Study of 3He (3H) Spin Structure via
3
dd
He n 3H p Reaction
T. Saito , V.P. Ladygin† , T. Uesaka , M. Hatano , A.Yu. Isupov† , H.
Kato , H. Kumasaka‡ , N.B. Ladygina† , Y. Maeda, A.I. Malakhov , J.
Nishikawa‡ , T. Ohnishi§ , H. Okamura‡ , S.G. Reznikov , H. Sakai, N.
Sakamoto§ , S. Sakoda , K. Sekiguchi§ , K. Suda‡, R. Suzuki‡ , A. Tamii , N.
Uchigashima and K. Yako
Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan
†
LHE-JINR, 141980, Dubna, Moscow region, Russia
Center for Nuclear Study (CNS), University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033,
Japan
‡
Department of Physics, Saitama University, 255 Shimo-okubo, Saitama 338-8570, Japan
§
The Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama
351-0198
Abstract. Measurements of the tensor and vector analyzing powers A yy , Axx , Axz , and Ay for the
3 He n and dd
3 H p reactions were performed at E 270 and 200 MeV over wide angular
dd
d
range. T20 at θcm 0Æ and 180 Æ were also measured at E d 270, 200, and 140 MeV. Obtained data
were compared with predictions based on one nucleon exchange approximation.
INTRODUCTION
It has been predicted from non-relativistic Faddeev calculations of the three nucleon
bound state that the main components of the 3 He ground state wave function are a
spatially symmetric S-state and a small contribution of a D-state [1].
In the last two decades, the structure of a 3 He nucleus has been investigated using
reactions of quasielastic knockout of the 3 He constituent nucleons. The momentum distribution of the constituent nucleons was extracted by plane wave impulse approximation
(PWIA) analyses of 3 Hee ep reaction [2] and 3 He p 2pd and 3 He p pd p reactions
[3]. It was found that the theoretical calculations using modern realistic 3 He wave functions did not reproduce the experimentally obtained momentum distribution functions
in the region of the internal nucleon momentum q 250 MeV/c. To investigate the spin
structure of 3 He, spin correlation for the quasi elastic 3Hep pN reactions was measured up to the internal nucleon momentum of q 400 MeVc, and the distribution
function of the nucleon polarization in a 3 He nucleus was extracted by a PWIA analysis
[4]. The distribution function by Faddeev calculations, however, did not reproduce the
experimental data in the region of q 300 MeV/c.
These deviations indicate that the structure of 3 He in the high-momentum region
has not been clearly understood. Since various kinds of mesons contribute to the nu-
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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3He (3H)
d1
n (p)
d1
(beam)
(beam)
p (n)
p (n)
d2
d2
n (p)
(target)
3He (3H)
(target)
(B)
(A)
FIGURE 1. ONE processes of the dd
reaction.
3 He n 3 H p
clear interaction in the high-momentum region, investigation of high-momentum 3 He
structure may reveal new physics which has not been observed in the low-momentum
region. Since the contribution from the D-state component becomes large in the highmomentum region, measurements of polarization observables sensitive to the D-state is
necessary to study the high-momentum 3 He structure.
ONE APPROXIMATION
In the framework of One Nucleon Exchange (ONE) approximation, tensor analyzing
powers for the dd
3He n and dd
3H p reactions at intermediate energies are
sensitive to the D-state component of 3 He or 3 H [5, 6]. The ONE processes of these
reactions are shown in Fig. 1. Let ud kd and wd kd be the S- and D-state radial wave
functions of a deuteron in the momentum space, respectively. Similarly, let u h kh and
wh kh respectively be the S- and D-state radial functions of a 3 He or 3 H in the d N
3 He n and dd
3H p
cluster configuration. The tensor analyzing powers for the dd
reactions in the framework of ONE approximation have following characteristics:
1. If only the diagram (A) (see Fig. 1) is considered, they are determined by the ratio
of the 3 He3 H wave function components wh kh uh kh .
2. Conversely, If only the diagram (B) is considered, they are determined by the ratio
of the deuteron wave function components wd kd ud kd .
3. If 3 He3 H is scattered at forward angles, the corresponding deuteron internal
momentum kd is very large, hence the contribution from the diagram (B) becomes
negligible. Consequently, they are determined by the 3 He3 H structure.
4. Conversely, if 3 He3 H is scattered at backward angles, corresponding internal momentum of 3 He3 H kh is very large, hence the contribution from the diagram (A)
becomes negligible. Consequently, they are determined by the deuteron structure.
Particularly, the tensor analyzing power T20 at θcm 3 He3 H 0Æ or 180Æ is simply given
by [5, 6]
1 2 2ukwk wk2
T20 (1)
uk2 wk2
2
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Here, uk and wk are respectively replaced by uh kh and wh hh if θcm 0Æ , or, by
3 He n
ud kd and wd kd if θcm 180Æ . Thus, the tensor analyzing powers for the dd
3H p reactions at forward angles are directly related to the DS ratio of
and dd
3 He3 H. With a 270 MeV deuteron beam, the 3 He3 H structure can be investigated
up to a relative momentum of the d N pair of 600 MeV/c in principle.
EXPERIMENT
The experiment was performed at RIKEN Accelerator Research Facility. A polarized
deuteron beam extracted from a polarized ion source was accelerated with AVF and
Ring Cyclotrons up to the energy of 270, 200, or 140 MeV. The accelerated beam was
transported to a spectrometer SMART [7] and were injected onto a target placed in the
scattering chamber. Scattered particles (3 He3 H, or protons) were momentum analyzed
with three quadrupole and two dipole magnets (Q-Q-D-Q-D configuration) and then
detected with a multi-wire drift chamber and three plastic scintillators at the focal plane.
The direction of the symmetry axis of the beam polarization was controlled with a Wien
filter located at the exit of the ion source. The magnitude of the beam polarization was
measured with beam-line polarimeters based on the d p elastic scattering. We used a
deuterated polyethylene (CD2 ) sheet [8] as the deuteron target. Measurement with a
carbon foil target was also performed to subtract the contribution from the carbon nuclei
in the CD2 target. We detected 3 He for the 3 He n channel. In the case of 3 H p channel,
we detected 3 H (protons) if 3 H were scattered in the forward (backward) angles in the
center-of-mass frame.
RESULTS AND DISCUSSION
The experimental results of the tensor analyzing power T20 at θcm 0Æ and 180Æ at
Ed 270, 200, and 140 MeV are presented in Fig. 2. The results for the 3 He n (3 H p)
channel are presented by filled (open) symbols. The curves are predictions by ONE
approximation [5, 6]. The upper fives symbols (two filled ones are hidden behind the
open ones) and the three curves are T20 at θcm 0Æ . The lower three symbols and a
curve are T20 at θcm 180Æ . The solid, dashed, and dot-dashed curves are respectively
calculated using 3 He wave functions of Urbana, Paris, and Reid soft core potentials.
Paris deuteron wave function was used for these calculations. The ONE predictions
reproduced the incident energy dependence and the signs of the experimental data. Since
T20 at 0Æ and 180Æ is directly connected with the DS ratio of 3 He (3 H) or deuteron by
Eq. (1), the difference in the signs of T20 at 0Æ and 180Æ reflects the difference in the
relative sign of uk and wk for 3 He (3 H) and deuteron. Angular distributions of the
analyzing powers at Ed 270 and 200 MeV are presented in Fig. 3. The meanings of the
symbols and curves are same as those in Fig. 2. The ONE predictions [6] reproduced the
global features of the experimental data at backward angles, where the tensor analyzing
powers depend mainly on the deuteron structure. At forward angles, however, significant
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discrepancies can be found. Since the tensor analyzing powers at forward angles are
mainly determined by the 3 He or 3 H structure, these discrepancies might be naively
ascribed to some problems of the wave function of 3 He or 3 H. However, since the ONE
approximation is very crude, calculation with more detail reaction mechanism is needed
to extract information of the 3 He or 3 H structure in the high-momentum region. Further
development in theoretical calculations of four body systems is expected.
FIGURE 2. The experimental results of T20 at θcm
Explanations are written in the text.
0Æ and 180Æ. The curves are ONE predistions.
FIGURE 3. Angular distributions of the analyzing powers for the dd
for the explanations.
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reactions. See text
3 He n 3 H p
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