Study of shell structure and order-to-chaos transition in warm rotating nuclei with the

radioactive beams of SPES

G.Benzoni, S.Leoni, A.Bracco, N.Blasi, F.Camera, F.C.L.Crespi, B.Million,O. Wieland, P.F. Bortignon, G. Colò, E. Vigezzi

Università degli Studi and INFN sez. Milano  

D. Bazzacco, S. Lenzi, S.Lunardi, D.Montanari, C.Ur, et al. INFN Padova and Università degli Studi di Padova

  G. DeAngelis, D. Napoli, J.J. Valiente-Dobon, et al.

Laboratori Nazionali di Legnaro INFN  

A. Maj, P. Bednarczyk, B. Fornal, M. Kmiecik, M. Ciemala et al., The Niewodniczanski Institute of Nuclear Physics, Polish Academy of

Sciences, Krakow, Poland

Warm rotating nuclei

Collective rotations: de-excitation spectra

Analysis of quasi-continuum γ-γ coincidence spectra with statistical and spectral shape analysis methods

168Yb

Eγ1

Eγ2

600 1200

1200

600

42/ℑ

42/ℑ 2

1

2

evepath P

1µµN N ×−

=

Fluctuation Analysis Method

onset of damping nb = 2

E2

8

E* (

MeV

)

I (h) 0

microscopic discrete levels

2

extrapolated ρ and Γrot

Γro

t

yrast I+2 I I-2

Γro

t

20 60

np

Bn 15

E1

Band-mixing Calculations => decay flow simulation

rot

2

2)(

ℑ−+−≈ zSDI

residualxdefJVJHIH ω

1

f

2if b S n

−

⎥⎦

⎤⎢⎣

⎡= ∑

168Yb

ε = 0.25 I = 20-61 400 levels U ≤ 2.5 MeV

A. Bracco et al. PRL76(1996) 4484

Realistic Simulation of γ-decay flow: E1/E2 competition

Evidence for rotational damping Ö  Sensitivity to the residual interaction Ö  Collectivity with thermal energy Ö  Mass dependence Ö  Configuration dependence Ö  Measurement of Compound and Rotational Damping Width Ö  Superdeformation at finite temperature

A. Bracco and S. Leoni, Rep. Prog. Phys. 65(2002)299

Main Results from the Analysis of Quasi-Continuum Rotational Spectra

i) how large the damping width Γrot is and how it changes with excitation energy and spin; ii) at which energy rotational damping sets in and how gradual is the process; iii) whether or not this process depends on the intrinsic nuclear configuration, therefore leading to different effects in connection with different quantum numbers of the shell-model states, such as the K-quantum number; iv) how high in excitation energy one has to go before a fully chaotic regime is reached.

I+2I

I-2

I+2I

I-2

Band Mixing Calculations H = Hdef

- ω Jx + Vres

Nilsson Cranking SDI inter.

600 800 1000 1200 1400Eγ (keV)

101102103104105106107

SDI

No Int

0

40

80

120

160

No Int

SDI

0

40

80

120

160

N(2

) path

Ridge

600 800 1000 1200 1400Eγ (keV)

101102103104105106107

N(2) path

Valley

0

40

80

120

160

N(2

) path

Ridge

600 800 1000 1200 1400Eγ (keV)

101102103104105106107

N(2) path

Valley

0

40

80

120

160

N(2

) path

Ridge

600 800 1000 1200 1400Eγ (keV)

101102103104105106107

N(2) path

Valley

600 800 1000 1200 1400Eγ (keV)

101102103104105106107

SDI

No Int

0

40

80

120

160

No Int

SDI

regular bands

strongly interacting bands

U0 = 1 MeV Γrot = 200 keV

B. Herskind et al., PRL68(1992)3008

Evidence for Rotational Damping Importance of Residual Interaction

600 800 1000 1200 1400Eγ (keV)

101

2345

102

2345

103N

(2) pa

th168Yb - Ridge

L ≤ 2

L ≤ 3

L ≤ 4

L ≤ 5

L ≥ 5

P+QQ

full

SDIM-COL Nov. 29, 2001 2:42:51 AM

SDI

Rotational Damping originates from

high-multiple terms of two-body residual interaction

Type of Interaction

1 2 3 4 5 6Steps

10

30

50

N(2) path

13.8/A27.5/A55/A

STEP_COL Nov. 29, 2001 2:48:21 AM

Fig. 28

STEP_COL Nov. 29, 2001 2:48:21 AM

√ <|V|2>SDI= 20 keV

√ <|V|2>EXP= 14 keV

Interaction Strength

from discrete spectroscopy

S. Leoni et al., Eur. Phys. J. A4, 229 (1999) M. Matsuo et al., NPA617,1 (1997)

Sensitivity to Residual Interaction Type of Interaction and Interaction Strength

EγForward

EγBa

ckwa

rd γ-γ spectrum

860 880 900 920Eγ (keV)

COUNTS

1000 1500Eγ (keV)

-100 0 100(Eγ1-Eγ2) keV

<Eγ>=800 keV

860 880 900 920Eγ (keV)

COUNTS

1000 1500Eγ (keV)

-100 0 100(Eγ1-Eγ2) keV

<Eγ>=800 keV

Forward

Backward

500 700 900 1100 1300 1500Eγ (keV)

0.0

0.2

0.4

0.6

0.8

1.0

F(τ)

E2 BUMPVALLEY (Covariance)RIDGEDISCRETEQt=5.5 eb

164Yb

Qt=7.6 eb

Qt=6.6 eb

Same Collectivity Qt=5.5 eb B(E2) = 200 W.u.

yrast discrete exc. bands mixed exc. bands

S. Frattini et al., PRL81(1998)2659

Collectivity with Thermal Energy Fractional Doppler Shift Analysis

Low K

High K

Smaller number of High-K states in the

damping regime

10

Chaotic regime: U ≥ 2.5 MeV

G. Benzoni et al.,PLB615 160-166 (2005)

Configuration Dependence & Onset of Chaos Persistence of selection Rules with Temperature:

Need for confirmation in other systems: egs. Hf nuclei 136Te+48Ca è 180Hf +4n

Warm rotation in exotic systems

Stable:48Ca(@ 215MeV)+124Sn→168Yb(63)+4n SPES: 132Sn(@ 560MeV)+48Ca→ 176Yb(76)+4n

Spin and temperature dependince of Γrot

Stable:48Ca(@ 215MeV)+124Sn→168Yb(63)+4n SPES: 132Sn(@ 560MeV)+48Ca→ 176Yb(76)+4n

0 1 2 3 4 5 60

100

200

300

5060

70

40I=30

168Yb

Γro

t [ke

V]

U [MeV]

0 10 20 30 40 50 60 700

2

4

6

8

<U>

[MeV

]

Spin [h]

γ-flow E1/E2

132Sn+48Ca 48Ca+124Sn

Γro

t I+2 I

I-2

S. Leoni et al., PRL93(2004)022501 F. Stephens et al., PRL88(2002)142501 M. Matsuo et al., PLB465(1999)1

20 30 40 50 60 700

50

100

150

200

250

300

350

400

<U> = 2 MeV

<U> = 1.4 MeV

U < 1 MeV

2Γµ

Γrot

discrete

Wid

th [k

eV]

Spin [h]

163Er – EUROBALL Data

2Γµ

Γrot

Γµ

|α>

I

I-2

Δω0

I-2

E2 strength

fine structure of rotational damping

Rotational Damping: I and T dependence Γrot and Γµ from γ-γ spectra

-200 -100 0 100 2000

50

100

150I = 40, 41 h levels 11-100

Γwide

Γnar

Coun

ts [a

.u.]

(Eγ1-E

γ2) [keV]

µΓ≈Γ 2narrow

rotwide 2Γ≈Γ

Γro

t

Shell effects dependence

Δω0 = √(Δω0N)2 + (Δω0

P)2 for U ≤ 2 MeV Γrot = 2(2Δω0)

168Yb I=40h,U=2MeV

98

neutron

106

no highly aligned orbits

highly aligned orbits

Γrot depends on 2 contributions: P and N . Accessing nuclei on an isotopic chain wll help define the 2 contributions

1000 1500Eγ (keV)

101

102

103

104

105

N(2) path

164Yb114Tetheory

VALLEY ANALYSIS

0

10

20

30

40N

(2) pa

th164Yb114Tetheory

RIDGE ANALYSIS

114Te

168Yb Γrot α I A-5/2 ε -1 U0 α A-2/3

So far MASS dependence has been addressed

comparative study

A=110 A=160 114Te ε ≈0.25

164Yb ε ≈0.25

Rotational Damping: I and T dependence

Proposed reactions

Experimental array

Need for a 4π γ array: Ge Ball (AGATA/GALILEO) + LaBr3 scintillators

Conclusions