys. Rev. C 72 (2005)
014001.