Quasi-continuum studies in superdeformed 151Tb and 196Pb

nucleiG. Benzoni

Outline:•SD decay out at T=0 and T≠0•The experiments•Analysis•Results•Perspectives

INFN sezione di Milano e Universita’ degli Studi di Milano

phase transition normal superfluid system

600 800 1000 1200 1400 1600

10

25

50

75100

250

yrast SD

Decay-out

Feeding

Plateau

Inte

nsi

ty %

E [keV]

SD bands are found in many nucleiA = 30,60,80,130,150,160,190

Typical intensity pattern: loss of intensity at low energies

quantum tunneling btw SD and ND minima

SDND

E*

NORMAL minimum

SUPER deformed minimum

FEEDING of SD bands

DECAY-OUT of SD bands:Coupling betweenordered and chaotic states

Rigid body

Super

def

orm

ed b

and

superfluid

100 200 300 400 500 600 700 800

0

2

4

6E

E [ keV ]

Con

teggi (

Arb

. U

nits

*103 )

Cou

nts

* 1

03

196Pb SD band

A.N. Wilson et al., Phys. Rev. Lett. 95 (2005)

Evidences of discrete linking transitions in few nuclei

•High-energy transitions • Low intensity

~ 10-4% channel• Highly fragmented decay

high level density

SD

ND

36984062

196Pb

Need for AGATA-like arrays

What can we do already now ???study of average properties of SD discrete

excited bands analysis of quasi-continuum spectra

= fn(, )

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

Rotational motion at finite temperature (T≠0)

0 < U < 1-2 MeV

= fn(, )

168Yb

R

IDG

E

V

ALLE

Y

Do SD ridges have same properties as discrete SD yrast band ???

-150 -100 -50 0 50 100 1500

1000

2000

3000

4000

5000

(E1 –E2) (keV)

Counts

282

E

2:1I+2I

I-2

Regular bands

2:1T0

Ridges: unresolved discrete regular

bands

HECTOR

Euroball, Strasburgo (Fr)

Two different nuclei in comparison 151Tb and 196Pb

BGO INNER BALL

Thin target, Ebeam = 155 MeV

27Al + 130Te 157Tb*

30Si + 170Er 200Pb*

Thin target, Ebeam = 150 MeV

- Moment of inertia ridge ≈ yrast

- Intensity of SD ridge- FWHM of SD ridge Comparison with

cranked shell model calculations + decay

out

Ridges analysis:

- Number of paths (discrete bands)

Up to now full analysis performed only in 143Eu

proved the need to include tunneling effects

750 1000 1250 1500 1750

E(keV)

0

20

40

60

80

N(2

) path

NPRID_CO May 25, 2001 12:37:10 PM

No Decay-Out

Decay-Out

S. Leoni at al. PLB 498(2001)137

196Pb

Need other cases in different/similar mass regions

151Tb152Dy

SpinN

(2) pa

thSpin

N(2

) path

192Hg

To be also compared to 192Hg and 152Dy for

which theory is available

FWHMridge ≈ 4×FWHMyrast

Intensityridge ≈ 3x Intensityyrast

Ridge consists of many discrete bands

0

2

4

6

8

10

12

14

16

0 500 1000 1500 2000

E [keV]

<FWHM> = 11.7 keV

FW

HM

[k

eV

]

SD

ND

Ridge

Discrete trans

151Tb

1600

1200

800

400

0

0-50 50-100

<E> = 532 keV

(E1 –E2) (keV)100-150 -100 -50 0 50 100 150

0

1000

2000

3000

4000

5000

C

ounts

(E1 –E2) (keV)

<E> = 1280 keV

151Tb

196Pb

100 200 300 400 500 600 700 800

0

2

4

6E

E [ keV ]

Conte

ggi (A

rb.

Units *

10

3 )

800 1000 1200 1400 16000,0

2,0x106

4,0x106

6,0x106

8,0x106

0.8-1.6 MeV

0.2-0.8 MeV

Ridges in coincidence with SD yrast band

600 800 1000 1200 1400 1600

10

100

yrast SD TOTALE in coincidenza yrast SD

E [keV]

Inte

nsi

ty % 150

300

151Tb

200 400 600 8000

102030405060708090

100

N(2

)

path

E [keV]

in coincidence with SD yrast total

900 1000 1100 1200 1300 1400 15000

20

40

60 total coincidence with SD yrast

N(2

) path

E [keV]

• Mean Npath = 25 151Tb

45 196Pb tot matrix

15 and 25 in direct coincidence

Fluctuation analysis

PN

N evepath

11

2

)2(

Npath number of

discrete unresolved bands forming the ridge

I+2I

I-2T0

I

E

151Tb

Npath decreasing at low energies

200 400 600 8000

100

200

300

~ 28

N(2

)

path

E [keV]

in coincidence with SD yrast total

~ 57

Theory

800 900 1000 1100 1200 1300 1400 15000

20

40

60

80

100

120 total coincidence with SD yrast

Theory

N(2

) path

E [keV]

Theory overestimates Npath

path 0

E)(V(q(s))M2dsS(E)

152Dy

Statistical model of decay-out

Vigezzi et al., PLB 249(1990)163.Gu and Weidenmuller, NPA660(1999)197Yoshida, Matsuo and Shimizu NPA 696 (2001) 85-122 .

ND SD

1S2SDt )e(1

π2

DΓ

Spacing of SD statesACTION

ND

SD

ND

tout Γ

Γ

D

Γ

π2

1P EM decay width

Spacing of ND states

Calculated along the tunneling path

Transmission coeff.

Probability to “fly out” from SD minimum

ND

SD

Pou

t

Eexc

0

20

40

60

80

100

120

600 800 1000 1200 1400 1600 1800

no decay-out

decay-out143Eu

151Tb

Cranked shell model T ≠ 0

Np

ath

E [keV]

Results for 196Pb

Need to use renormalization factors

Theory Iout =12 Exp. Iout = 6 (Eexc = 0 MeV )

Results for 151Tb

comparison with theory including tunneling not yet

readyRescaled curve of 143Eu

already gives good agreement

ND C ND

S Cmass S

— C = 2e-4— Cmass = 3

200 400 600 800 1000

0

50

100

150

200

250

196Pb

no decay out exp data192Hg no decay out c=1 c

m=1

c=1 cm=3

c=2e-4 cm=1

192Hg

N(2

)

path

E [keV]

No decay-out

decay-out

(pairing)

Conclusions

• Investigation of SD excited bands in 151Tb and 196Pb

• SD ridge structures found in both nuclei

• Npath ~ 25 151Tb

~ 45 196Pb in tot matrix

• Comparison with cranked shell model calculations including tunneling

Good agreement for 196Pb…still to finalise for 151Tb

• additional info on pairing (Cmass) and level density (C)

•MONTECARLO simulation to study decay flux in coincidence with SD yrast•Comparison with existing analysis on 192Hg

(T.L.Khoo and A.Lopez-Martens)

Perspectives

Acknowledgments…

G.Benzoni, S.Leoni, A.DeConto, D.Montanari, A.Bracco, N.Blasi, F.Camera, B.Million, O.Wieland

Dipartimento di Fisica, Universita’ degli Studi di Milano and INFN sezione di Milano, Via Celoria 16, 20133 Milano, Italy

A. Maj, M.KmiecikNiewodniczanski Institute of Nuclear Physics, 31-342 Krakow, Poland

B.HerskindThe Niels Bohr Institute, Blegdamsvej 15-17, 2100, Copenhagen

G.Duchene, J.Robin, Th.Bysrki, F.A.Beck,Institut de Recherches Subatomiques, 23 rue du Loess,F-67037, Strasbourg, France

P.J.TwinOliver Lodge Laboratory, University of Liverpool, P.O. Box 147, Liverpool L69 7ZE, UK

A.Odahara, K.LagergrenKTH,Royal Institute of Technology,Physics Department, Frescativägen 24,S-104 05,

Stockholm, Sweden

M.Matsuo, Y.R.Shimizu and E.Vigezzi for CSM calculations (Niigata University) (INFN Milano)

Participants to the experiments

100 200 300 400 500 600 700 800

10

100

SD ridge

yrast SD in coincidence with SD total

~300 %

Inte

nsity

%

E [keV]

~150 %yrast SD

Intensity of SD ridge vs. intensity of yrast SD

600 800 1000 1200 1400 1600

10

100

yrast SD TOTALE in coincidenza yrast SD

E [keV]

Inte

nsi

ty % 150

300151Tb

196Pb

0 300 600 900

2

6

10

8.5 keV

Ridge

SD

ND

FW

HM

[ke

V]

Discrete trans

196Pb

0 10 20 30 40 500

1

2

3

4

5

6

7

8

9

10

S

Spin [hbar]

EExc

=0-4.0 MeV

Action for 151Tb (conf a)

0 10 20 30 40 500

1

2

3

4

5

6

7

8

9

10

S

Spin [hbar]

EExc

=0-4.0 MeV

Action for 196Pb (conf a)

Actions decreasing at increasing spin decreasing at increasing Eexc

0 10 20 30 40 50 600.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Nou

t

Spin [hbar]

EExc

=0-3.0 MeV

Pout

Different behaviour for 151Tb and 196Pb

Decay-out properties (Iout, Eout) expected to

be different

Easier to “fly out”