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奇質量核での2フォノン・ガンマ振動バンド. Thanks to 松柳さん、清水さん. if really collective, multiple excitations (possibly with anharmonicity). Bohr and Mottelson, “Nuclear Structure II”. 2 phonon states in even-even nuclei. ・ Exp. observ. 168Er Davidson et al. (\'80). 2 phonon states in even-even nuclei.

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slide2

if really collective,

multiple excitations

(possibly

with anharmonicity)

Bohr and Mottelson, “Nuclear Structure II”

slide3

2 phonon states in even-even nuclei

・Exp. observ.

168Er Davidson et al. (\'80)

slide4

2 phonon states in even-even nuclei

・Exp. observ.

168Er Davidson et al. (\'80)

・Theories

IBM Warner et al. (‘80) --- s,dボソン harmonic vib. のみ

slide5

2 phonon states in even-even nuclei

・Exp. observ.

168Er Davidson et al. (\'80)

・Theories

IBM Warner et al. (\'80)

general framework Bohr and Mottelson (\'82)

slide6

2 phonon states in even-even nuclei

・Exp. observ.

168Er Davidson et al. (\'80)

・Theories

IBM Warner et al. (\'80)

general framework Bohr and Mottelson (\'82)

macro and micro Dumitrescu and Hamamoto (‘82) --- γ変形

slide7

2 phonon states in even-even nuclei

・Exp. observ.

168Er Davidson et al. (\'80)

・Theories

IBM Warner et al. (\'80)

general framework Bohr and Mottelson (\'82)

macro and micro Dumitrescu and Hamamoto (\'82)

QPM Soloviev and Shirikova (‘81) --- “2 phonon ない”

slide8

2 phonon states in even-even nuclei

・Exp. observ.

168Er Davidson et al. (\'80)

・Theories

IBM Warner et al. (\'80)

general framework Bohr and Mottelson (\'82)

macro and micro Dumitrescu and Hamamoto (\'82)

QPM Soloviev and Shirikova (\'81)

SCCM Matsuo and Matsuyanagi (\'85)

MPM Piepenbring and Jammari (\'88)

実験を再現

slide9

2 phonon states in even-even nuclei

・Exp. observ.

168Er Davidson et al. (\'80)

・Theories

IBM Warner et al. (‘80), Yoshinaga et al. (’86) --- s,d,gボソン

general framework Bohr and Mottelson (\'82)

macro and micro Dumitrescu and Hamamoto (\'82)

QPM Soloviev and Shirikova (\'81)

SCCM Matsuo and Matsuyanagi (\'85)

MPM Piepenbring and Jammari (\'88)

slide10

2 phonon states in even-even nuclei

・Exp. observ.

168Er Davidson et al. (\'80)

・Theories

IBM Warner et al. (\'80), Yoshinaga et al. (\'86)

general framework Bohr and Mottelson (\'82)

macro and micro Dumitrescu and Hamamoto (\'82)

QPM Soloviev and Shirikova (\'81)

SCCM Matsuo and Matsuyanagi (\'85)

MPM Piepenbring and Jammari (\'88)

・Exp. --- some are as predicted

166Er, 164Dy, 232Th, 106,104Mo, ...

TPSM Sun et al. (\'00)

also K=0

slide12

G. Gervais et al., NPA624, 257 (\'97)

slide13

2 phonon states in odd-A nuclei

・Theo.

MPM Durand and Piepenbring (\'96)

・Exp. observ. fission fragments of 252Cf

105Mo Ding et al. (\'06)

103Nb Wang et al. (\'09)

107Tc Long et al. (\'09)

10 years

slide14

2 phonon states in odd-A nuclei

--- interplay between single-particle and collective modes

・Theo.

MPM Durand and Piepenbring (\'96)

・Exp. observ. fission fragments of 252Cf

105Mo Ding et al. (\'06)

103Nb Wang et al. (\'09)

107Tc Long et al. (\'09)

・Theo.

TPSM Sheikh et al. (\'10)

slide15

ground(1qp)

??

slide16

Mean field

Residual interaction

RPA

particle-vibration coupling

slide20

Mean field

Residual interaction

RPA

particle-vibration coupling

slide21

Eigenstates

1qp (0γ)

slide22

Eigenstates

--- signature dependence

M.M., Shimizu, Matsuyanagi, PTP 77 (\'87)

1qp (0γ)

--- intensity relation

Gervais et al. (\'97)

slide23

parameters

from literatures

and

to fit signature splitting in 1qp,

to fit γ bandhead in 104Mo

slide24

probabilities of

in the wave function

at each

vs

routhian

two 1γ and three 2γ

are collective !!

slide25

K scheme vs signature scheme

States with lower Khave lower intrinsic energies than those with higher K and the same I.

slide27

probabilities of

in the wave function

at each

vs

routhian

two 1γ and three 2γ

are collective !!

slide28

K=Ω+4

K=Ω

K=|Ω-4|

K=Ω+2

K=Ω+4

K=Ω+2

curves are

exp. data

converted to

the rot. frame

K=|Ω-2|

slide30

Summary (1)

・ 2γ bands in odd-A 103Nb are calculated by means of the particle-vibtration coupling

model in the signature scheme

・ K=Ω+4 state is the most collective at zero rotation, but small rotation immediately delivers

its collectivity to other two sequences (K=Ω, |Ω-4|)

・ Three 2γ bands keep collectivity up to high spins

・ Excitation energies of 2γ bands are higher than observed  3γ basis states are necessary

slide32

TSD1: 0 phonon

TSD2: 1 phonon

TSD3: 2 phonon

TSD4: another conf.

slide33

2 phonon

1 phonon

slide35

163

Lu

Not ∝ω

Automatically

!

rot

ω

-dependent

rot

MM, Y.R.Shimizu and K.Matsuyanagi, PRC 65, 041303(R) (2002)

slide40

163

162

Lu (1QP)

Yb (0QP)

角運動量ベクトルの向きの関数としてのエネルギー

z

y

x

Shallow

Tilted !

M. M. and S. –I. Ohtsubo, PR C69, 064317 (‘04)

slide41

2 phonon

1 phonon

slide43

146

Gd

相転移後

shallow

θ

slide44

相転移後

stiff

M. Matsuo and K. Matsuyanagi, PTP 74, 1227 (‘85)

summary 2
Summary (2)
  • Instability of wobbling leads to tilted axis rotation --- “Phase transition”
  • Correspondence between RPA and TAC is good
  • Anharmonicity in 2 phonon wobbling suggests softening of potential surface
slide46

のみ

Dumitrescu and Hamamoto, NPA383, 205 (‘82)

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