Transcript Document

重い不安定核における集団運動
山上 雅之 (理化学研究所)
トピックス
新しい独立粒子運動
集団運動の質的変化：超流動、低励起振動状態
中性子過剰Ni同位体（球形核）
中性子過剰Mg同位体（変形核）
集団運動 -多彩な“形”の物理原子核 ⇒ 様々な“形”が出現する最小の量子多体系
粒子密度の変形（実空間回転対称性の破れ）
エキゾチック変形(非軸対称８重極変形）!?
４重極変形
プロレート
オブレート
Refs. S.Takami, K.Yabana, and M.Matsuo: Phys. Lett. B431, 242 (1998)
M.Y., K.Matsuyanagi, and M.Matsuo, Nucl. Phys. A693, 579 (2001)
超流動性（ゲージ空間・実空間回転対称性の破れ）
対称性の破れと集団モードの発生
V
• 自発的対称性の破れ（β、Δ）を回復する
集団モード（回転、対回転）
• 様々な振動モード（形、対振動）
（各モードのエネルギースケール、モード結合）
vibration
,
zero-freq. mode
Gammasphere:
www-gam.lbl.gov
Motivation
理研RIBF
軽い不安定核
重い不安定核
A , N / Z  large
どのような新しい物理の可能性が拓けるか？
重い不安定核における新しい集団運動の物理
に焦点を当てる。
キーワード：弱束縛、連続状態、対相関
Pairing correlation in borromean nucleus 11Li
Two-particle density in 11Li
n
9Li
 12
n
K.Hagino, H.Sagawa, Phys.Rev. C 72, 044321 (2005)
Soft E1 excitation
New data:
T. Nakamura, et al., Phys. Rev. Lett. 96,
252502 (2006)
B  E 1   1.42  18  e fm , E rel  3 M eV
2

2
 14
 12  48  18 degree
cf.  12
no  correlation
 90 degree
Appreciable two neutron spatial correlation
Di-neutron correlation is implied.
NN force and di-neutron formation

D.M.Brink, R.A.Broglia, Nuclear Superfluidity,
Cambridge University Press, 2005
 / 0
Questions
In heavy n-rich nuclei with many weakly-bound neutrons,
• Formation of multi di-neutrons and their condensation?
• Collective excitations?
A  large
“Core”
11Li
??
Pairing correlation in weakly-bound nuclei
Pair scattering into continuum states
Break down of BCS approximation
F
 u k  E , r   BCS  u k  r  
 k r   

  
HF
 vk  E , r  
 vk k  r  
HF
k
 F erm i   p a ir
• Pairing correlation dose NOT change the spatial structure.
• Neutron gas problem
 r  
 v 
k
HF
  k , r 
k 0
k
HF
2


dn  
  v 
HF
  , r 
2
 0
 ex p    k r  / r

HF
 sin  kr   lj  / r
J.Dobaczewski, H.Flocard, J.Treiner, Nucl. Phys. A422, 103 (1984)
 di v .
Coordinate space Hartree-Fock-Bogoliubov theory
 Tˆ  V H F  r   


 r 

 r 
 Tˆ  V H F
  uk  E , r  
 uk  E , r  

 E


 r      vk  E , r  
 vk  E , r  
A. Bulgac, FT-194-1980, CIP-IPNE, Bucharest Romania, 1980 (nucl-th/9907088)
J. Dobaczewski, H. Flocard, J. Treiner, Nucl. Phys. A422, 103 (1984)
Asymptotic behavior at infinity
ˆ E,r   E   u E,r 
Tu
k
k
ˆ E,r    E   v E,r 
Tv
k
k
 D eterm ined by E  Pairing correlation changes the spatial structure
 u k  E , r  , v k  E , r   Different asymptotic behavior
Quasiparticle states in weakly-bound nuclei
u  E k , r   sin   k r   k  / r
 F erm i  E k
e . g ., 3 s1 / 2 state at 
 v ( r )
v  E k , r   exp    k r  / r
HF
 -0.5 M eV
2
No neutron gas
 u ( r )
2
HFB
HF+BCS
HFB
HF+BCS
VHF  r     r 
Pairing anti-halo effect
l  0
K. Bennaceur, et al., Phys. Lett. 496B, 154 (2000)
New features of collective excitations
In weakly-bound superfluid nuclei,...
New type independent particle motions
Novel features?
Collective excitations
Coherent motions involving
many two-quasiparticle states
First 2+ states in neutron rich Ni isotopes
Comparison (Skyrme SLy4)
• HFB + QRPA
• HF-resonant BCS + QRPA
• HF + RPA
Ref. M.Y. Phys. Rev. C72, 064308 (2005)
High-l non-resonant continuum states
2 r  
 r  , r   10 fm
3
2
corr , n
1
2
h11/2 res. (l=5)
HFB
Vpair fixed
High-l continuum states
z = 0 plane
Spatial localization of correlated pair
(di-neutron picture)
l  1/
2
r
r2 
 12   2   1
12
Ref. M.Matsuo, et. al., Phys. Rev. C 71, 064326 (2005)
z-axis
1
r
r1 
4


Role of high-l continuum
lmax → larger
Steeper slope
E pair fixed
l m a x  10

V pair   555 M e V fm
-3
lm ax  5

V pair   755 M e V fm
-3
Neutron rich Mg isotopes
Collaborators
• K. Matsuyanagi (Kyoto)
• K. Yoshida (Kyoto)
Deformed multi-weakly-bound nucleon system
40Mg
region
N=28
X
44S
X
Z=12
X
X
42Si
N=28
HFB (Gogny DIS)
36Mg 38Mg 40Mg
R.Rodriguez-Guzman, J.L.Egido, L.M.Robledo
Phys. Rev. C65, 024304 (2002)
X
Z=12
HFB (Skyrme SIII)
X
X
J.Terasaki, H.Flocard, P.-H.Heenen, P.Bonche
Nucl.Phys. A621, 706 (1997)
Ingredients taken into account in this calculation
HFB, QRPA calculation simultaneously taking into account
Continuum
Deformation
Pairing

Directly solve HFB eq. in coordinatespace mesh-representation
0
z
H.O. basis
X
Spatially extended structure
Neutron two-body correlation density in 40Mg
External region
High-W states are required for
convergence
 r  
1
2
 r  0
Reference
neutron
Indication of spatial localization of
the correlated pair (di-neutron picture)
Di-neutron correlation in 36,38Mg
Quadrupole vibrations in n-rich Mg isotopes
(1W.u.=6 - 8fm4)
 2  0 .3
K
K

0


2

Microscopic structure of the low-lying K=0+ mode
[310]1/2
3.16%
5.86%
[321]3/2
35.7%
[202]3/2
[330]1/2
[330]1/2
32.2%
[200]1/2
3.19%
1.07%
[202]5/2
[202]3/2
Soft K=0+ mode in deformed nuclei
Two-level model (Bohr and Mottelson)
1
| 0 
a b
2
( a |  1 1   b |  2 2  )
2
1
| 0 ' 
a b
2
2
2
(  b |  1 1   a |  2 2  )
1
Transition matrix element
 0 ' | r Y 20 | 0 
2
2 ab
a b
2
2
 
| r Y 20 |  2     1 | r Y 20 |  1  
2
2
2
opposite sign
Enhancement
Deformation of pairing field
Two neutron pair transition strengths
Monopole pairing

P00 


 d r  ( r ,  ) ( r ,  )
Quadrupole pairing

P20 


 d r r Y 20 ( rˆ ) ( r ,  ) ( r ,  )
2
More exotic soft K=0+ mode in 36Mg
K



 0 2 r Y20 0 gs 
2
M
 ,
20
 ,
(e)
Configurations
 ,
2
M 20  fm 
(a) [310]1/2, [330]1/2
-2.11
(b) ([321]3/2)2
-1.61
(c) ([310]1/2)2
-1.58
(b)
(d) ([330]1/2)2
-1.50
(d)
(e) [301]1/2, [310]1/2
…
-0.51
(c)
(a)
Violation of selection rule valid for H.O. like w.f.
If [ N , n3 ,  ]W is good quantum number
 N  2 for non-zero transition matrix elements with r Y 20
2
Octupole vibrations
Microscopic structure of the K=0- mode at β=0.3
 2  0 .3
~8 W.u. (intrinsic)
  | Qˆ 30 | 0  
M
30 ,

[321]3/2
[202]3/2
Single 2qp excitation is
dominant, but
contribution of
many 2qp excitations
(1W.u.=60fm6)
Enhancement of transition strength
Microscopic structure of the K=0- mode atβ=0.55
 2  0 .5 5
Strikingly enhanced
transition strengths
~100 W.u. (intrinsic)
  | Qˆ 30 | 0  
M
30 ,

Coherent coupling of many 2qp excitations
Striking enhancement of transition strength
(1W.u.=60fm6)
Good indicator of large deformation
Systematic features
Soft octupole vib.
associated with SD
shell structure
cf. Soft K=0- and 1- modes
on SD state in 40Ca and 44Ti
T.Inakura et al.,
NPA768(2006)61
Gamma vibration
Excitation of protons Z=12
Coupling between pair fluctuation
and beta vibration
Soft K=0+ mode
まとめ
中性子過剰Ni、Mg同位体を例に、重い不安定核での新しい物理の
可能性の“一端”を議論した。
Continuum
Deformation
Pairing
•新しい独立粒子運動
•新しい超流動性（BCSからBEC（ダイニュートロン凝縮）の可能性）
•低励起振動状態の質的変化（連続状態、対相関、対ポテンシャルの変形）
展望
• より系統的な計算（中性子過剰Si、S、Arなど、正負パリティ振動、回転運動）
• 理論計算の精密化（変形Skyrme-QRPA、連続状態の取り扱い、など）
5-D quadrupole zero point energy corrections for 32Mg
V  q   V  q 
A verag e
  , 
GOA
Hˆ coll g k  q   E k g k  q 
Hˆ coll  
2
2

 q
ij
M

i
1
 q   ij
X

q j
 V  q   V  q 
g
I 0
  , 
V  q    q H  q : C onstrained H FB
 V  q  : 5-D zero point energy corrections
S.Peru, M.Girod, J.F.Berger, Eur.Phys.J. A 9, 35 (2000)
空間回転対称性の回復： 32Mgの場合
HFB
I  0
X
X
X
X
X
X
R.Rodriguez-Guzman, J.L.Egido, L.M.Robledo, Nucl.Phys. A709, 201 (2002)
q
intrinsic
20
 q
I 0
20
概念図
intrinsic
q 20
Intrinsic frameが上手く定義できない

IM

 dq 20 f
I
 q 20 

IM
??
 q 20 
Generator Coordinate Method (GCM)
0
q 20
Angular correlation
2
3
4
2    corr , n  r1  , r2   10 fm 
r1    1   , z1  0,  1 
r2    2   , z 2  0,  2 
z = 0 plane
2

z-axis
(symmetry axis)

 12   2   1

1

Our approach
Ground state
Coordinate-space HFB
Mean-field
Deformed Woods-Saxon potential
Pair-field
~
V0
 (r ) ~
h (r ) 
(1 
)  (r )
2
0
V 0   480 . 0 MeV  fm
3
E cutoff  50 MeV
 max  z max  10 (fm)  12.8 (fm)
Excited states
QRPA in matrix formulation
Residual interaction
p-h channel
p-p channel
v ph ( r , r ')  [ t 0 (1  x o P ) 
v pp ( r , r ')  V 0 (1 
 (r )
0
t3
6
(1  x 3 P )  ( r )] ( r  r ')
) ( r  r ')
Difference of K=0+ mode between 34Mg and 40Mg
 | Qˆ 20 | 0 
M
20 ,

proton excitations
B ( E 2 )  21 . 1 e fm
2
2   excitation
 [110]1/2 
 [211]3/2 
 [101]3/2 
 [220]1/2 
s:
 [330]1/2
 [431]3/2
 [321]3/2
 [440]1/2
4
B ( E 2 )  3 . 35 e fm
2
4
Spatial structure of 2qp excitations in 40Mg
 | Qˆ 20 | 0  
Q 20 , (  , z )
 d  dzQ 20 , (  , z )
Qˆ 20 



 d r r Y 20 ( r ,  ) ( r ,  )
2
Quadrupole1p-1h states in 86Ni
Decoupling region
Quadrupole 1p-1h states
Quadrupole 1p-1h states
No pairing
3s1/2 → d3/2
(res)
2d5/2 → d3/2
(res)
2d5/2 → g7/2
(res)
Correlated region
 p   h  5 M eV
L
L
 0
R ph 
 r F ph

L
F ph
L
ph
r
L
dr
dr
 r F  r  dr
ph

L

 R ph
L
F
 r  dr

  ph
2

r


2





1/ 2
Quadrupole two-quasiparticle states in 86Ni
Neutrons in 86Ni
Increase of available configurations: p-h, p-p, h-h channels
Correlations between s1/2, d3/2 and d5/2 states in spatially extended region
Competition between the pairing anti-halo effect in the lower components
and the broadening effect in the upper components
Di-neutron correlation in medium mass region
Extensive discussion for spherical nuclei (O, Ca, and Ni)
M.Matsuo, K.Mizuyama, and Y.Serizawa, Phys. Rev. C 71, 064326 (2005)
Two-body correlation density (spin anti-parallel)
 co rr , n  r  , r '    
p a ir , n
 r , r '  
l  7
2
Coordinate space HFB
O
High-l states → Spatial localization of the correlated pair
θ
l  1 /
Di-neutron correlation becomes stronger as approaching the neutron drip line
Deformations of neutron-rich Mg isotopes
K.Yoneda et al., PLB499(2001)233
“Skyrme-HFB deformed nuclear mass table”
M.Stoitsov et al.,PRC68(2003),054312
Gogny-HFB calculation using D1S
R. Rodríguez-Guzmán et al.,
NPA709(2002)201

E ( 41 )

1
E (2 )
34Mg

2120 ( keV )
 3 .2
660 ( keV )
is well deformed.
Convergence of two-body correlation density
High-W states are required in nuclei close to
the neutron drip line
Spatial localization of the correlated pair
(di-neutron picture)
Size of neutron Cooper pair
M.Matsuo, nucl-th/0512021
 pair / d
P / d
P 
2
0.2  F /  F
k F / m  F
BCS-BEC crossover in fermionic 40K atoms
Experiment: Regal et al., 2004
Analytically solvable BCS-BEC
crossover model
BEC
BCS
BEC
BCS
 B  0.6 [gau ss]
1/ k F a  1
Courtesy of M. Matsuo
Schematic level schemes for 40Mg
K
B  E 2; K  0 2 I i  K  0 1 I f
 I i 020 | I f 0
2
M1
2

0


1  a  I  I
0
i
i
 1  I f  I f  1

2
36Mg 周辺（変形した中性子過剰核）
24
HFB (Skyrme SIII):
J.Terasaki, H.Flocard, P.-H.Heenen, P.Bonche, Nucl.Phys. A621, 706 (1997)
 F erm i 
36
Mg
RIKEN RIBF
N=2Z
Neutron drip line
http://www.rarf.riken.go.jp/RIBF/nuclearchart-e.htm
r-process pass
Onset of weak binding in nuclear structure
N  2Z
 F erm i  S 2 n / 2   p a ir
S 2 n [M eV]
M. V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, D. J. Dean, Phys. Rev. C 68, 054312 (2003)
J. Dobaczewski, M.V. Stoitsov, W. Nazarewicz, nucl-th/0404077
Characteristic Pattern of Excited Spectrum
80Zr
: Spherical + Y32 deformation (Td group)
Rigid rotation…
sequence of levels 0+, 3-, 4+, 6+, 7-, …
with rotational energy relation E bg
I  E bg
0 
b g
I I 1 / 2J
Octupole vibration…
low-lying Jπ=3- state
68Se
: Oblate + Y33 deformation (D3h group)
Octupole vibration
low-lying Jπ=3- state
Kπ=0+ rotational band (associated with the ground state)
0+, 2+, 4+, …
Kπ=3- rotational band (associated with the low-lying 3- state)
3-, 4-, 5-, …
Ref. S. Takami, K. Yabana, M. Matsuo: Phys. Lett. B431 (1998) 242