1 S. Gojuki , K. Sonoda, Y. Hiratsuka and S. Oryu
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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. OryuDepartment of Physics, Tokyo University of Science
1SGI Japan Ltd.
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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
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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
http://grin.hq.nasa.gov/
TOKAMAK
Nucleosynthesis
http://www.fusionscience.org
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IntroductionWhat’s our Purpose?
T.W.Bonner et al., Phys.Rev.88,473 (1952), W.H.Geist et al., Phys.Rev.C60,054003-1 (1999)
3/2+ R
eson
ance
2
11 1
2
1
S-wave S-wave
np
p
np
np
pn
p
3He 3Hed d
Jπ=1/2+ Jπ=3/2+
The 3/2+ state can be set by the double parallel polarization.
Get the cross section enhancement !?
Double Parallel Polarization
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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)
Three cluster Faddeev calculation(Reduce the degree of freedom)
Potentials(p-n, p-3He, and n-3He)
p-n p-3Hen-3He
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Three Cluster Faddeev Equation
Faddeev Equation
Amado-Lovelace-Mitra Equation
Separable Expansion (reduce degree of freedom)
We calculate this equation on the each energy.
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Potential p-n• Paris Potential (EST expanded)
– One of the most popular nucleon-nucleon potential
1S0
3S1
3D1
M.Lacombeet al., Phys. Rev. C21 (1980) 861
0
20
40
60
80
100
120
140
160
180
0 100 200 300 400 500
Lab. Energy [MeV]
Phas
e Sh
ift [d
egre
e] rank=1rank=4rank=6rank=8Exp. AExp. B
-40
-30
-20
-10
0
10
20
30
40
50
0 100 200 300 400 500
Lab. Energy [MeV]
Phas
e Sh
ift [d
egre
e] rank=1rank=4rank=6rank=8Exp. AExp. B
-40
-30
-20
-10
0
10
20
30
40
50
60
70
0 100 200 300 400 500
Lab. Energy [MeV]
Phas
e Sh
ift [d
gere
e]
rank=1rank=3rank=5Exp. AExp. B
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)
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Potentials p-3He, n-3He
Base TheoryResonating Group Method(RGM)
Pauli PrincipleOrthogonal Condition Model
Separable PotentialEST Expansion
I.Reichstein,P.R.Thompson,and Y.C.Tang., Phys. Rev. C3, 2139 (1971)H.Kanad and T.Kaneko., Phys. Rev. C34, 22 (1986)
S.Saito, Prog. Theor. Phys. 40, 893 (1968)S.Saito, Prog. Theor. Phys. 41, 705 (1969)
D.J.Ernst,C.M.Shakin,and R.M.Thaler, Phys. Rev. C8, 46 (1973)
Just theory!
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Potential p-3He
1S0
EST Expansion
Resonating Group Method & Orthogonal Condition Model
-160
-140
-120
-100
-80
-60
-40
-20
0
0 5 10 15 20 25 30
Lab. Energy [MeV]
Phas
e Sh
ift [d
egre
e]
rank=1rank=3
○;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)
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Potential n-3He
1S0
EST Expansion
Resonating Group Method & Orthogonal Condition Model
-100
-80
-60
-40
-20
0
0 5 10 15 20
Lab. Energy [MeV]
Phas
e Sh
ift [d
egre
e]
rank=1rank=3
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1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
340 350 360 370 380 390 400 410
Lab. Energy [keV]
Tota
l Cro
ssSe
ctio
n [m
b]
Total Cross Sectionp-n: 1S0, 3S1-3D1 ,p-3He: 1S0 ,n-3He: 1S0
Total Jπ=1/2(+-) – 9/2(+-)
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)
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)
Converged!
Polarized Total Cross Section
Unpolarized Total Cross Section
x2.2
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0.000001
0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
10000
100000
340 350 360 370 380 390 400 410
Lab. Energy [keV]
Tota
l Cro
ss S
ectio
n [m
b]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
The 375keV peak is made from the 3/2+ state!
Jπ=3/2- Polarized
Jπ=1/2- Polarized
Jπ=1/2- UnpolarizedJπ=3/2- UnpolarizedJπ=1/2+ Polarized
Jπ=5/2+ Polarized
Jπ=5/2+ Unpolarized
Jπ=5/2-PolarizedJπ=5/2- Unpolarized
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Summary
• The double parallel polarization effects– The total cross section in the 375 keV grows up to 2.2 times by th
e double parallel polarization effects.• The 3/2+ peak is found by the 1S0 rank=3 of the N-3He poten
tial. – 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)