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Transcript of 11 Role of tensor force in light nuclei based on the tensor optimized shell model Hiroshi TOKI RCNP,...
11
Role of tensor force in light nuclei based on
the tensor optimized shell model
Hiroshi TOKI RCNP, Osaka Univ. Manuel Valverde RCNP, Osaka Univ.Atsushi UMEYA RIKEN Kiyomi IKEDA RIKEN
Takayuki MYO 明 孝之 Osaka Institute of Technology
International conference on the structure of baryons "BARYONS’10” @ Osaka Univ. , 2010.12
Outline
2
Tensor correlation in light nuclei
• Tensor Optimized Shell Model (TOSM)to describe tensor correlation
• Unitary Correlation Operator Method (UCOM)for short-range correlation
• TOSM+UCOM with bare nuclear force
• Application of TOSM to Li isotopes
• halo formation in 11Li
• Tensor force (Vtensor) plays a
significant role in the nuclear structure.
– In 4He, Vtensor ~ Vcentral
– ~ 80% (GFMC)
3
Importance of tensor force
R.B. Wiringa, S.C. Pieper, J. Carlson, V.R. Pandharipande, PRC62(2001)
• We would like to understand role of Vtensor in the nuclear
structure by describing tensor correlation explicitly.
tensor & short range correlations from VNN (bare)
He, Li isotopes (LS splitting, halo formation, level inversion)
V
VNN
S
D
Energy -2.24 MeV
Kinetic 19.88
Central -4.46
Tensor -16.64
LS -1.02
P(L=2) 5.77%
Radius 1.96 fmVcentral
Vtensor
AV8’
Deuteron & tensor force
Rm(s)=2.00 fm
Rm(d)=1.22 fmd-wave is “spatially compact”
r
AV8’
TM, Sugimoto, Kato, Toki, Ikeda
PTP117(2007)257
5
Tensor-optimized shell model (TOSM)
5
4He
• Tensor correlation in the shell model type approach.
• Configuration mixingwithin 2p2h excitationswith high-L orbits. TM et al., PTP113(2005) TM et al., PTP117(2007) T.Terasawa, PTP22(’59))
• Length parameters {b} such as b0s, b0p , … are optimized
independently (or superposed by many Gaussian bases).
– Describe high momentum component from Vtensor (Shrinkage)HF by Sugimoto et al,(NPA740) / Akaishi (NPA738)RMF by Ogawa et al.(PRC73), AMD by Dote et al.(PTP115)
Configurations in TOSM
proton neutron
Gaussian expansion
nlj
particle states
hole states (harmonic oscillator basis) c.m. excitation is
excluded by Lawson’s methodApplication to Hypernuclei by Umeya
coupling
C0 C1 C2 C3
7
4He in TOSM
Orbit bparticle/bhole
0p1/2 0.65
0p3/2 0.58
1s1/2 0.63
0d3/2 0.58
0d5/2 0.53
0f5/2 0.66
0f7/2 0.55
7
Length parameters
good convergence Higher shell effect 16 Lmax
0 1 2 3 4 5 6
vnn: G-matrix
Cf. K. Shimizu, M. Ichimura and A. Arima, NPA226(1973)282.( ) in q V
shrink
8
Unitary Correlation Operator Method
8H. Feldmeier, T. Neff, R. Roth, J. Schnack, NPA632(1998)61
corr. uncorr.C
12
( ) ( )exp( ), r ij ij rij iji j
p s r s r pC i g g
short-range correlator
† H E C HC H E
† 1 (Unitary trans.)C C
rp p p
Bare HamiltonianShift operator depending on the relative distance r
† 12( ) ( ) ( )C rC r s r s r s r
TOSM
2-body cluster expansion
9
Short-range correlator : C (or Cr)
3GeV repulsion Originalr2
C
Vc
1E
3E
1O3O
s(r)
[fm]
We further introducepartial-wave dependencein “s(r)” of UCOM
S-wave UCOM
Shift function Transformed VNN (AV8’)
10
T
VT
VLS
VC
E
(exact)Kamada et al.PRC64 (Jacobi)
• Gaussian expansion with 9 Gaussians
• variational calculation
TM, H. Toki, K. IkedaPTP121(2009)511
4He in TOSM + S-wave UCOM
good convergence
11
Configurations of 4He in TOSM + short-range UCOM
(0s1/2)4 83.0 %
(0s1/2)−2JT(p1/2)2
JT JT=10 2.6
JT=01 0.1
(0s1/2)−210(1s1/2)(d3/2)10 2.3
(0s1/2)−210(p3/2)(f5/2)10 1.9
Radius [fm] 1.54
11
• 0 of pion nature.
• deuteron correlation with (J,T)=(1,0)
Cf. R.Schiavilla et al. (GFMC) PRL98(’07)132501
• 4He contains p1/2 of “pn”-pair.
5,6He in TOSM+UCOM
• Argonne V8’ with no Coulomb force.
• Convergence for particle states.– Lmax ~10
– 6~8 Gaussian for radial component
• Lawson method to eliminate CM excitation.
• Bound state approximation for resonances.
Cf) GFMC : K.M. Nollett et al. , PRL99 (2007) 022502 NCSM : S. Quaglioni, P. Navrátil, PRL101 (2008) 092501 SVM : Y.Suzuki, W.Horiuchi, K. Arai, NPA823 (2009) 1
4,5,6He with TOSM+UCOM
• Difference from 4He in MeV
AV8’
Preliminary
5He : Hamiltonian component
• Difference from 4He in MeV
5He 3/2 1/2
T 24.1 17.9
Central 9.0 7.0
Tensor 5.6 1.1
LS 2.6 1.0
E 6.9 10.8 Diff.=3.9 [MeV]
=18.4 MeV (hole)
bhole=1.5 fm for 4,5He
Tensor correlation & Splitting in 5He
Vtensor~exact
in 4He
Enhancement of Vtensor
LS splitting in 5He with tensor correlation
• T. Terasawa, A. Arima, PTP23 (’60) 87, 115.• S. Nagata, T.Sasakawa, T.Sawada, R.Tamagaki, PTP22(’59)• K. Ando, H. Bando PTP66 (’81) 227• TM, K.Kato, K.Ikeda PTP113 (’05) 763 (+n OCM)
30% of the observed splitting from Pauli-blocking d-wave spliiting is weaker than p-wave splitting
Pauli-Blocking
Phase shifts of 4He-n scattering
18
Characteristics of Li-isotopes
Breaking of magicity N=8• 10-11Li, 11-12Be• 11Li … (1s)2 ~ 50%. (Expt by Simon et al.,PRL83)
• Mechanism is unclear
11LiTanihata et al., PRL55(1985)2676. PLB206(1998)592.
Halo structure
19
9Li in TOSM• Tensor-optimized shell model
TM et al., PTP121(2009), PTP117(2007).
• 0s+0p+1s0d within 2p2h excitations, G-matrix (Akaishi)
• Length parameters b0s, b0p , … are determined independently and variationally (or Gaussian expansion).
– Describe high momentum component from Vtensor cf. CPP-HF by Sugimoto et al.,NPA740 / Akaishi NPA738
Energy surface for b-parameter in 9Li
Vtensor is optimized with shrunk HO basis
cf. 1st order (residual interaction): T. Otsuka et al. PRL95(2005)232502.
TOSM
pairing correlation
nn
Dominant part of the tensor correlation
pn
21Pairing-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.
22
11Li in coupled 9Li+n+n model• System is solved based on RGM
11 9( Li) ( Li) nnH H H 11 9
1
( Li) ( Li) ( )N
i ii
nn
A
9 11 9
1
( Li) ( Li) ( Li) ( ) 0N
j i ii
H E nn
A
9 shell model type configu( Li) rat: on ii
• Orthogonality Condition Model (OCM) is applied.
91 2 1 2 12
1
( Li) ( ) ( ) ( )N
ij c c ij j ii
H T T V V V nn E nn
9 99( Li) : Hamilt ( Li onian for ) Liij i jH H
9 Orthogonality to the Pauli0 -, forbidden { Li} : st t s a ei
1 2 hybrid-TVmodel with Gaussi( an expansion) : nn A{
TOSM
23
11Li G.S. properties (S2n=0.31 MeV)
Tensor+Pairing
Simon et al.
P(s2)
Rm
E(s2)-E(p2) 2.1 1.4 0.5 0.1 [MeV]
Pairing correlation couples (0p)2 and (1s)2 for last 2n
(pn)(nn)
24
Coulomb breakup strength of 11Li
E1 strength by using the Green’s function method
+Complex scaling method+Equivalent photon method (TM et al., PRC63(’01))
• Expt: T. Nakamura et al. , PRL96,252502(2006) • Energy resolution with =0.17 MeV.E
11 9Li (G.S.) Li n n
No three-body resonance
T.Myo, K.Kato, H.Toki, K.IkedaPRC76(2007)024305
25
Summary
• TOSM+UCOM with bare nuclear force.
• Vtensor enhances LS splitting energy.
• Coexistence of tensor and pairing correlations, explicitly
• Halo formation in 11Li
Review Di-neutron clustering and deuteron-like tensor
correlation in nuclear structure focusing on 11Li
K. Ikeda, T. Myo, K. Kato and H. Toki Springer, Lecture Notes in Physics 818 (2010)
"Clusters in Nuclei" Vol.1, 165-221.