1. Mean-field calculations with the Gogny force including the Tensor force
Daisuke ABE
Department of Physics, University of Tokyo
JSPS Research Fellow
and
Takaharu OTSUKA
Center for Nuclear Study
RIKEN
August 2nd 2006
KEK

2. Motivation To understand exotic phenomena appearing in unstable nuclei
To investigate, in particular, Tensor-force effect on single-particle energies (SPE) because its effect on them is quite different from that of the LS force
August 2nd 2006
KEK

3. Brief description of the Tensor Force
originates from the p- (and r-) meson exchange.
plays an important role in nuclear properties, such as binding energies.
can influence on SPE in the different way compared to the LS force.
August 2nd 2006
KEK

4. Monopole Contribution of the Tensor Force
Repulsive j> j’> or j< j’<
Attractive j> j’< or j< j’>
1g9/2
1f5/2
1f7/2　
1h11/2
1g7/2　
August 2nd 2006
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5. Tensor Gogny Interaction
D1S J. F. Berger, et al., Nucl. Phys. A428 (1984) 23c
GT2 T. Matsuo, Ph.D. Thesis, University of Tokyo (2004)
Central
Spin-orbit
Density-
dependent
Tensor
August 2nd 2006
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6. Radial dependences of the tensor force in various interactions
August 2nd 2006
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7. One-body potential Proton Neutron
August 2nd 2006
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8. Results Z=8 0d3/2, 0d5/2 N=28 0f5/2, 0f7/2, 1p1/2, 1p3/2
Z=28 0f5/2, 0f7/2
Z=50 0h11/2, 0g7/2
(Z=82 0i13/2, 0h9/2)
Z=114 0j15/2
August 2nd 2006
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9. 17F and 23F S. Michimasa et al., CNS-REP-67
5.00
EXP:-0.94 MeV
3/2+
4.06
D1S:+1.89
GT2:- 0.56
1.78
1/2+
0.50
0.00
0.00
5/2+
17F
23F
August 2nd 2006
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10. Z=8 isotopes p0d3/2 p0d5/2 D1S GT2 n0d5/2 n1s1/2 n0d5/2 n1s1/2
August 2nd 2006
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11. 47Ar and 49Ca f:-0.875 MeV p:-0.890 MeV 49Ca 47Ar L. Gaudefroy et al.
5/2-
1/2-
3/2-
f: MeV p: MeV
7/2-
49Ca
August 2nd 2006
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47Ar

12. N=28 isotones n0f5/2 n0f7/2 n1p1/2 n1p3/2 GT2 D1S p0d3/2 p0d3/2
August 2nd 2006
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13. 68Ni and 78Ni (Neutron SPE) T. Matsuo, Ph. D
68Ni and 78Ni (Neutron SPE) T. Matsuo, Ph. D. Thesis, University of Tokyo (2004)
1f7/2
1f5/2 40 50
Neutron number
Energy [MeV]
1g9/2
1g9/2
August 2nd 2006
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14. Proton SPE T. Matsuo, Ph. D. Thesis, University of Tokyo (2004)
Energy [MeV]
1f7/2 40 50 40 50
1g9/2
1g9/2
August 2nd 2006
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Neutron number

15. Z=28 isotopes n0f5/2 n0f7/2 p0f5/2 p0f7/2 D1S GT2 n0g9/2 n0g9/2
August 2nd 2006
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16. Variation of the gap between 1f5/2 and 1f7/2 (N= 40-50)
August 2nd 2006
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17. Density and spin-orbit potential
1f5/2
1f7/2
August 2nd 2006
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18. 51Sb isotopes (Proton SPE) J. P. Schiffer et al. , Phys. Rev. Lett
Energy [MeV]
1g7/2 64 70 82
Neutron number
August 2nd 2006
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19. Sb isotopes (Proton SPE) J. P. Schiffer et al. , Phys. Rev. Lett
August 2nd 2006
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20. Z=50 isotopes p0h11/2 p0g7/2 n0h11/2 n0g7/2 D1S GT2 n0h11/2 n0h9/2
August 2nd 2006
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21. Z=82 isotopes
p0h9/2
p0i13/2
GT2
D1S
n0i13/2
n0i13/2
Exp: -1.5 MeV (N=126->100) (Hurstel et al., Eur. Phys. J. A15, 329)
August 2nd 2006
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22. Super-heavy element p0i13/2 p1f7/2 GT2 D1S n0j15/2 n0j15/2
August 2nd 2006
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23. Summary
Tensor force can influence on SPE in the different way compared to the LS force.
For example,
Z=8, N=28, Z=28, Z=50, Z=82, Z=114
Pairing, deformation etc.
August 2nd 2006
KEK