軽い不安定核における 共鳴状態の構造 明　孝之 大阪工業大学 1 KEK 理論セミナー 　2010.10.07

Outline Structures of He isotopes “core+valence neutrons” with complex scaling Results 7He (a+3n) , 8He (a+4n) Tensor correlation in 4,5,6He using “TOSM” TM, K. Kato, K. Ikeda PRC76 (2007) 054309 TM, K. Kato, H. Toki, K. Ikeda, PRC76 (2007) 024305 TM, R. Ando, K. Kato PRC80 (2009) 014315 TM, R. Ando, K. Kato PLB691(2010)150 TM, H. Toki, K. Ikeda PTP121(2009)511

11Li Nuclear Chart Observation of halo structure in 11Li I.Tanihata et al. PRL55(1985)2676. 3 3

Characteristics of He isotopes (expt.) 4-body resonance 5-body resonance 3-body resonance Halo Skin Cf. TUNL Nuclear Data Evaluation Golovkov et al., PLB672(2009)22 4 4 4

Method (4He) Cluster Orbital Shell Model (COSM) Complex Scaling Method Open channel effect is included. – 8He : 7He+n, 6He+2n, 5He+3n, ... Complex Scaling Method Resonances with correct boundary condition as “Gamow states” Give continuum level density (resonance+continuum) E=Er- iG/2 (4He) Y. Suzuki, K. Ikeda, PRC38(1988)410, H. Masui, K. Kato, K. Ikeda, PRC73(2006)034318 5 S. Aoyama, T. Myo, K. Kato, K. Ikeda, PTP116(2006)1 (review)

Cluster Orbital Shell Model System is obtained based on RGM equation valence neutron number i : configuration index  No explicit tensor correlation , Gaussian expansion Orthogonarity Condition Model (OCM) is applied. Remove Pauli Forbidden states (PF) 6

Hamiltonian (4He) V4He-n : microscopic KKNN potential phase shifts of 4He+n scattering Vn-n : Minnesota potential with slightly strengthened Fit 6He(0+) (4He) A. Csoto, PRC48(1993)165. K. Arai, Y. Suzuki and R.G. Lovas, PRC59(1999)1432. TM et al. PTP113(2005)763. TM, S. Aoyama, K. Kato, K. Ikeda, PRC63(2001)054313

Completeness relation Complex scaling for 3-body case Completeness relation B.G. Giraud, K. Kato, A. Ohnishi J. Phys. A 37 (‘04)11575 T. Berggren, NPA109(’68)265. J.Aguilar and J.M.Combes, Commun. Math. Phys.,22(’71)269. E.Balslev and J.M.Combes, Commun. Math. Phys.,22(’71)280. 8

Schrödinger Eq. and Wave Func. in CSM Asymptotic Condition in CSM State No scaling Scaling Bound Resonance Continuum

Treatments of the unbound states in CSM i: configuration index Gaussian expansion Exact asymptotic condition for resonances Discretize continuum states. cf. Continuum Discretized Coupled Channel (CDCC) calculation by Kyusyu Group 10

Spectrum of 6He with 4He+n+n model Eth(4He+n+n) 4He+n+n 6He(*) 5He+n A. Csoto, PRC49 (‘94) 3035, S. Aoyama et al. PTP94(’95)343, T. Myo et al. PRC63(’01)054313 11

He isotopes : Expt vs. COSM (4He:(0s)4) 3-body resonance 4-body resonance 5-body resonance a TM, K.Kato, K.Ikeda PRC76(’07)054309 TM, R.Ando, K.Kato PRC80(’09)014315 TM, R.Ando, K.Kato, PLB691(‘10)150 12 12 12 12 TUNL Nuclear Data Evaluation

Matter & Charge radii of 6,8He [fm] Expt Theor Rm Rch I. Tanihata et al., PLB289(‘92)261 G. D. Alkhazov et al., PRL78(‘97)2313 O. A. Kiselev et al., EPJA 25, Suppl. 1(‘05)215. P. Mueller et al., PRL99(2007)252501 13

6He=4He+n+n with ACCC+CSM Eth(4He+n+n) soft dipole resonance in 6He (1−). E=(3.02i15.6) MeV ACCC: Analytical Continuation in Coupling Constant (Niigata group) Large decay width is obtained. S. Aoyama (Niigata) PRC68(’03)034313 14

Continuum Level Density in CSM S. Shlomo, NPA539(’92)17 K. Arai and A. Kruppa, PRC60(’99)064315 R. Suzuki, T. Myo and K. Kato, PTP113(’05)1273. CLD in CSM (Kinetic) 15

4He+n scattering with complex scaling Energy eigenvalues P3/2 scattering phase shift 30 Gaussian basis functions 16

4He+n scattering with discretized continuum Energy eigenvalues measured from Eth(4He+n) Phase shifts (s,p-waves) R. Suzuki, T. Myo and K. Kato, PTP113(’05)1273.

Strength function in CSM Bi-orthogonal relation Green’s function and Response function 18 T. Berggren, NPA109(’68)265, T. Myo, A. Ohnishi and K. Kato, PTP99(’98)801

E1 of 6He into 4He+n+n (3-body breakup) Energy eigenvalues E1 transition

Coulomb breakup strength of 6He E1+E2 Equivalent photon method TM, K.Kato, S. Aoyama and K.Ikeda PRC63(2001)054313. Kikuchi, TM, Takashina, Kato, Ikeda PTP122(2009)499 PRC81 (2010) 044308 6He : 240MeV/A, Pb Target (T. Aumann et.al, PRC59(1999)1252) 20

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)) T.Myo, K.Kato, H.Toki, K.Ikeda PRC76(2007)024305 Expt: T. Nakamura et al. , PRL96,252502(2006) Energy resolution with 　　　=0.17 MeV.

7He (unbound) : Expt vs. Complex Scaling Experiments TM, K.Kato, K.Ikeda PRC76(’07)054309 22 22 22 22 4-body resonance complex scaling

Experiments of 7He a) RIKEN p(8He,d)7He A. A. Korsheninnikov et al., PRL82(1999)3581. b) Berlin 9Be(15N,17F)7He G. Bohlen et al. ,PRC64(2001)024312. c) GSI 8He breakup M. Meister et al., PRL88(2002)102501. d) ANL 2H(6He, p)7He at 11.5 MeV/u A. H. Wuosmaa et al., PRC72(2005) 061301. e) SPIRAL p(8He,d)7He F. Skaza et al., PRC73(2006)044301. f) KVI, 7Li(d,2He)7He N. Ryezayeva et al., PLB639(2006)623. 23

S-factor of 6He-n component in 7He Bi-orthogonal relation T. Berggren, NPA109(1968)265 TM, K.Kato, K.Ikeda, PRC76(2007)054309 Weak coupling of 6He(0+)+n(p1/2) 6He(halo) 7He(Jp) 24 24

complete set of (A-1) SYSTEM One-neutron removal strength in CSM Bi-orthogonal relation Strength function and response function energy of (A-1) SYSTEM Response function complete set of (A-1) SYSTEM Complex scaled-Green’s function T. Berggren, NPA109(’68)265, T. Myo, A. Ohnishi and K. Kato, PTP99(’98)801 25 25 S.Aoyama, TM, K.Kato, K.Ikeda, PTP116(2006)1 (review)

One-neutron removal strength of 7HeGS TM, Ando, Kato PRC80(2009)014315 ” 4He+n+n” complete set using CSM 7He(3/2−) n−1 6He(*) 5He+n 4He+n+n 4He+2n 2+1 26 26

Energy spectrum 8He with complex scaling 32000 dim. Full diagonalization of complex matrix @ SX8R of NEC TM, R.Ando, K.Kato, PLB691(‘10)150 27

a 8He : 0+1 & 0+2 states lj 0+1 0+2 0+1 : (p3/2)4 ~ 87% sum=4 0+2 : (p3/2)2(p1/2)2 ~ 96%

a 8He : 0+1 & 0+2 states Jp 0+1 0+2 (p3/2)4 0+ : 2+ = 1 : 5 Cf. AMD by Kanada-En’yo a,b : orbit 0+1 a 0+2 Jp (p3/2)4 0+ : 2+ = 1 : 5 (p3/2)2(p1/2)2 0+ : 1+ : 2+ = 2 : 1.5 : 2.5 sum=4C2=6

Monopole Strength of 8He (Isoscalar) 0+2 6He+2n Spin flip : p3/2 → p1/2 CSM q=20 deg. 4He+4n 7He+n 30

Monopole Strength of 8He (Isoscalar) 7He+n 0+2 6He+2n Spin flip : p3/2 → p1/2 CSM q=20 deg. 4He+4n 7He+n 31

Summary Cluster Orbital Shell Model + Complex Scaling (Level density) Coulomb breakups of 6He and 11Li 7He : Importance of 6He(2+1) resonance 8He : Five-body resonances Differences between 0+1 and 0+2 Monopole strength : 8He → 7He+n → 6He+n+n Cf: Coulomb breakup, Iwata et al. PRC62 (2000) 064311 32

2n density in 6He Y. Kikuchi a Dineutron a Lowest config. Cigar a

6He(t,p)8He reaction (2n transfer) PLB672(2009)22, JINR, Dubna 0+2