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Report on Report on ““International Conference on Finite Fermionic SystemsInternational Conference on Finite Fermionic Systems””
Quest for low-frequency modes of excitation unique to deformed neutron drip-line nuclei
京都大学21COEプログラム「物理学の多様性と普遍性の探求拠点」外国旅費補助成果報告
物理第二教室 原子核理論
吉田賢市
Part
icle
den
sity
(fm
-3)
100Zn
2 4 6 8 10R (fm)
(p)
(n)
J.Dobaczewski
中性子と陽子の密度分布は殆ど同じ
密度分布に非対称性
スキン・ハローの出現
不安定核の物理 ~密度分布~
Z=30N=70
安定核:
不安定核:
魔法数、変形 ~シェル構造の変化~
変形したスキン核、ハロー核の存在?
0
20
40
60
80
100
0 20 40 60 80 100 120 140 160 180Neutron Number
N=Z
N=2Z
deformation βProt
on N
umbe
r
Theory
< -0.2-0.2 ÷ -0.1
-0.1 ÷ +0.1+0.1 ÷ +0.2
+0.2 ÷ +0.3+0.3 ÷ +0.4
> +0.4
SLy4volume δ pairing
M.V
. Sto
itsov
, et a
l., P
hys.
Rev
. C68
, 054
312
(200
3)
s軌道の特異性
新しい魔法数、ハローの形成
I.Hamamoto
stable nuclei
FεFε
unstable nuclei
| tightly bound > | tightly bound >| loosely bound >
| loosely bound >
| resonance >
| continuum >
| tightly bound >
対相関を考えると、更に豊富な組み合わせ
ph p h ph h pph
O f a b g b aλ+ + += −∑ RPA| vib. | 0Oλ
+>= >
中性子ドリップ線近傍核の集団運動
Soft modes expected to neutron-rich nuclei
Soft dipole mode
Soft monopole mode
Soft modes unique associated with neutron skins
手法・ グループ continuum pairing deformation commentcontinuum RPAShlomo-Bertsch ◎ --- ---Hamamoto-Sagawa ○ --- ◎continuum QRPAMatsuo ◎ ◎ ---Orsay ◎ ◎ ---Yamagami ○ ◎ --- Box
Milano ○ ◎ --- Box
Hagino-Sagawa ○ ○ Box, BCS
Oak Ridge ○ ◎ --- canonical basis
relativistic QRPAMunchen ○ ◎ --- canonical basis
Ma △ --- --- H.O. basis
TDHF plus ABCNakatsukasa-Yabana ◎ --- ◎mixed representation RPAImagawa-Inakura ○ --- ◎ Box
○
AB matrix Yoshida ○ ◎ ◎ Box
多くのグループ、様々なアプローチ
International Conference on Finite Fermionic Systems – Nilsson Model 50 Years
原子核の変形を取り扱った最初の微視的モデル
日 程 : 6月14日~18日
場 所 : ルンド大学 (スウェーデン)
参加者 : スウェーデン(31)、米国(11)、日本(10)、
ポーランド(9)、英国(8)、イタリア(7)、
ドイツ(7)、デンマーク(7)など 計23カ国118人
International Conference on Finite Fermionic Systems
•Shell structure and deformations (6人)•The heaviest elements and beyond (6人)•Nuclei at high spins (7人)•Nuclei with large deformation (3人)•Nuclei far from stability (8人)•Pairing correlations (4人)•Order and chaos (6人)•Quantum dots (2人)•Cold fermionic atoms (2人)
Topics
Invited talk (30+10) : 14人
Contributed talk (15+5) : 29人+1人
Poster: 33人
「表面」
「形」変形、回転、振動
?
変形するメカニズム
一粒子運動と集団運動
規則的
普遍性と多様性
Nuclei
Quantum dots
Fermionic atoms
有限の量子多体系
自己束縛系
存在領域
どこまで重い原子核が存在?
中性子と陽子のアンバランスさの限界は?
カオス的
Mean field
Shape Shell structure
量子多体系
Periodic Orbit Theory
Level density
Periodic orbitoscillation
Gutzwiller’s trace formula
Gross shell structure given by the shortest orbits.
Tarucha et al., PRL, 1996, Oosterkamp et al., PRL, 2001Coulomb blockade spectra
in a magnetic field
T.H. Oosterkamp et al, PRL 82, 2931 (1999)
Trapped fermions in quasi – 2D
Shell structure
S.M. Reimann, M. Manninen, M. Koskinen and B. Mottelson, PRL 83, 3270 (1999)
自己束縛した多体系 “存在領域”がある
極限状態にある原子核
自らがその環境を作る 高アイソスピン
高スピン
超変形
高励起状態・・・
超重核
8人(日本人4人)7人(日本人1人)3人
6人(日本人1人)
不安定原子核の物理に対する日本人の寄与
非常に大きい理論・実験共に
2人
原子核の面白さ
http://www.rarf.riken.go.jp/RIBF/
http://www.rarf.riken.go.jp/RIBF/
278113
274111
270Mt
266Bh
CN11.68 MeV (PSD)344 μs30.49 mm
11.15 MeV6.15+5.00 (PSD+SSD)9.26 ms30.40 mm
10.03 MeV 1.14+8.89(PSD+SSD)7.16 ms29.79 mm
9.08 MeV (PSD)2.47 s30.91 mm
36.75 MeVTOF 44.61 ns30.33 mm
23-July-2004 18:55 (JST)E (70Zn) = 349.0 MeV
209Bi + 70Zn → 278113 + n
α
α
α
α
Strip #12
262Db
204.1 MeV(PSD)40.9 s30.25 mm
σ = 55 fb +154-47
Taken from K.Morita
100 102 104 106 108 110 112 114Atomic Number
1μb
1nb
10nb
100nb
100pb
10pb
1pb
0.1pb
208Pb,209Bi(HI,1n) reaction
RIKEN
preliminary209Bi + 70Zn → 278113 + n
278113
274111
270Mt
266Bh
CN11.52 MeV (PSD)4.93 ms30.16 mm
0.88+10.43=11.31 MeV(PSD+SSD)34.3 ms29.61 mm
2.32 MeV (escape)1.63 s29.45 mm
9.77 MeV (PSD)1.31 s29.65 mm
36.47 MeVTOF 45.69 ns30.08 mm
2-April-2005 2:18 (JST)
α
α
α
α
262Db
192.32 MeV(PSD)0.787 s30.47 mm
2nd chain
s.f.Taken from K.Morita
Kenichi Yoshida (Kyoto Univ.)In collaboration with
Masayuki Yamagami (RIKEN)
Kenichi Matsuyanagi (Kyoto Univ.)
Dynamic Pairing Effects on LowDynamic Pairing Effects on Low--Frequency Frequency Modes of Excitation in Deformed Mg Isotopes Modes of Excitation in Deformed Mg Isotopes
close to the Neutron Drip Lineclose to the Neutron Drip Line
International Conference on Finite Fermionic Systems -Nilsson Model 50 Years
Low-lying modes unique to neutron-rich nuclei
dens
ity
core skin
r
Quadrupole vibration of neutron skin
Effect of Deformation ? Pairing ?
Soft K=0+ mode ?In deformed superfluid system close to the drip line
Continuum ?
Deformation
Pairing
Continuum
QRPA calculation simultaneously taking into account
Deformed HFB
Box discretization
z
ρ
0
Directly solving HFB eq. in coordinate-space mesh-representation
First results of such a calculation
Investigation of deformed neutron-rich nuclei
Ground state
Coordinate-space HFB equation
Mean-field Deformed Woods-Saxon potential
Pair-field pair 00
( )( , ') (1 ) ( ')v V ρ δρ
= − −rr r r r
Residual interaction
pp 00
( )( , ') (1 ) ( ')v V ρ δρ
= − −rr r r r
p-h channel
p-p channel
3ph 0 3( , ') [ (1 ) (1 ) ( )] ( ')
6otv t x P x Pσ σ ρ δ= + + + −r r r r r
QRPA equation in the AB matrix formulation
30 450 MeV fmV = −
cutoff 50MeVE =Excited state
Isoscalar quadrupole transition strengths
Enhancement of neutron excitation
Neutron number increasing1.79
2.93
0.9391.12
1.34
0
0.5
1
1.5
2
2.5
3
3.5
24 26 28
0+
2+
Neutron number
Low-frequency quadrupole vibrations in deformed Mg isotopes close to the drip line
2K π +=
| | /n
p
M NM Z
HFB, SIII
0K π +=
(intrinsic)
J.Terasaki et al.deformed
0306090
120150180 isoscalar 40
MgKπ=0+
0
10
20
30
40
50
0 1 2 3 4 5
Str
engt
h (f
m4 )
�ω (MeV)
unperturbed
6.78 2.92.33
n
p
M NM Z
= =
41 W.u.=8.13 fm
Soft K=0+ mode in deformed 40Mg
2020| |0Q M αβ
αβ
λ< >=∑
Pair correlationPair correlation
Weakly bound systemWeakly bound system
How to generate the coherent mode?
Why are the transition strengths large ?
Collective both in p-h and in p-p channel
~ 10-20 W.u. (intrinsic)
Two key points
Effect of dynamical pairing
Spatial structure of quasiparticle wave functions
Mechanism for generation of soft K=0+ mode
0
30
60
90
120
150 40Mg Kπ=0+
no dynamical pairing
0
30
60
90
120
150
180
0 1 2 3 4 5
Str
engt
h (f
m4 )
�ω (MeV)
Kπ=2+
0
30
60
90
120
150 40Mg Kπ=0+
0
30
60
90
120
150
180
0 1 2 3 4 5
Str
engt
h (f
m4 )
�ω (MeV)
Kπ=2+
Superposition of p-h, p-p and h-h vibrations
Generation of the coherence
Dynamical pairing
(c) [310]1/2 → [301]1/2(b) [312]3/2 → [312]3/2
02468
101214
z (f
m)
(a) [310]1/2 → [310]1/2
0 2 4 6 8 10ρ (fm)
(f) [321]3/2 → [321]3/2
0 2 4 6 8 10ρ (fm)
(e) [303]7/2 → [303]7/2
02468
101214
0 2 4 6 8 10
z (f
m)
ρ (fm)
(d) [301]1/2 → [301]1/2
2020| | ( , )Q d dzQ zαβα β ρ ρ< >≡ ∫2
2020 ( , ) ( , )Q d r Yσ
ψ σ ψ σ+=∑∫ r r r
20 ( , )Q zαβ ρ
Spatial structure of 2qp excitations (p-h channel)
Summary
We have investigated properties of excitation modes in deformed Mg isotopes close to the neutron drip line.
Deformed QRPA calculation based on coordinate-space HFB including the continuum
We have obtained soft K=0+ and 2+ modes in 36-40Mg.
K=0+ mode is particularly sensitive to the dynamical pairing.
Spatial extension of two-quasiparticle wave functions
Coupling between quadrupole vib. and pairing vib.
Large transition strengths
Generating coherent mode
Good indicator of pair correlation in deformed drip-line nuclei
Similar spatial structure of quasiparticle w.f. near the Fermi level
聴衆の反応
質問1.Woods-Saxonポテンシャルのパラメータは?
質問2.Spurious modeとのdecouplingは?
質問3.カットオフは?
質問4.得られた状態の幅は?
発表が終わった後にも、質問・コメントをもらった。
良く理解してくれた様子で、“まともな”質問
良い宣伝・情報収集ができた