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1 S. Gojuki , K. Sonoda, Y. Hiratsuka and S. Oryu

A Three-Body Faddeev Calculation of the Double Polarized 3 He(d,p) 4 He Reaction in the Super Low-Energy Region. 1 S. Gojuki , K. Sonoda, Y. Hiratsuka and S. Oryu Department of Physics, Tokyo University of Science 1 SGI Japan Ltd. Agenda. Introduction What’s interesting?

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1 S. Gojuki , K. Sonoda, Y. Hiratsuka and S. Oryu

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  1. A Three-Body Faddeev Calculation of the Double Polarized 3He(d,p)4He Reaction in the Super Low-Energy Region 1S. Gojuki, K. Sonoda, Y. Hiratsuka and S. Oryu Department of Physics, Tokyo University of Science 1SGI Japan Ltd.

  2. Agenda • Introduction • What’s interesting? • What’s our purpose? • How to calculate the 3He(d,p)4He reaction? • Three body Faddeev theory • Potentials • Results • Summary

  3. IntroductionWhat’s Interesting? • What’s interesting for the 3He(d,p)4He in super low-energy region? • Nucleosynthesis in Universe • Nuclear-Fusion Power Generation • Mirror Reaction of the 3H(d,n)4He • Neutronless reaction • Polarization effects Nucleosynthesis http://grin.hq.nasa.gov/ TOKAMAK http://www.fusionscience.org

  4. S-wave S-wave 3He 3He d d n n n n p p p p p p IntroductionWhat’s our Purpose? Double Parallel Polarization Jπ=1/2+ Jπ=3/2+ The 3/2+ state can be set by the double parallel polarization. 3/2+ Resonance Get the cross section enhancement !? T.W.Bonner et al., Phys.Rev.88,473 (1952), W.H.Geist et al., Phys.Rev.C60,054003-1 (1999)

  5. How to calculate the 3He(d,p)4He reaction? • Five nucleon Problem • (Big degree of freedom) • Select three clusters (3He, p, and n) • (Because of super low energy) • Potentials • (p-n, p-3He, and n-3He) • Three cluster Faddeev calculation • (Reduce the degree of freedom) p-3He p-n n-3He

  6. Three Cluster Faddeev Equation Faddeev Equation Separable Expansion (reduce degree of freedom) Amado-Lovelace-Mitra Equation We calculate this equation on the each energy.

  7. Potential p-n M.Lacombeet al., Phys. Rev. C21 (1980) 861 • Paris Potential (EST expanded) • One of the most popular nucleon-nucleon potential 3S1 1S0 3D1 Exp. A :R.A.Arndt, L.D.Roper, R.A.Bryan, R.B.Clark, B.J.VerWest, and P.Signell, Phys. Rev. D28, 97 (1983) Exp. B : R.A.Arndt, J.S.Hyslop III, and L.D.Roper, Phys. Rev. D35, 128 (1987)

  8. Potentials p-3He, n-3He • Base Theory • Resonating Group Method(RGM) I.Reichstein,P.R.Thompson,and Y.C.Tang., Phys. Rev. C3, 2139 (1971) H.Kanad and T.Kaneko., Phys. Rev. C34, 22 (1986) • Pauli Principle • Orthogonal Condition Model S.Saito, Prog. Theor. Phys. 40, 893 (1968) S.Saito, Prog. Theor. Phys. 41, 705 (1969) • Separable Potential • EST Expansion D.J.Ernst,C.M.Shakin,and R.M.Thaler, Phys. Rev. C8, 46 (1973) Just theory!

  9. Potential p-3He ○;T.A.Tombrello, Phys.Rev.138,B40(1965) □;D.H.Mc Sherry and S.D.Baker, Phys.RevC1,888(1970) △;J.R. Morales, T.A. Cahill, and D.J. Shadoan, Phys.Rev..C11,1905(1975) ◊;D.Müller, R.Beckmann, and U. Holm, Nucl.Phys.A311,1.(1978) +;L.Beltrmin, R.del Frate, and G. Pisent, Nucl.Phys.A442,266(1985) ●;Y.Yoshino, V.Limkaisang, J.Nagata, H.Yoshino, and M.Matsuda, Prog. Theor.Phys.103,107(2000) Resonating Group Method & Orthogonal Condition Model EST Expansion 1S0

  10. Potential n-3He Resonating Group Method & Orthogonal Condition Model EST Expansion 1S0

  11. Total Cross Sectionp-n: 1S0, 3S1-3D1 ,p-3He: 1S0 ,n-3He: 1S0 p-n: 1S0(rank=3 or 5), 3S1-3D1(rank=4 or 6 or 8) p-3He: 1S0(rank=3) ,n-3He: 1S0(rank=3) x2.2 Converged! p-n: 1S0(rank=1), 3S1-3D1(rank=1) p-3He: 1S0(rank=3) ,n-3He: 1S0(rank=3) p-n: 1S0(rank=1 or 3), 3S1-3D1(rank=1 or 4) p-3He: 1S0(rank=1) ,n-3He: 1S0(rank=1) Polarized Total Cross Section Unpolarized Total Cross Section Total Jπ=1/2(+-) – 9/2(+-)

  12. Total Cross Sectionp-n: 1S0, 3S1-3D1 ,p-3He: 1S0 ,n-3He: 1S0 Jπ=3/2+ Polarized Jπ=3/2+ Unpolarized Jπ=1/2+ Polarized Jπ=3/2- Unpolarized Jπ=1/2- Unpolarized Jπ=5/2-Polarized Jπ=5/2- Unpolarized Jπ=5/2+ Unpolarized Jπ=1/2- Polarized Jπ=3/2- Polarized Jπ=5/2+ Polarized Jπ=1/2+ Polarized The 375keV peak is made from the 3/2+ state!

  13. Summary • The double parallel polarization effects • The total cross section in the 375 keV grows up to 2.2 times by the double parallel polarization effects. • The 3/2+ peak is found by the 1S0 rank=3 of the N-3He potential. • The more realistic 4He structure is important. • But the peak is not broad…(experiment is broad. ) • Future • More exact two-body potential (higer rank and partial wave) • Internal Coulomb effect (Now: only initial and final states)

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