Study of the Spin Dependent 3He-Nucleus
Interaction at 450 MeV
J. Kamiya , K. Hatanaka, Y. Sakemi , T. Wakasa, H.P. Yoshida ,
E. Obayashi , K. Hara , Y. Kitamura , Y. Shimizu , K. Fujita ,
N. Sakamoto , H. Sakaguchi†, M. Yosoi† , M. Uchida† , Y. Yasuda† ,
Y. Shimbara , T. Adachi , T. Noro‡ and T. Kawabata§
Research Center for Nuclear Physics (RCNP) Ibaraki, Osaka 567-0047, Japan
†
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
‡
Department of Physics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan
§
RIKEN-BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA
Abstract. The cross sections and analyzing powers were measured for 3 He+12 C, 58 Ni, and 90 Zr
elastic scattering at T3 He =450 MeV. The incident energy dependence of the volume integral per
nucleon for 3 He shows the similar behavior to that of protons if the spin-orbit potential is taken
into account. This result supports the assumption that interactions between 3 He and nucleus are
dominated by the interactions between constituent nucleons of 3 He and target nucleus in the
intermediate energy region. The results of the single folding calculation suggest the interaction
between point nucleon and target nucleus is modified in the 3 He+nucleus elastic scattering.
INTRODUCTION
The interaction between complex nuclei is one of the most fundamental subjects in
nuclear physics and many studies have been performed both experimentally and theoretically. The origin of the nucleus-nucleus spin-orbit interaction is of special interest
because it is closely related to the nuclear structure and reaction mechanism. Unlike
the case of an electron moving in a Coulomb field, where the force arises from electro
magnetic interaction, the difficulties in the nuclear case arise from the complex meson
exchange nature of the nucleon-nucleon interaction. 3 He elastic scattering is good tool
to study the interaction between the complex nuclei because the reaction mechanism is
simple compare to more fragile projectiles like deuteron or 6 Li. It is also important to
determine the optical potential parameters including the spin-orbit potentials to study inelastic scatterings and charge exchange reactions like (3 He,t) reactions. Spin dependent
part of the interaction between 3 He and nucleus, however, has not been studied well because of the lack of the experimental data for polarization observables. The experimental
data are limited to cross sections in the intermediate energies, where the phenomenological optical model calculations show that the spin-orbit terms do not affect the cross
section data. Therefore, the spin-orbit interaction has been considered to be negligible at
intermediate energies. Recently, however, theoretical investigations using microscopic
optical models have been reported and the results show the folding model calculations
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
691
predict the large effects of the spin-orbit component on the cross sections and analysing
powers for 3 He-nucleus elastic scattering at intermediate energies [1]. Therefore it is
very effective to perform the experiment at intermediate energy to study the spin dependent 3 He-nucleus interactions precisely.
EXPERIMENT
The experiment was performed at RCNP, Osaka University. We measured the cross sections and analyzing powers for 3 He+12 C, 58 Ni, 90 Zr elastic scatterings at a bombarding
energy of 450 MeV. The analyzing powers Ay , which has the same values as the polar1
izations for spin 12 0
2 0 reactions, were measured by using the double scattering
method. The calorimeter for 3 He was specially designed and constructed behined the
normal focal plane polarimeter system of the Grand Raiden spectrometer. The calorimeter consisted of plastic scintillators and measured the energies of the secondarily scattered 3 He particles from the analyzer target. Preceding the Ay measurement, the focal
plane polarimeter system was calibrated. At first we measured the absolute value of the
polarization for 3 He+12 C elastic scattering at θlab 7Æ , where the double folding model
predicts the large value of the polarization. The absolute value of the polarization was
obtained as
py 0547 0018
(1)
The effective analyzing power Aey f f was calibrated using a plastic scintillator as an
analyzer target as
1
Aey f f Asym 0232 0010
(2)
py
where the py is the obtained value in Eq.(1), and Asym is the left-right asymmetry in the
second scattering.
RESULTS AND DISCUSSIONS
Fig. 1 shows the results of the angular distribution of the cross sections and analyzing
powers for the 3 He elastic scattering off 12 C, 58 Ni, 90 Zr nuclei. The experimental results
show the large values of the analyzing powers even in the middle angular range. Solid
curves shows the results of the phenomenological optical model calculations with central
and spin-orbit potentials.
The Fig. 2 shows the incident energy dependence of the volume integral per nucleon
for 90 Zr target. The upper and lower panels shows the real JR and imaginary JI terms,
respectively. Solid curves show the volume integrals for protons obtained by fitting
the experimental data by Arnold et al. [2], while the open circles the experimental
results for 3 He. The dotted curve is the guide for eyes. The closed circles shows the
present results given by the central optical potentials fitted to the cross sections. The
closed squares also shows the present results but by using both central and spin-orbit
optical potentials fitted to cross sections and analyzing powers. The energy dependence
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FIGURE 1. The differential cross sections and analyzing powers for 3 He+12 C, 58 Ni, and 90 Zr elastic
scattering. The experimental data are shown by the closed circles. The solid lines show the results of the
optical model calculation which give the minimum χ 2 to the data.
of JR show the similar behavior to protons in the intermediate energy region, where it
decreases monotonically. The behavior of the JI of 3 He was not understandable without
spin-orbit effect because it decrease monotonically with increasing the incident energy,
while JI of the protons exhibit a gradual rise above 100 MeV/nucleon reflecting a pionproduction effect. However, by including the spin-orbit interaction, the values of JI of
3 He at 150 MeV/nucleon increase and the energy dependence shows the very similar
behavior to the protons. This results support the assumption that interactions between
3 He and target nucleus are dominated by the interactions between constituent nucleons
in 3 He and target nucleus in the intermediate energy region. Therefore, the single folding
model is possible to be the good model to reproduce the experimental data.
The central component of the single folding model is calculated as
C
VSF
R ρ3HevC R rdr WSFC R ρ3HewC R rdr
(3)
where ρ3 He represents the nucleon density distribution of 3 He, while vwC is the real
(imaginary) central part of a proton-target optical potential at the incident energy of
Tp T3 He A. Assuming a simple harmonic oscillator as a wave function of 3 He, the
density distribution reduces to a single Gaussian form, allowing its width to be consistent
with the 3 He charge radius evaluated from electron scattering data. The spin-orbit
component is written as
SO
USF
R φ3Her ρ uSOR 23ρ φ3Her ρ ln σn F SORL σ (4)
where only neutron in the s state in 3 He contributes to the spin-orbit component of the
single folding potential. ρ3 He r ρ represents the internal wave function of 3 He, where
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FIGURE 2. The incident energy dependence of the volume integral per nucleon for 90 Zr target. The
closed circles and squares show the present results given by the only central optical potentials and both
central and spin-orbit potentials, respectively. The solid curves shows volume integrals for protons. The
dotted curves are guide for eyes.
r and ρ is the relative coordinate between the two protons and that between the neutron
and the center of mass of the two protons in 3 He, respectively. ln and σn represent the
orbital angular momentum operator and the Pauli spin operator of the neutron in 3 He.
L and σ are the corresponding operators for 3 He-target system. The total single folding
potential is written as
C
R iNIWSFC NSOF SORL σ USF R NRVSF
(5)
where renomarization factors (NR NI NSO ) are introduced to examine modification of
the strength of the each potential.
Fig. 3 shows the results for the 90 Zr target. The dotted curves represent the results of
the folding potential without renormalization factors, while the dashed curves are bestfit calculations with renormalization factors (NR NI NSO )=(080 108 050). By using
the renormalization factors, experimental data can be reproduced except for the cross
sections in the backward angles. This results suggest the interaction between point
nucleon and target nucleus is modified in the 3 He+nucleus elastic scattering. Therefore
a double-folding model using density dependent effective nucleon-nucleon interaction
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FIGURE 3. The differential cross sections and analyzing powers for 3 He+90 Zr with the results of
the single folding model calculations. The dotted curves are the results of the folding potential without renormalization factors. The dashed curves are best-fit calculations with renormalization factors
(NR NI NSO )=(080 108 050).
is expected to be the good approach. The calculation is been performed now. The results
can be shown near the future.
ACKNOWLEDGEMENTS
We thank Professor Y. Sakuragi for helpful discussions and Dr. M. Katsuma for the nice
advise for the folding calculations and many helpful comments. This experiment was
performed under the Program No. E157 and E182 at RCNP.
REFERENCES
1.
2.
Y. Sakuragi and M. Katsuma, Nucl. Instr. Meth. A 402, 347 (1998).
L. G. Arnold et al., Phys. Rev. C 25, 936 (1982).
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