1. Nuclei at the Extremes of Spin: The Superdeformed Bands in 131,132Ce
Liverpool, Daresbury, Lyon, Grenoble,
Strasbourg, Debrecen, Padova, Camerino
Euroball IV
4/22/2019
Lund Conference June 2005 : E.S. Paul

2. Nuclei at the Extremes of Spin: The Superdeformed Bands in 131,132Ce
4/22/2019
Lund Conference June 2005 : E.S. Paul

3. The Nucleus is a Mesoscopic System at the Femtoscale
Mesoscopic: The atomic nucleus consists of a large, yet finite, number of strongly interacting constituent fermions (nucleons)
Femtoscale: The size of the nucleus is of the order of femtometres (10-15 m)
Similar to nanoscale (10-9 m) mesoscopic systems, e.g. metallic clusters, the properties (shell structure, deformation) are determined by the finite number of constituents
4/22/2019
Lund Conference June 2005 : E.S. Paul

4. At the Limits of Angular Momentum: Band Termination
Fundamentally, nuclear angular momentum is generated by the (finite number of) constituent nucleons
Hence there must be a “maximum” value for a given nucleus, or rather nucleonic configuration
Experimentally this is seen as “termination” of a rotational band in nuclei when the nuclear angular momentum is generated entirely from the constituent nucleons rather than collective excitations of the nucleus
4/22/2019
Lund Conference June 2005 : E.S. Paul

5. Experimental Band Termination
A band terminates when all valence particles outside a doubly magic (spherical) core are aligned
4/22/2019
Lund Conference June 2005 : E.S. Paul

6. Superdeformed Shell Structure
New shell gaps appear when the lengths of the nuclear axes occur in the ratio of small integers:
2:1 (A = 150, dysprosium)
3:2 (A = 130, cerium)
3:1 (“hyperdeformation”)
But they occur at different particle numbers to the spherical case
4/22/2019
Lund Conference June 2005 : E.S. Paul

7. Lund Conference June 2005 : E.S. Paul
To Terminate or Not?
For modest (i.e. small) deformation, solutions of the Harmonic Oscillator suggest that configurations will terminate into a noncollective oblate state where the spin is simply given by the sum of the angular momenta of the ‘pure’ single particle configuration: Imax
For large deformation (e.g. 2:1 superdeformation), however, spin above Imax can be generated
The SD Ce deformation (3:2 axes ratio) occurs at the intersection of these two regimes
The (experimental) question is: will the SD bands in cerium nuclei ‘terminate’ or not?
4/22/2019
Lund Conference June 2005 : E.S. Paul

8. Superdeformation in 132Ce
The first SD band was discovered in 132Ce:
PJ Nolan et al., J. Phys G 11, L17 (1985)
Its “enhanced” quadrupole moment showed it to correspond to the 3:2 shape
AJ Kirwan et al., Phys. Rev. Lett. 58, 467 (1987)
The TESSA3 array
at Daresbury
4/22/2019
Lund Conference June 2005 : E.S. Paul

9. Lund Conference June 2005 : E.S. Paul
EUROBALL IV Results
A BGO inner ball calorimeter allowed measurement of the total (summed) γ ray energy and also the number of emitted γ rays in an event
Gating on these quantities enhanced the yield of 132Ce (top)
4/22/2019
Lund Conference June 2005 : E.S. Paul

10. Lund Conference June 2005 : E.S. Paul
Yrast SD Band in 132Ce (SD1)
Top: triples (double gated) γ-ray spectrum of SD1 in 132Ce with a high ‘sum-energy/fold’ condition
Bottom: triples γ-ray spectrum from the whole data set
4/22/2019
Lund Conference June 2005 : E.S. Paul

11. Lund Conference June 2005 : E.S. Paul
SD1 in 132Ce
The lowest energy (yrast) superdeformed band in 132Ce spans 50ħ (from 20ħ to 70ħ) of angular momentum (in a finite fermionic system) !
4/22/2019
Lund Conference June 2005 : E.S. Paul

12. Lund Conference June 2005 : E.S. Paul
SD2 and SD3 in 132Ce
4/22/2019
Lund Conference June 2005 : E.S. Paul

13. Lund Conference June 2005 : E.S. Paul
132Ce SD1 Rigid-Rotor Plot
The yrast SD band in 132Ce shows similarities to smoothly terminating bands in A ~ 100 nuclei. It is approaching the maximum spin for its configuration (termination at 78ħ)
4/22/2019
Lund Conference June 2005 : E.S. Paul

14. Lund Conference June 2005 : E.S. Paul
Theory: Protons (Z = 58)
Important orbitals (relative to Z = 50):
h11/2 ‘intruder’ levels (particles) - red
g9/2 ‘extruder’ levels (holes) - blue
Cerium has a 10 particle 2 hole configuration
A ‘finite’ number of valence protons to generate angular momentum
4/22/2019
Lund Conference June 2005 : E.S. Paul

15. Lund Conference June 2005 : E.S. Paul
Theory: Neutrons (N = 74)
Important orbitals (relative to N = 82):
h9/2 and f7/2 intruder orbitals – blue
i13/2 intruder orbitals – green
h11/2 holes – red
Again a finite number of ‘constituents’ to generate the angular momentum
4/22/2019
Lund Conference June 2005 : E.S. Paul

16. Lund Conference June 2005 : E.S. Paul
132Ce SD1 Theory
Cranked Nilsson Strutinsky calculations have been performed
The yrast SD1 band in 132Ce cannot be described over its whole range by a single configuration
Look at dynamic moment of inertia
4/22/2019
Lund Conference June 2005 : E.S. Paul

17. Dynamic Moments of Inertia
4/22/2019
Lund Conference June 2005 : E.S. Paul

18. Lund Conference June 2005 : E.S. Paul
131Ce SD1 and SD2
4/22/2019
Lund Conference June 2005 : E.S. Paul

19. Lund Conference June 2005 : E.S. Paul
131Ce SD1 – SD2 Links
100%
90%
10%
4/22/2019
Lund Conference June 2005 : E.S. Paul

20. 131Ce: SD1 & SD2 Extension + Links
The excited band in 131Ce (SD2) has the same configuration as the yrast band in 132Ce (SD1)
131Ce SD2 becomes favoured (yrast) at high spin
131Ce SD2 has a larger quadrupole moment (8.2 eb) compared to all other bands in 131,132Ce (7.3 eb)
4/22/2019
Lund Conference June 2005 : E.S. Paul

21. Lund Conference June 2005 : E.S. Paul
131Ce Theory
4/22/2019
Lund Conference June 2005 : E.S. Paul

22. Nuclei at the Extremes of Spin: The Superdeformed Bands in 131,132Ce
The End
4/22/2019
Lund Conference June 2005 : E.S. Paul

23. Gammasphere Expt (Nov 2004)
(AC Milan)
4/22/2019
Lund Conference June 2005 : E.S. Paul

24. Lund Conference June 2005 : E.S. Paul
132Ce SD1 Decay & Links
Aled Evans
4/22/2019
Lund Conference June 2005 : E.S. Paul