物理学第2教室原子核理論研究室 杉本 聡 - PowerPoint PPT Presentation

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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

物理学第2教室原子核理論研究室

杉本 聡


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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


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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


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不安定核物理の発展

From http://www.rarf.riken.go.jp/

  • 理研→RIBF

  • GSI→FAIR

  • GANIL→SPIRAL2 etc.


Pigmy resonance l.jpg

Pigmy resonance

From Aumann

6th CNS International Summer SCHOOL CISS07

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

中性子スキンと芯核の相対的な振動運動モード


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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)


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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)


One pion exchange potential l.jpg

One-pion exchange potential


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Particle-hole interaction

2p-2h correlation

Tensor correlation

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)


Charge and parity projected hartree fock cpphf method l.jpg

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.


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CPPHF results for 4He and 16O

  • By performing the parity and charge projection the potential energy from the tensor force becomes sizable value.

4He

(Volkov No. 1

+G3RS)

16O

(MV1

+G3RS)

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


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Density and charge form factor of 16O

  • The tensor correlation induces higher momentum component.

Density

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 l.jpg

d3/2

s1/2

p3/2

d5/2

p1/2

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


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Mixing of the opposite parity components in single-particle states

0p1/2

1s1/2

  • 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.


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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


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0h

0g

0f

Klinkenberg RMP 24 (1952) 63


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The effect of the tensor forceon 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) 232502

VT does not act.


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The tensor force does not act

The tensor force reduces the ls splitting


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Michimasa et al.

(from NPA 787 (2007) 569)

5 MeV

3/2+

23F

5/2+

17F

Bohr & Mottelson vol. 1


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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


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  • The tensor force reduces the ls-splitting.

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

in40Ca


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Shell evolution induced by the tensor force?

Otsuka et al. PRL 87 (2001) 082502


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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.


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