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Di-neutron Role of the tensor correlation on the halo formation in 11Li Takayuki Myo

RCNP, Osaka Univ.

Kiyoshi Katō

Hokkaido Univ.

Hiroshi Toki

RCNP, Osaka Univ.

Kiyomi Ikeda

RIKEN

RIKEN mini workshop “核子交換反応で探る 6He 核内 2 中性子の空間分布”/ 2006.6
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Contents◦ core+n+n picture of halo nuclei and di-neutron correlation.
◦ Mechanism of the halo structure and breaking of the magicity
in 11Li based on the core+n+n picture.

1. Naive 9Li+n+n model with a deep s-wave core-n potential.
2. Coupled 9Li+n+n model with tensor and pairing correlations.
– Configuration mixing for 9Li.
– Effects of two correlations on the halo formation.
◦ Coulomb breakup strengths.
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Description of Halo nuclei based on the “core+n+n” model◦ Our approach.

◦ 6He : 4He((0s)4) + n + n.

– ”core+n+n” picture+correlation– Successful results for G.S., 2+.
– many theoretical works.

hybrid-VT modelnnnn◦ 11Li : 9Li + n + n.
– Large (1s)2-mixing in G.S.
– Inversion phenomena in 10Li
– Problem of soft dipole resonance.
– Theoretical ambiguity

corecore

Mean Field like(Shell Model like)n-n correlation(di-neutron, pairing)

Configuration mixing[Ref]:K. Ikeda, NPA538,355c(’92)
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Application to 6He◦ 4He+n+n with OCM :Φ(6He)= A{ Φ(4He) Φ(nn) }◦ Interaction: 4He-n : KKNN potential,

n-n : Minnesota

0.6
0.4

(p3/2)2Energy [MeV]

0.2nnnPairing correlation

4He+n+n0-0.2

core

core

COSM (V)ECM (T)(d3/2)2-0.8-1-1.2

COSM+ECM (Hybrid-VT)(di-neutron like)for val-2n is important.

COSM(V)-0.4-0.6

nExp.(-0.975)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
2Channel Number ([lj]ν)[Ref]: S.Aoyama, S.Mukai, K.Katō, K.Ikeda, PTP93(’95)99.
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2n Correlation density for 6He G.S.
rR

Rc-2n

rn-n
Funada, Kameyama, Sakuragi, NPA575(1994)

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Structures of 11Li
◦ Expt. : S2n=0.31 MeV, Rm=3.12±0.16 / 3.53±0.06 fm (9Li: 2.32 fm).
◦ Breaking of magic number N=8, halo structure in G.S.
– Simon et al.(expt) : s2∼50%,Mechanism is unclear.

◦ Virtual s-state in 10Li :– Expt. : Invariant mass spectrum of 9Li-n.
– Many theories assume a deep s-wave 9Li(inert)-n potential.
• Thompson-Zhukov(PRC49) / Garrido-Fedorov-Jensen(NPA700).
• Halo structure can be explained in 11Li G.S., and soft dipole resonances appear.
◦ Excited states: 1.3 MeV (Korsheninnikov,PRL78) / partner of G.S.? (Aoyama)◦ Our group performs the extended three-body model analysis
with configuration mixing for 9Li (PTP101, PTP108, PLB576, pairing).
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2n Correlation density for 11Li G.S. (Zhukov et al.,Phys.Rep.231(1993))

rn-n

Rc-2n
2

p -dominantNielsen-Garrido-Fedorov-Jensen
Phys. Rep. 347 (2001)

Pauli-Blocking
for S=1 component of 2n22p +s

sharow s-wave pot.

Rc-2n
7 / 21rn-n

B(E1) of 11Li in a naive 3-body model with deep s-wave potential.
1.2

1/2+
3/2
5/2+Total

1.00.8113.0+

dσ/dE [b/MeV]

dB(E1)/dE [e2fm2/MeV]

dσ/dE of

0.6
0.4
0.2

Li (T=Pb)

RIKEN

2.5

SDRfold

2.0
1.5
1.0
0.5
0.0

0.0
00.5
11.5
Energy [MeV]

02

12

34

Energy [MeV]◦ Strength has two peaks : 3/2+ and {1/2+, 5/2+} due to spin of 9Li (3/2–).
9Li : 3/2–.
– (1s1/2)⊗(0p1/2) = 0– / 1–,– 0–⊗3/2– = 3/2+,

1–⊗3/2– = 1/2+, 3/2+, 5/2+.

[Ref] T. Suzuki, H. Sagawa, P.F. Bortignon, NPA662(2000)282
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Explicit tensor and pairing correlations in 9Li for analysis of 11Li
◦ We introduce the internal degrees of freedom in 9Li (PTP108, pairing).
◦ We would like to understand the physical aspects of the tensor force.
◦ Configuration mixing with H.O. basis function (TM, K.Katō, K. Ikeda, PTP113)— ——(S. Sugimoto et al. for 12C, 16O )– 0s + 0p + 1s0d within 2p2h excitations.
– Length parameters {bα} are determined independently and variationally.
This is useful to represent the high momentum component.

9Li

0p1/20p3/2

0p1/2
0p3/2

0s1/2

0s1/2πν

LowestπνPairing
9 / 21πνTensorHamiltonian and variational equations for 9Li◦AAH = Σ ti – TG + Σ vij, vij = vCij + vTij + vijLS+ vClmb
ij ,i<ji=1hΦ| H |Φiδ=0hΦ|Φi⇒∂hH – E i=0,∂ bαof the tensor force survive.
– Central part : We adjust the intermediate
range to fit B.E. and Rm of 9Li.

3Tensor Force ( E)

50

VT(r) [MeV]⇒ Long and intermidiate rangesn∂hH – E i= 0.
∂ Cn◦ Interaction : Akaishi force (AK) (NPA738)– G-matrix using AV8’ with kQ = 2.8 fm–1
( > kF = 1.4fm–1 )Φ(9Li)= Σ Cn φn0-50

AK-100AV8’-150010 / 210.5

11.5r [fm]22.53Energy surface of 9Li for length parameters of HO (b0s= 1.45 [fm])(exp: 45.3 [MeV])

B.E.=36.4 [MeV]

9E( Li) [MeV]

B.E.=39.2 [MeV]◦ two minima-15-20-25-30-35-40

with a common b0p3/2 value.
0.5
1
1.5
1.5

b0p3/2=1.8 fm

2b0p

3/2 [fm]

2.5

322.5

11 / 21b0p1/2 [fm]

=b0d

0-5
-10-15-20-25-30-35-40

100

Probability [%]Energy of 9Li [MeV]

Properties of two minima in 9Li〈VT〉
Energy80

0p0h6040
20

tensor×2

pairing

0
0.5

b0p

1
1/2

1.5/ b0s [fm]20.5b0p3/2 / b0s

b0p1
1/2

1.5/ b0s [fm]2
◦ Tensor correlation (pn) : (0s)–2(0p)10
1/2 10,b0p1/2 ∼ b0s / 2 .

2◦ Pairing correlation (nn) : (0p3/2)–2(0p)01
1/2 01,b0p1/2 ∼ b0p3/2 .

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Superposition of the tensor and pairing correlations in 9Li
Energy [MeV]−44.3

hVTi [MeV]−31.9

Rm [fm]

2.30

0p0h

78.5 %–2 —2(0p3/2) 01(0p1/2)01

8.8 %

–2 —
2 (JT)=(10)(0s1/2) JT(0p1/2)JT(JT)=(01)

6.8 %
0.2 %

——
(0s1/2)–2[(1s)(101/2 0d3/2)]10–2 —2(0s1/2) 10(0d3/2)10

1.9 %1.2 %13 / 21• Tensor correlation:◦ 0– coupling of 0s1/2 – 0p1/2⇒ pion nature of VT◦ (J,T)=(1,0)⇒ deuteron correlationEffect of pairing and tensor correlation in 11Li
1s1/2

9Li(GS)

0p1/2
0p3/2
0s1/2πν

Lowest11Li2(p )πνPairingπνTensor

1s1/2
0p1/2
0p3/2
0s1/2

energy lossπ

ν

π

ν

π

ν

Pauli blocking
11Li(s2)

energy gain

1s1/2
0p1/2
0p3/2
0s1/2πνπν
14 / 21πν

increases2 mixing

Tensor and pairing correlations in 11Li in a coupled 9Li+n+n model◦ We prepare 9Li with pairing and tensor correlations.
– Superposition : 0p0h + pairing(nn) + tensor(pn)◦ The system is solved based on the RGM equation
H(11Li) = H(9Li) + H–rel,nn,N11
Φ( Li) = A{ Σ ψ i(9Li) · χi(nn) }i=1

N– Σ h ψ j(9Li) | H(11Li) – E | A{ ψ i(9Li) · χJi(r) }i = 0, for j=1,· · ·,N.
i=1

◦ The Orthogonality Condition Model(OCM) is applied to solve the equations.
NΣ [ hij(9Li) + (T1+T2+Vc1+Vc2+V12+ Λ1,i+Λ2,i) δ ij ] χJj(r) = E χJi(r)i=1

Λi = λ · Σα∈9Li |φαihφα|15 / 21

Hamiltonian for 11Li in the orthogonarity condition mdoel
hybrid-VT model◦ Folding potential with MHN(G-matrix)+ Yukawa Tail for 9Li-n (Sn(9Li)=4 MeV)

nnnn

– Same strength for s- and p-waves.
– Adjust to reproduce S2n=0.31 MeV.
◦ Argonne potential (AV8’) for last 2n.

corecore

Mean Field like(Shell Model like)n-n correlation(di-neutron, pairing)

Configuration mixing[Ref] TM, S. Aoyama, K.Kato, K.Ikeda, PTP108(2002)

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Boundary condition of the coupled 9Li+n+n model◦ The 9Li core in 11Li in the asymptotic region is the isolated 9Li
fully with the tensor and pairing correlations.

2asymptotic region

internal region (2n: p )ncore
G.S. : [0p0h]+[2p2h]ncore nn

Excited: [0p0h]+[2p2h]

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11Li G.S. properties with tensor and pairing correlations
3.7

Rm50
40

3.5

Simon et al.

3.3

30

3.1202.92P(s )100E(s2)-E(p2)Rm [fm]P(s2) in 11Li [%]

60

2.7

InertcorePairing

TensorTensorTensor+Pairing+Pairing

2.1

1.4

0.5

−0.1

2.5

[MeV]
22

pairing correlation couples (0p) with (1s) for last 2n18 / 21

dσ/dE [b/MeV]

Coulomb breakup strength into 9Li+n+n systemdσ/dE of 11Li (Target=Pb)

3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0

RIKEN
Tensor+Pairing
fold01234

Energy [MeV]◦ No three-body resonances.
◦ Exp. : Nakamura et al., RIKEN Accel.Prog.Rep.38.
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22dB(E1)/dE [e fm /MeV]

Effect of the correlations in the final states of 11Li breakup

E1 of1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

11Li

Full cal.

nVnn

VCn

Vnn=0n

VCn
core

VCn=0
Vnn=VCn=00

0.5

1

1.5

2

2.5

Energy [MeV]

20 / 213

3.5

4

Summary
1. We develop the three-body model of halo nuclei
with tensor and pairing correlations.
2. 9Li : Tensor(pn) and pairing(nn) correlations
exhibit different 2p2h excitations and spatial properties.
3. 11Li : Tensor suppression leads to the large admixture of (1s)2 in G.S.
– “Tensor+Pairing” naturally explains 50 % of (1s)2.
4. Coulomb breakup strength depends on the model.
– Naive three-body model produces three dipole resonances.
– “Tensor+Pairing” produces no dipole resonances.
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