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2nd International Conference on F rontiers in Nu clear St ructure, A strophysics and R eactions (FINUSTAR 2) Aghios Nikolaos, Crete, Greece, September 10-14, 2007 21 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. 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

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2nd International Conference on Frontiers in Nuclear Structure, Astrophysics and Reactions(FINUSTAR 2)Aghios Nikolaos, Crete, Greece, September 10-14, 200721世紀COE外国旅費補助・成果報告会


杉本 聡

  • 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     





  • 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


  • 理研→RIBF
  • GANIL→SPIRAL2 etc.
pigmy resonance
Pigmy resonance

From Aumann

6th CNS International Summer SCHOOL CISS07

P. Adrichet al., PRL 95 (2005) 132501



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)

tensor force
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)
tensor correlation

Particle-hole interaction

2p-2h correlation

Tensor correlation

It can be treated in the Hartree-Fock method.


Attractive energy

It cannot be treated in a simple Hartree-Fock method.

->Go beyond mean field (Charge- and parity-projected Hartree-Fock method)

charge and parity projected hartree fock cpphf method
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) 014317; Ogawa et al., Prog. Thoer. Phys. 111 (2004) 75; Phys. Rev. C 73 (2006) 034301.

cpphf results for 4 he and 16 o
CPPHF results for 4He and 16O
  • By performing the parity and charge projection the potential energy from the tensor force becomes sizable value.


(Volkov No. 1





Sugimoto et al., Nucl. Phys. A 740 (2004) 77; PRC 75 (2007) 014317

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


Charge form factor

v t and v ls per particle in closed subshell oxygen isotopes 14 o 16 o 22 o 24 o 28 o






VT and VLS per particlein closed-subshell Oxygen isotopes(14O, 16O, 22O, 24O, 28O)
  • 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.

2p2h tensor correlation

mixing of the opposite parity components in single particle states
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 ablocking effect.
  • The excess neutrons around 16O do not contribute the tensor correlation strongly.
ls splitting and the tensor force
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:0705.1419





Klinkenberg RMP 24 (1952) 63

the effect of the tensor force on ls splitting
The effect of the tensor forceon ls-splitting



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) 232502

VT does not act.


The tensor force does not act

The tensor force reduces the ls splitting


Michimasa et al.

(from NPA 787 (2007) 569)

5 MeV





Bohr & Mottelson vol. 1

effective interaction in the hf cal
Effective Interaction in the HF cal.
  • Central partModified Volkov No.1, m=0.59
  • LS partd-LS:W0=115 MeV fm5to be determied to reproduce D(0p3/2-1-0p1/2-1) cf. Gogny force D1
  • Tensor partG3RS
The tensor force reduces the ls-splitting.

cf. D(0d5/2-0d3/2)= 6~7.5 MeV


shell evolution induced by the tensor force
Shell evolution induced by the tensor force?

Otsuka et al. PRL 87 (2001) 082502

  • 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.