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2nd International Conference on Frontiers in Nuclear Structure, Astrophysics and Reactions (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 • 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 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 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 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 Study of the tensor correlation in a neutron-rich sd-shell region with the chargeand parity-projected HartreeFock methods Satoru Sugimoto Kyoto University, Japan Hiroshi Toki (RCNP, Japan), Kiyomi Ikeda(RIKEN, Japan) 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 V (O P E P ) (r ) = - fp 2 4p mp 2 1 r r r r r r e t 1 ×t 2 ( s 1 ×Ñ 1 )( s 2 ×Ñ 2 ) mp r r ù é ú ê ì ü m r m r 2 ú p p ï ï ö r ÷ 1 f p r r êr r æ e 4p 3 3 ï e ï ç ú = t 1 ×t 2 ês 1 ×s 2 ç d ( r )÷ + S12 í 1 + + 2 ý ÷ 2 ê ÷ çè r ï ï r ú 3 4p mp mp r ø m r ( ) ï ï ú p ïþ ê144444444 442 444 44444443 1444444444442 îï 4 44444444444 43ú ê C entr al ë ú T enso r û r r r r (0) r r r r (2) 3 ( s 1 ×r )( s 2 ×r ) é ù ˆ S 12 = - s 1 ×s 2 = 2 4 p ê[s 1 ´ s 2 ] ´ Y 2 ( r ) ú 2 ë û0 r j1 å j2 å m1 = - j1 m 2 = - j 2 l1 j1 m1 , l 2 j 2 m 2 V (O P E P ) l1 j1 m 1 , l 2 j 2 m 2 = 0 Tensor correlation 2p-2h correlation Particle-hole interaction 0d3/2 0d3/2 0d3/2 1s1/2 1s1/2 1s1/2 0d5/2 0d5/2 0d5/2 0p1/2 0p1/2 0p1/2 0p3/2 0p3/2 0p3/2 Proton Proton Neutron 0p-0h Neutron 2p-2h VT VT Proton Neutron j j VT j j j j VT j j Attractive energy It cannot be treated in a simple Hartree-Fock method. ->Go beyond mean field (Charge- and parityprojected Hartree-Fock method) It can be treated in the Hartree-Fock method. ->ls-splitting 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. n p - p - + n + CPPHF results for 4He and 16O 4He xTE HF 1.00 (Volkov No. 1 PPHF 0.96 +G3RS) CPPHF 0.92 16O Etot HF (MV1 +G3RS) PPHF CPPHF Etot KE Vtot VC VT Rm P(D) -27.9 49.7 -77.6 -77.6 0.0 1.45 0.00 -28.3 52.5 -80.8 -75.1 -5.7 1.45 0.68 -28.7 57.8 -86.5 -73.2 -13.3 1.42 3.22 VT VLS KE VC VCoul V3B Rm -123.4 228.9 -416.9 0.0 -0.2 13.4 51.5 2.57 -126.6 236.5 -423.6 -5.3 -0.2 13.5 52.5 2.55 -133.3 256.5 -440.0 -17.8 -0.2 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) 014317 Density and charge form factor of 16O Density Charge form factor 0 0.20 10 -1 0.15 HF CPPHF -2 10 -3 density (fm ) 10 HF CPPHF |F(q )| -3 2 0.10 10 -4 10 -5 10 -6 0.05 10 -7 10 0.00 -8 0 1 2 3 R (fm) 4 5 10 0 10 20 2 -2 q (fm ) • The tensor correlation induces higher momentum component. 30 VT and VLS per particle in closed-subshell Oxygen isotopes (14O, 16O, 22O, 24O, 28O) VT and VLS VT/A and VLS/A (MeV) 0.2 2p2h tensor correlation 0.0 -0.2 s1/2 -0.4 p3/2 -0.6 -0.8 p1/2 d5/2 0d3/2 1s1/2 d3/2 VT HF VT CPPHF VLS CPPHF -1.0 12 14 16 18 20 22 24 26 28 30 16O Mass number • 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. 0d5/2 0p1/2 0p3/2 0s1/2 Mixing of the opposite parity components in single-particle states 0p1/2 1s1/2 0s1/2' 0d3/2 1s1/2 0p3/2' 0.2 Pmix 0p1/2' 0d5/2 0d5/2' 0.1 1s1/2' 0p1/2 0p3/2 0d3/2' 0.0 14 16 18 20 22 24 Mass Number 26 28 16O 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. 0s1/2 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(d) in 17F(16O+p) ~ 5 MeV → D(d) in 23F(22O+p) ~ 4 MeV • We study the effect of the tensor force on the lssplitting with the Hartree-Fock method. Sugimto et al. PRC (to be published); arXiv:0705.1419 0h V 1 d Vl s r dr V 0g 0f 50 M eV , ls 1 0.5fm 2 ( l 1) for l j 1 / 2 2 1 l for l j 1 / 2 2 Dl s l 1 / 2 Klinkenberg RMP 24 (1952) 63 The effect of the tensor force on ls-splitting j =l+1/2 > j<=l-1/2 j<’ VT() j> VT() j>’ j< j>’ j< j> VT reduces ls-splitting. j<’ VT enhances ls-splitting. 1. j<-j<’ or j<-j<’: repulsion 2. j<-j>’: attraction 3. 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 j<’ VT() j>’ j< j> VT does not act. 17F(16O+p) 23F(22O+p) VT() VT() 0d3/2 1s1/2 0d3/2 1s1/2 0d5/2 0d5/2 0p1/2 0p3/2 0p1/2 0p3/2 0s1/2 The tensor force does not act 0s1/2 The tensor force reduces the ls splitting Michimasa et al. (from NPA 787 (2007) 569) 3/2+ 0d3/2 1s1/2 0d5/2 5 MeV 23F 5/2+ 17F Bohr & Mottelson vol. 1 Effective Interaction in the HF cal. • Central part Modified Volkov No.1, m=0.59 • LS part iW 0s [ k 21 d ( r12 ) k 12 ] 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 7.2MeV 3/2+ 5MeV <VLS>~-3MeV <VLS>~+4.5MeV 4.2MeV 3/2+ <VLS>~-3.3MeV 5/2+ 5/2+ 17F 23F 23F VLS+VT only VLS VLS+VT <VT>~-1.8MeV <VT>~1.3MeV • The tensor force reduces the ls-splitting. cf. D(0d5/2-0d3/2)= 6~7.5 MeV in 40Ca VT 0d3/2 1s1/2 0d5/2 Shell evolution induced by the tensor force? Otsuka et al. PRL 87 (2001) 082502 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.