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 692 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 693 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 694 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). 695
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