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