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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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slide1

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.

agenda
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
introduction what s interesting
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

introduction what s our purpose

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)

how to calculate the 3 he d p 4 he reaction
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

three cluster faddeev equation
Three Cluster Faddeev Equation

Faddeev Equation

Separable Expansion (reduce degree of freedom)

Amado-Lovelace-Mitra Equation

We calculate this equation on the each energy.

potential p n
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)

potentials p 3 he n 3 he
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!

potential p 3 he
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

potential n 3 he
Potential n-3He

Resonating Group Method & Orthogonal Condition Model

EST Expansion

1S0

total cross section p n 1 s 0 3 s 1 3 d 1 p 3 he 1 s 0 n 3 he 1 s 0
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(+-)

slide12

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!

summary
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)