1. Exotic Nuclear Shapes Probing the limits of nuclear stability
Nicolas Schunck
Departamento de Fisica Teorica,
Universidad Autonoma de Madrid
Cantoblanco 28049, Madrid, Spain
Oak Ridge National Laboratory,
Bldg. 6025, MS6373, P.O. Box 2008,
Oak Ridge, TN-37831, USA
Workshop Isolde - CERN 10-12nd February 2007

2. Workshop Isolde - CERN 10-12nd February 2007
Point Symmetries
Synthetic inorganic-organic compound with ZnO4 tetrahedral clusters linked by C6H4-C-O2 “struts” (Li, Nature, 1999).
Workshop Isolde - CERN 10-12nd February 2007

3. Point Symmetries and Nuclear Stability
Shell Gaps  Stable configurations
In nuclei: Higher degeneracies  Larger shell gaps
Degeneracies are a direct consequence of the underlying point symmetry of the shape
J. Dudek, A. Góźdź, N. Schunck and M. Miskiewicz
Phys. Rev. Lett (2002)
Workshop Isolde - CERN 10-12nd February 2007

4. Point Groups and Level Degeneracy
Degeneracies and Point groups
Properties
High symmetries
Low symmetries
Type
Spherical
Tetrahedral
Octahedral
Any other…
Number of Symmetry Elements  48 96 …
New
Degeneracies
2j + 1
4, 2, 2
2, 2
Kramers Degeneracy ( = time-reversal symmetry)
Survey of the properties of a few point groups
Workshop Isolde - CERN 10-12nd February 2007

5. Tetrahedral Shell Gaps
Spherical Td
J. Dudek, A. Góźdź and N. Schunck
Act. Phys. Pol. B (2003)
Workshop Isolde - CERN 10-12nd February 2007

6. Tetrahedral Magic Numbers
Shell Gaps (2)
From a WS potential:
20, 32, 40, 56-58, 64, 70, 90, 100, 112, …
Existence of Td magic numbers independent of the realization of the mean-field = Universality
Yb isotopes
Zr isotopes
Whole regions of potential candidates…!
J. Dudek, A. Góźdź, N. Schunck and M. Miskiewicz
Phys. Rev. Lett (2002)
Workshop Isolde - CERN 10-12nd February 2007

7. Neutron-rich Zr Isotopes
Shell Gaps and Real Minima
N. Schunck, J. Dudek, A. Góźdź, P. Regan
Phys. Rev. C (R) (2004)
Workshop Isolde - CERN 10-12nd February 2007

8. Experimental signatures
Stable tetrahedral minimum: Shape isomer
Low-spin physics: don’t expect I > 10 ħ…
Static octupole moment Q3
No dipole moment
No quadrupole moment
Specific p.-h. patterns
Schematic illustrations of where to look for tetrahedral states in E(I) plots
Workshop Isolde - CERN 10-12nd February 2007

9. Workshop Isolde - CERN 10-12nd February 2007
Examples in mass A~150
Members of a same rotational band not connected by E2 transitions
J. Dudek, D. Curien, N. Dubray J. Dobaczewski, N. Dubray, V. Pangon, P. Olbratowski and N. Schunck
Phys. Rev. Lett (2006)
Workshop Isolde - CERN 10-12nd February 2007

10. Workshop Isolde - CERN 10-12nd February 2007
Summary (for Part I)
Mean-field Theories predict tetrahedral configurations in islands of nuclei throughout the nuclear chart
Low-lying states (by opposition to cluster states)
New types of shape coexistence: prolate, oblate, spherical, tetrahedral, octahedral, pear-shaped, etc.
The best candidates are found either in or away from the valley of stability
The nuclear tetrahedral symmetry reflects the quantal nature of the nucleus (always competing with the macroscopic, liquid-drop aspects)
Workshop Isolde - CERN 10-12nd February 2007

11. Deformed nuclei… in motion
Consequence of the breaking of the rotational invariance: deformed nuclei can rotate…
Example of a super-deformed rotational band
Jacobi Shape transition
Workshop Isolde - CERN 10-12nd February 2007

12. The Jacobi Shape Transition
Workshop Isolde - CERN 10-12nd February 2007

13. Jacobi transition and Hyper-deformation
Liquid drop = High-temperature Limit
Workshop Isolde - CERN 10-12nd February 2007

14. Hyper-deformed configurations
Neat Jacobi Transition = a prerequisite for populating SD and HD states
Mean-field at the limits:
Single-particle structure
Effective interaction
Jacobi Shapes and many-body problem
Hyperintruder: N=8 orbital in N=5 shell
Workshop Isolde - CERN 10-12nd February 2007

15. Dynamical Moments of Inertia J(2)
Nucleus
118Te
121I
122Xe
124Xe
125Cs
126Xe
126Ba
J(the) 97
102
108
111
110
118
J(exp) 77
100 83
N. Schunck, J. Dudek and B. Herskind
To be published in Phys. Rev. C
Workshop Isolde - CERN 10-12nd February 2007

16. Workshop Isolde - CERN 10-12nd February 2007
Summary (Part II)
Hyper-deformation (and Jacobi shapes) can be observed only at very high angular momentum
Short spin-window in-between the Jacobi transition and fission
Mass A ~ 100 among the best candidates
Strong indications that such states have been observed already
When discrete transitions in the 3rd Well ?
The Jacobi shape transition reflects the macroscopic, liquid-drop nature of the nucleus (always competing with the quantal aspects)
Workshop Isolde - CERN 10-12nd February 2007

17. Conclusion: How to tackle the problem ?
The nuclear shape is a probe to nuclear structure
Questions existing theoretical models:
Influence on Effective Interaction/Lagrangians
Extension of Microscopic and Collective Models
Opening Connections with Related Disciplines (Condensed Matter Physics, Cluster Physics, etc.)
On-going Projects
USA: Universal Nuclear Effective Density Functional. Among others: Probing deformation effects to constraint effective interactions
Europe: Similar Project under way
Workshop Isolde - CERN 10-12nd February 2007

18. Collaboration Network
IReS-ULP, Strasbourg, France
Oak Ridge National Laboratory, Oak Ridge, USA
Institute of Theoretical Physics, Warsaw University, Poland
Universidad Autonoma de Madrid, Cantoblanco, Spain
University Marie Curie-Skłodowska, Lublin, Poland
University of Notre Dame, USA
Université Libre de Bruxelles, Bruxelles, Belgium
Niels Bohr Institute, Copenhagen, Denmark
Henrik Niewodniczanski Institute of Nuclear Physics, Kraków, Poland
University of Surrey, Guildford, UK
Workshop Isolde - CERN 10-12nd February 2007

19. Tetrahedral Shell Effects
Shell Correction [MeV]
Tetrahedral Deformation (Rank 7)
Workshop Isolde - CERN 10-12nd February 2007

20. Around Td Doubly-Magic Nuclei
Minima and Barriers
Barriers between Td minimum and prolate deformed minimum
J. Dudek, D. Curien, N. Dubray J. Dobaczewski, N. Dubray, V. Pangon, P. Olbratowski and N. Schunck
Phys. Rev. Lett (2006)
Workshop Isolde - CERN 10-12nd February 2007

21. Workshop Isolde - CERN 10-12nd February 2007
Branching Ratios
Spin
152Gd
156Gd
154Dy
160Er
164Er
162Yb
164Yb
222Th
19- - 50
0.3
17- 16
0.4
15- 6 60 24 10 17
13- 14 7 15 18 23 11
11- 4 5 9 9- 7-
Branching Ratios BE(2)in/BE(1)out
Workshop Isolde - CERN 10-12nd February 2007

22. Workshop Isolde - CERN 10-12nd February 2007
Why Hyperdeformation ?
Super-def
Hyper-def ?
Hyper-def (HD) characterized by (N+3) intruder orbitals into N-shell
Workshop Isolde - CERN 10-12nd February 2007