1. 2nd International Conference on Frontiers in Nuclear Structure, Astrophysics and Reactions (FINUSTAR 2) Aghios Nikolaos, Crete, Greece, September 10-14, 世紀COE外国旅費補助・成果報告会
物理学第２教室原子核理論研究室
杉本　聡

2. 会議概要１
場所： ギリシア　クレタ島　アギオス・ニコラウス Iberostar Mirabello Beach Hotel and Village
開催日程：　２００７年９月１０～１４日　　　　　
ミノタウロス
クノッソス宮殿
（部屋数１２００以上）
アギオス・ニコラウス

3. 会議概要２
参加人数：　１４０名 （フランス1４、イタリア１３、アメリカ・ベルギー・ドイツ各１０、ギリシア９、 日本８、イギリス７、チェコ・フィンランド・南アフリカ各５、他２２カ国４４名）
講演数　口頭発表　７８、ポスター　４３
招待講演　２１、Invited Contribution 9 核構造理論６，核構造実験１０，核反応理論４，核反応実験６，次期計画４ そのうちγ線分光関係８，天体核関係７

4. 不安定核物理の発展 理研→RIBF GSI→FAIR GANIL→SPIRAL2 etc.
From
理研→RIBF
GSI→FAIR
GANIL→SPIRAL2 etc.

5. Pigmy resonance P. Adrichet al., PRL 95 (2005) 132501
From Aumann
6th CNS International Summer SCHOOL CISS07
P. Adrichet al., PRL 95 (2005)
中性子スキンと芯核の相対的な振動運動モード

6. Study of the tensor correlation in a neutron-rich sd-shell region with the charge- and parity-projected Hartree-Fock methods
Satoru Sugimoto
Kyoto University, Japan
Hiroshi Toki (RCNP, Japan), Kiyomi Ikeda(RIKEN, Japan)

7. Tensor force
The strong tensor force is characteristic of nuclear many-body systems
The tensor force (pion) plays important roles in nuclear structure.
The tensor force produces large attractive energy in nuclei.
The tensor force is responsible for the saturation mechanism of nuclear matter.
We want to reveal the roles of the tensor force in nuclei.
The effect of the tensor force on shell structure.
Shell evolution (Otsuka, Suzuki et al.)
The change of the tensor correlation in neutron-rich nuclei. （テンソル力は陽子‐中性子間に強く働く）

8. One-pion exchange potential

9. Tensor correlation Attractive energy 2p-2h correlation
Particle-hole interaction
It can be treated in the Hartree-Fock method.
->ls-splitting
Attractive energy
It cannot be treated in a simple Hartree-Fock method.
->Go beyond mean field (Charge- and parity-projected Hartree-Fock method)

10. Charge- and parity-projected Hartree-Fock (CPPHF) method
Tensor force is mediated by the pion.
Pseudo scalar (s)
To exploit the pseudo scalar character of the pion, we introduce parity-mixed single particle state. (over-shell correlation)
Isovector (t)
To exploit the isovector character of the pion, we introduce charge-mixed single particle state.
Projection
Because the total wave function made from such parity- and charge-mixed single particle states does not have good parity and a definite charge number. We need to perform the parity and charge projections before variation. -> Charge and parity-projected Hartree-Fock equaiton
Refs. Toki et al., Prog. Theor. Phys. 108 (2002) 903.
Sugimoto et al., Nucl. Phys. A 740 (2004) 77; PRC 75 (2007) ; Ogawa et al., Prog. Thoer. Phys. 111 (2004) 75; Phys. Rev. C 73 (2006)

12. CPPHF results for 4He and 16O
xTE
Etot KE
Vtot VC VT Rm
P(D) HF
1.00
-27.9
49.7
-77.6
0.0
1.45
0.00
PPHF
0.96
-28.3
52.5
-80.8
-75.1
-5.7
0.68
CPPHF
0.92
-28.7
57.8
-86.5
-73.2
-13.3
1.42
3.22
4He
(Volkov No. 1
+G3RS)
16O
(MV1
+G3RS)
Etot KE VC VT
VLS
VCoul
V3B Rm HF
-123.4
228.9
-416.9
0.0
-0.2
13.4
51.5
2.57
PPHF
-126.6
236.5
-423.6
-5.3
13.5
52.5
2.55
CPPHF
-133.3
256.5
-440.0
-17.8
13.9
54.4
2.52
By performing the parity and charge projection the potential energy from the tensor force becomes sizable value.
Sugimoto et al., Nucl. Phys. A 740 (2004) 77; PRC 75 (2007)

13. Density and charge form factor of 16O
The tensor correlation induces higher momentum component.

14. VT and VLS per particle in closed-subshell Oxygen isotopes (14O, 16O, 22O, 24O, 28O)
2p2h tensor correlation
The potential energy from the tensor force has the same order in magnitude as that from the LS force.
The tensor potential energy decreases as neutron numbers.
Excess neutrons around 16O does not contribute to the 2p2h correlation because there are no protons in the sd shell.

15. Mixing of the opposite parity components in single-particle states
Because the tensor correlation is exploited by parity mixing, the mixing probability of opposite parity components is one of the measure for the strength of the tensor correlation.
j=1/2 states are affected largely by the tensor correlation.
If a next j=1/2 orbit is occupied newly, the mixing probabilities of the j=1/2 orbit reduce by a blocking effect.
The excess neutrons around 16O do not contribute the tensor correlation strongly.

16. ls splitting and the tensor force
The effect of the tensor force on ls splitting
HF correlation： Tarbutton et al.(HF), Bouyssy et al.(Relativistic HF), etc.
Shell evolution induced by the tensor force.（Otsuka, Suzuki, Abe, Utsuno, etc)
2p2h correlaton: Terasawa and Arima, Andō and Bandō, Myo et al., etc.
Does ls splitting change in neutron-rich nuclei?
The experiment at RIKEN (Michimasa et al. PLB 638 (2006) 146) D(pd) in 17F(16O+p) ~ 5 MeV → D(pd) in 23F(22O+p) ~ 4 MeV
We study the effect of the tensor force on the ls-splitting with the Hartree-Fock method.
Sugimto et al. PRC (to be published); arXiv:

17. 0h 0g 0f
Klinkenberg RMP 24 (1952) 63

18. The effect of the tensor force on ls-splitting
j>=l+1/2
j<=l-1/2
VT reduces ls-splitting.
VT enhances ls-splitting.
j<-j<’ or j<-j<’: repulsion
j<-j>’: attraction
If both j<’ and j>’ orbits are fully occupied the tensor force does not act.
cf. Bouyssy et al. PRC 36 (1987) 380
Otsuka et al. PRL 95 (2005)
VT does not act.

19. The tensor force does not act
The tensor force reduces the ls splitting

20. 23F 17F Michimasa et al. (from NPA 787 (2007) 569) 5 MeV 3/2+ 5/2+
Bohr & Mottelson vol. 1

21. Effective Interaction in the HF cal.
Central part Modified Volkov No.1, m=0.59
LS part d-LS: W0=115 MeV fm5 to be determied to reproduce D(0p3/2-1-0p1/2-1) cf. Gogny force D1
Tensor part G3RS

22. The tensor force reduces the ls-splitting.
cf. D(0d5/2-0d3/2)= 6~7.5 MeV
in 40Ca

23. Shell evolution induced by the tensor force?
Otsuka et al. PRL 87 (2001)

24. Summary We study the 2p2h tensor correlation with the CPPHF method.
The tensor correlation induces high-momentum component in single-particle wave functions.
The 2p2h tensor correlation becomes smaller with neutron number.
The tensor force reduces the ls-spitting for the proton d-orbits by 3MeV in 23F. This reduction is important to explain the experimental value in the Hartree-Fock method.
We also study the effect of the 2p2h tensor correlation on the ls-splitting with the PPHF method. It does not affect the ls-splitting largely.