Harissopulos GAMMA2004 finalnpgroup.pd.infn.it/GASP/gamma2004/documents/SHarissopulos.pdf · S. Harissopulos, Nu*STAR Group, Institute of Nuclear Physics, NCSR “Demokritos”, Athens

From the first E(5) to the last Z(5) dynamical symmetryFrom the first E(5) to the last Z(5) dynamical symmetryA research program for GASP/CLARA ?A research program for GASP/CLARA ?

S. HarissopulosS. HarissopulosInstitute of Nuclear Physics, NCSR “Demokritos”, Athens, Greece Institute of Nuclear Physics, NCSR “Demokritos”, Athens, Greece

Inst. für Inst. für Experimentalphysik Experimentalphysik III, RuhrIII, Ruhr--UniUni--BochumBochum, , BochumBochum, Germany, Germany

INP/NCSR “Demokritos”, Athens Nu*STAR Group

Workshop on “Future of Gamma Spectroscopy at LNL: GASP and CLARA Arrays - GAMMA2004” Legnaro - Padova, Italy, March 3 - 5, 2004

S. Harissopulos, Nu*STAR Group, Institute of Nuclear Physics, NCSR “Demokritos”, Athens

Workshop on “Future of Gamma Spectroscopy at LNL: GASP and CLARA Arrays - GAMMA2004” , Legnaro - Padova, Italy, March 3 - 5, 2004

Basis : : The Bohr Hamiltonian

5 dim. space : 3 Euler angles θθi (i=1,2,3) + 2 intrinsic (collective) variables ββ and γγ

γγ = ?

V(ββ,γγ) = u(ββ) or V(ββ,γγ) = u(ββ) + u(γγ)

u(ββ) = ? u(γγ) = ?

Dynamical symmetry : a theoretical tool to describe a shape phase transition

F. F. IachelloIachello: PRL 85, 3580 : PRL 85, 3580 (2000)(2000) PRL 87, 052502 PRL 87, 052502 (2001)(2001) PRL 91, 132502 PRL 91, 132502 (2003)(2003)



V(ββ,γγ) = U(ββ)

γ ≈ 0

E(5)

u(ββ)= (2B/hh2)U(ββ)

ε = (2B/hh2) E

u(ββ)

γ ≈≈ 0

X(5)

u= (2B/hh2)V(ββ, γγ)

ε = (2B/hh2) E

u(ββ, γγ) =u(ββ)+υυ(γγ)

υυ(γγ)u(ββ)

γ : sinγ ≈ γ

Y(5)


ε = (2B/hh2) E


υυ(γγ)u(ββ)

Excitation energies and E2-strengthsParameter-free predictions (except for scale) for



E(5) X(5)



γ : sinγ ≈ γ

Y(5)


ε = (2B/hh2) E

F. Iachello, Phys. Rev. Lett. 91(2003)132502


υυ(γγ)u(ββ)



R. M. Clark et al., Phys. Rev. C 68, 037301 (2003) : X(5) candidates

X(5) : R4=2.91

35 candidates ?



R. M. Clark et al., Phys. Rev. C 68, 037301 (2003)

vibrator

rotor

X(5)



R. M. Clark et al., Phys. Rev. C 68, 037301 (2003)

vibrator

rotor

X(5)

N=90 N=90 N=90 N=90 N=90



Empirical proofsEmpirical proofs

E(5) cases134Ba : R.F. Casten, and N.V. Zamfir, Phys. Rev. Lett. 85, 3584 (2000).

104Ru : A. Frank et al., Phys. Rev. C 65, 014301 (2001).

102Pd : N.V. Zamfir et al., Phys. Rev. C 65, 044325 (2002).

108Pd : Da-li Zhang, and Yu-xin Liu, Phys. Rev. C 65, 057301 (2002).

• • •• • •• • •• • •

••••

Spec

trum

ô in

gsb

(J<

6h)

ô in

gsb

(J>

6h)

ôin

sid

e ba

nds

Y(5) cases

NONE ! only suggestions



1.6

1.8

2.0

2.2

2.4

2.6

2.8

2.0

2.5

3.0

3.5

4.0

4.5

5.0

96 100 104 108 112 116

3

4

5

6

7

96 100 104 108 112 116

4

5

6

7

8

9

10

E(5)

U(5)

E(5)

O(6)

R4 :=

E(4

1) / E

(21)

O(6)

U(5)

R6 :=

E(6

1) / E

(21)

U(5)

E(5)

O(6)

R8 :=

E(8

1) / E

(21)

Mass Number A

U(5)

E(5)

O(6)

R10

:= E

(10 1)

/ E(2

1)

Mass Number A

E(5) symmetry and Pd isotopes

102



4 6 8 10

2

4

6

8

10102Pd

U(5)

E(5)

O(6)

R:=

E(I

) / E

(21)

Spin I ( h )

102Pd : an E(5) symmetry paradigm



A Plunger & DSAM experiment with GASP-I





102Pd : plunger lifetimesSome preliminary results

G. KALYVA et al.



102Pd : an E(5) symmetry paradigmG. Kalyva et al., 2/2004: preliminary



V(ββ,γγ) = U(ββ)

γ ≈≈ 0

E(5)- ββ2n

u(ββ)= (2B/hh2)U(ββ)

ε = (2B/hh2) E

new

u(ββ) = ββ2n/2

n=1,2,3,4,…

γ ≈≈ 0


ε = (2B/hh2) E


υυ(γγ)

X(5)- ββ2n

new

u(ββ) = ββ2n/2

n=1,2,3,4,…≈≈E(5)

X(5)- β2

≈≈X(5)

U(5)

D. Bonatsos et al., arXiv:nucl-th/0312120 v1 29Dec2003

arXiv:nucl-th/0311092 v1 26Nov2003



Z(5) , the last (?) one !for nuclei undergoing a shape phase transition from for nuclei undergoing a shape phase transition from prolateprolate to oblate shapeto oblate shape

u(ββ)

γγ=30O, u= (2B/hh2)V(ββ, γγ) , u(ββ, γγ) =u(ββ)+υυ(γγ)

υυ(γγ)

u(ββ)= { 0 (ββ ≤≤ ββ W) ∞∞ (ββ >ββ W) υυ(γγ)=(1/2)c(γγ-ππ/6)2=(1/2)cγγ2∼∼

D. Bonatsos, priv. comm. and arXiv:nucl-th/0402087

it provides parameterit provides parameter--free predictions (up to overall scale factors)free predictions (up to overall scale factors)

triaxialvibrator

⇓⇓triaxialrotator



E(5)- ββ2n

D. Bonatsos et al., arXiv:nucl-th/0312120 v1 29Dec2003

B(E2) values (g. band)Energies



X(5)- ββ2n : Energies and B(E2) values (g. band)

D. Bonatsos et al., arXiv:nucl-th/0311092 v1 26Nov2003



X(5)- β2nE(5)- β2n

Comparison to data



Comparison of Z(5) predictions to exp. data

energy levels B(E2) values (B(E2;21,0=1)

D. Bonatsos, priv. comm. and arXiv:nucl-th/0402087



Dynamical symmetry studies at LNL ?Dynamical symmetry studies at LNL ?

GASP – II (must !)

Cologne Plunger (must3 !)

ISIS - Euclides (optional)

and

PRISMA / CLARA



Why CLARA ?



Documents

Harissopulos GAMMA2004 finalnpgroup.pd.infn.it/GASP/gamma2004/documents/SHarissopulos.pdf · S. Harissopulos, Nu*STAR Group, Institute of Nuclear Physics, NCSR “Demokritos”, Athens