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

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