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Role of Tensor Correlation on the Spin-Orbit Splitting in Neutron Halo Nuclei. Takayuki Myo RCNP, Osaka Univ. 4 He with tensor-optimized shell model. Tensor correlation in 5,6 He. 11 Li with tensor and pairing correlations for halo formation.

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## Role of Tensor Correlation on the Spin-Orbit Splitting in Neutron Halo Nuclei

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**Role of Tensor Correlation on the Spin-Orbit Splitting in**Neutron Halo Nuclei Takayuki MyoRCNP, Osaka Univ. • 4He with tensor-optimized shell model. • Tensor correlation in 5,6He. • 11Li with tensor and pairing correlations for halo formation. In collaboration with Satoru Sugimoto (Kyoto), Kiyoshi Kato (Hokkaido) Hiroshi Toki (RCNP) and Kiyomi Ikeda (RIKEN) The 17th International Spin Physics Symposium, SPIN2006@Kyoto Univ.**Motivation**• Tensor force (Vtensor) plays a significant role in the nuclear structure. • In 4He, • GFMC shows ~ 70-80% of two-body attraction energy. • Physical effect of Vtensor is not easy to understand in a transparent manner. We would like to understand the roles of Vtensor on the nuclear structure by describing tensor correlation (TC) explicitly in the model space. • Spectroscopy of neutron-rich nuclei , 5,6He, 10,11Li**Tensor-optimized shell model for 4He**• We start the study of TC from 4He in the shell model type approach. • Configuration mixing within 2p2h excitationsTM et al., PTP113(2005)TM et al., nucl-th/0607059T.Terasawa, PTP22(’59)) • Length parameters such as are determined independently and variationally. • Describe high momentum component from Vtensor( cf. CPPHF by Sugimoto et al,(NPA740) / Akaishi (NPA738)) 4He**Hamiltonian and variational equations for 4He**• Effective interaction : Akaishi force (NPA738) • G-matrix from AV8’ with kQ=2.8 fm-1 • Long and intermediate ranges of Vtensor survive. • Adjust Vcentral to reproduce B.E. and radii of 4He**4He with 0s+0p space**Energysurface • Narrow 0p-orbit • = 0- coupling of 0s1/2-0p1/2 • (J,T)=(1,0), p-n pair**4He with adding high-L orbits**Length parameters Solutions shows a good convergence Higher shell effect**4He with 0s+p+1s+d+f+g**4 Gaussians instead of HO c.m. excitation = 0.6 MeV • Three cases are mixed. • 0- of pion nature. • Deuteron correlationwith (J,T)=(1,0)**LS splitting in 5He with tensor correlation**[Ref] T. Terasawa, PTP22(’59), S. Nagata, T. Sasakawa, T. Sawada and R. Tamagaki, PTP22(’59), K. Ando and H. Bando PTP66(’81) • Orthogonarity Condition Model (OCM) is applied.**6He in coupled 4He+n+n model**• (0p3/2)2 can be described in Naive 4He+n+n model • (0p1/2)2 loses the energy Tensor suppression in 0+2**Characteristics of 11Li**• S2n = 0.31 MeV • Rm = 3.12±0.16 / 3.53±0.06 fm (9Li: 2.32±0.02 fm) Halostructure Borromeansystem No bound state in any two-body subsystem 10Li(*)+n 9Li+n+n 0.31 MeV 11Li • Breaking of magic number N=8 • Simon et al.(exp,PRL83) (1s)2~50%. • Mechanism is unclear**11Li with coupled 9Li+n+n model**• System is solved based on the RGM equation Up to 2p2h • Orthogonarity Condition Model (OCM) is applied.**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.**9Li with tensor and pairing correlations**• Configuration mixing with H.O. basis function(TM, K.Kato, K. Ikeda, PTP113(2005), nucl-th/0607059). • 0s+0p+1s0d within 2p2h excitations. • Length parameters such as are determined independently and variationally.**Properties of local minimum in 9Li**(a) : Tensor correlation with (0s1/2)–2(0p1/2)2 excitation of p-n pair (T=0). Vtensor is optimized with spatially shrunk H.O. basis. Pairing correlationof p-shell neutrons**Superposition of two minima in 9Li**(exp. : －45.3 MeV) (exp. : 2.32±0.02) Pairing correlation of n-n pair • Tensor correlation of p-n pair • 0– coupling of 0s1/2–0p1/2 • pion nature of Vtensor**Hamiltonian for 11Li**• V9Li-n : folding potential • Same strength for s- and p-waves • Adjust to reproduce S2n=0.31 MeV • Vn-n : Argonne potential (AV8’) [Ref] TM, S. Aoyama, K. Kato, K. Ikeda, PTP108(2002)**11Li G.S. properties(S2n=0.31 MeV)**Rm Simon et al. P(s2) Tensor +Pairing Pairing correlation couples (0p)2 and (1s)2 for last 2n**Charge Radii of 11Li**9Li G RC-2n Charge Radii 11Li 9Li Tensor +Pairing Inert Core Pairing Tensor Expt. (Sanchez et al., PRL96(2006))**Coulomb breakup strength of 11Li**No three-body resonance E1 strength by using the Green’s function method +Complex scaling method +Equivalent photon method (TM et al., PRC63(’01)) • Energy resolution is considered with =0.17 MeV. • Expt: T. Nakamura et al. , PRL96,252502(2006)**Summary**• We investigate the explicit effects of the tensor correlation in 4,5,6He and 9,10,11Li. • 4He with tensor-optimized shell model • Spatial shrinkage of particle states • Specific 2p2h excitations with 0- coupling 0s1/2(h)-0p1/2(p) • 5He and 6He • Pauli-blocking effect on 0p1/2 orbit • 11Li • Breaking of magic number, halo formation • Charge radii, Coulomb breakup strength**microscopic 4He[(0s)4]-n int. Kanada et al. ,RGM,**PTP61(’79). Tensor-optimized 4He, Expt: Th. Stammbach, and R. L.Walter, NPA180(’72) No Tensor: S. Aoyama, S. Mukai, K. Kato and K. Ikeda, PTP93.(’95)**2n correlation density in 11Li**Talk by Y. Kikuchi (9/21PM) n n 9Li Cf. H.Esbensen and G.F.Bertsch, NPA542(1992)310**Gaussian expansion for 4He**• We determin variationally. • Solutions converge with 4 Gaussians • Gaussian with narrow lengths are important Gaussian expansion of particle states instead of HO for the quantitative description of the radial shrinkage**Hamiltonian and variational equations for 9Li**• Effective interaction : Akaishi force (NPA738) • G-matrix from AV8’ with kQ=2.8 fm-1 • Long and intermediate ranges of Vtensor survive. • Adjust Vcentral to reproduce B.E. and radii of 9Li**Energy surface of 9Li for length parameters of HO**two minima, (a), (b) with a common b0p3/2 value. • (a) shows b0p1/2 ~b0s x 0.5 • (b) shows b0p1/2 ~b0p3/2 Pairing correlation of neutrons with (0p3/2)-2(0p1/2)2 excitation.

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