1. 1 軽い核におけるテンソル相関と 短距離相関の役割 核子と中間子の多体問題の統一的描像に向けて＠ RCNP 2007. 12.14-15 1.Tensor correlation for He and Li isotopes in Tensor-Optimized Shell Model (TOSM) 2.Short-range correlation by Unitary Correlation Operator Method (UCOM) 3.TOSM + UCOM with bare interaction 明 孝之 大阪大学 ＲＣ ＮＰ

2. 2 Motivation (tensor force) Spectroscopy of neutron-rich nuclei : He and Li isotopes Tensor force (V tensor ) plays a significant role in the nuclear structure. –In 4 He, – ~ 80% (GFMC) R.B. Wiringa, S.C. Pieper, J. Carlson, V.R. Pandharipande, PRC62(2001) We would like to understand the role of V tensor in the nuclear structure by describing tensor correlation explicitly. model wave function (shell model and cluster model). spatial properties, p-h correlation, …

3. 3 Variational calculation in real space C.Pieper, R.B.Wiringa, Annu.Rev.Nucl.Part.Sci.51(2001) R.B.Wilinga,S.C.Pieper,J.Carlson, V.R.Pandaripande, PRC62(2000)014001.  -  structure Green’s function Monte Calro mass  12

4. 4 Tensor correlation in the shell model type approach. Configuration mixing within 2p2h excitations with high-L orbit TM et al., PTP113(2005) TM et al., PTP117(2007) T.Terasawa, PTP22(’59)) Length parameters such as are determined independently and variationally. –Describe high momentum component from V tensor CPP-HF by Sugimoto et al,(NPA740) / Akaishi (NPA738) CPP-RMF by Ogawa et al.(PRC73), CPP-AMD by Dote et al.(PTP115) Tensor-optimized shell model (TOSM) 4 He

5. 5 Hamiltonian and variational equations Effective interaction : Akaishi force (NPA738) –G-matrix from AV8’ with k Q =2.8 fm -1 –Long and intermediate ranges of V tensor survive. –Adjust V central to reproduce B.E. and radius of 4 He TM, Sugimoto, Kato, Toki, Ikeda PTP117(’07)257

6. 6 4 He in TOSM Orbitb particle /b hole 0p 1/2 0.65 0p 3/2 0.58 1s 1/2 0.63 0d 3/2 0.58 0d 5/2 0.53 0f 5/2 0.66 0f 7/2 0.55 Length parameters good convergence Higher shell effect L max Shrink

7. 7 Pion exchange interaction vs. V tensor Delta interaction Yukawa interaction Involve large momentum Tensor operator - V tensor produces the high momentum component.

8. 8 4 He in TOSM (0s 1/2 ) 4 85.0 % (0s 1/2 ) 2 JT (0p 1/2 ) 2 JT JT=10 5.0 JT=01 0.3 (0s 1/2 ) 2 10 (1s 1/2 )(0d 3/2 ) 10 2.4 (0s 1/2 ) 2 10 (0p 3/2 )(0f 5/2 ) 10 2.0 P[D] 9.6 Energy (MeV)  28.0  51.0 0  of pion nature. deuteron correlation with (J,T)=(1,0) 4 Gaussians instead of HO c.m. excitation = 0.6 MeV Cf. R.Schiavilla et al. (GFMC) PRL98(’07)132501

9. 9 LS splitting in 5 He with tensor corr. Orthogonarity Condition Model (OCM) is applied. T. Terasawa,PTP22(’59) S. Nagata, T. Sasakawa, T. Sawada R. Tamagaki, PTP22(’59) K. Ando, H. Bando PTP66(’81) TM, K.Kato, K.Ikeda PTP113(’05)

10. 10 Phase shifts of 4 He-n scattering

11. 11 Tensor correlation in 6 He Ground stateExcited state

12. 12 Theory With Tensor 6 He in coupled 4 He+n+n model (0p 3/2 ) 2 can be described in Naive 4 He+n+n model (0p 1/2 ) 2 loses the energy Tensor suppression in 0 + 2

13. 13 Characteristics of Li-isotopes Breaking of magicity N=8 10-11 Li, 11-12 Be 11 Li … (1s) 2 ~ 50%. (Expt by Simon et al.,PRL83) Mechanism is unclear Halo structure 11 Li

14. 14 Pairing-blocking : K.Kato,T.Yamada,K.Ikeda,PTP101(‘99)119, Masui,S.Aoyama,TM,K.Kato,K.Ikeda,NPA673('00)207. TM,S.Aoyama,K.Kato,K.Ikeda,PTP108('02)133, H.Sagawa,B.A.Brown,H.Esbensen,PLB309('93)1.

15. 15 11 Li in coupled 9 Li+n+n model System is solved based on RGM Orthogonality Condition Model (OCM) is applied. TOSM

16. 16 11 Li G.S. properties (S 2n =0.31 MeV) Tensor +Pairing Simon et al. P(s 2 ) RmRm TM, K.Kato, H.Toki, K.Ikeda, PRC76(’07)024305 TM. Y.Kikuchi, K.Kato, H.Toki, K.Ikeda, sumitted to JPG

17. 17 G Tensor +Pairing Charge Radii of Li isotopes R C-2n Inert core Expt. (Sanchez et al., PRL96(2006)) 9 Li 11 Li Charge Radius 9 Li R C-2n 4.675.69[fm] P(s 2 )447%

18. 18 Coulomb breakup strength of 11 Li E1 strength by using the Green’s function method +Complex scaling method +Equivalent photon method (TM, Aoyama, Kato, Ikeda, PRC63(’01)054313) Expt: T. Nakamura et al., PRL96,252502(2006) Energy resolution with =0.17 MeV. No three-body resonance

19. 19 Tensor & Short-range correlations Tensor correlation in TOSM – –2p2h mixing optimizing the particle states (radial & high-L) H. Feldmeier, T. Neff, R. Roth, J. Schnack, NPA632(1998)61 T. Neff, H. Feldmeier NPA713(2003)311 Short-range correlation –Short-range repulsion of the bare NN force in the relative wave function of nuclei –Unitary Correlation Operator Method (UCOM)

20. 20 Unitary Correlation Operator Method H. Feldmeier, T. Neff, R. Roth, J. Schnack, NPA632(1998)61 short-range correlator Bare Hamiltonian Shift operator depending on the relative distance r

21. 21 Short-range correlator : C 1GeV repulsion Original  r 2 CC

22. 22 4 He in UCOM (Afnan-Tang) CC

23. 23 Charge form factor and Corr. Func. (0s) 4 CC 1E1E Form Factor

24. 24 4 He in TOSM+UCOM R. Roth et. al, PRC72(2005)034002 (Kamada et al. PRC64) Central+ LS+Tensor

25. 25 Summary Tensor correlation in nuclei –Tensor-optimized shell model (TOSM) –He isotopes, Li isotopes Short-range correlation –Unitary Correlation Operator Method (UCOM) In TOSM+UCOM, we can study the nuclear structure starting from the bare interaction –Spectroscopy of light nuclei (p-shell region)

26. 26 4 He in TOSM+UCOM (0s 1/2 ) 4 88.1 % (0s 1/2 ) 2 JT (0p 1/2 ) 2 JT JT=10 3.6 % JT=01 0.1 (0s 1/2 ) 2 10 (1s 1/2 )(0d 3/2 ) 10 1.9 (0s 1/2 ) 2 10 (0p 3/2 )(0f 5/2 ) 10 1.6 P[D] 7.6 0 - of pion nature deuteron corr. with (J,T)=(1,0) c.m. excitation = 0.4 MeV V nn : AV8’

27. 27 Properties of 4 He TOSM+UCOMBenchmark Energy-19.20-25.94 Kinetic87.00102.39 Central-55.02-55.26 Tensor-50.21-68.35 LS-0.98-4.72 Radius1.51 fm1.49 fm (Kamada et al. PRC64)

28. 28 Property of the tensor force Centrifugal potential (1GeV@0.5fm) pushes away the L=2 wave function.

29. 29 Form of R + in UCOM Functional form given by referring to the Deuteron’s exact case Afnan-Tang : central only about 1GeV repulsion 1E1E Original CC

30. 30 16 O with UCOM (Afnan-Tang) CC

31. 31 6 He with 4 He+n+n model Pairing correlation is important S.Aoyama, S. Mukai,K.Kato, K. Ikeda, PTP93(1995)99. V V+T K.Ikeda, NPA538(1992)355

32. 32 G Q-moment of Li-isotopes R C-2n 9 Li 2n~0 + Varga et. al Kanada-En’yo Vanish due to 0 + state of 2n