Exotic Nuclear Shapes

1
Exotic Nuclear Shapes
I 0 T 0
I gtgt 1 T gt 0

• Nicolas Schunck
• Departamento de Fisica Teorica,
• Universidad Autonoma de Madrid
• Cantoblanco 28049, Madrid, Spain

2
Standard Nuclear Shapes

• Types of nuclear shapes
• Spherical
• Prolate
• Oblate
• Tri-axial
• Pear-shape

3
Point Symmetries in the Microscopic World

• Synthetic inorganic-organic compound with ZnO4
  tetrahedral clusters linked by C6H4-C-O2 struts
  (Li, Nature, 1999).
• 1.29 nm spacing between centers of adjacent
  clusters.

4
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
5
Point Groups and Level Degeneracy
Survey of the properties of a few point groups
6
Symmetry Groups Td and Oh

• Parameterization of the shape symmetries
• Tetrahedral a32 ? 0
• Octahedral a40, a44 ? 0
• Other possibilities involving higher order
  multipoles a?µ

7
Tetrahedral Shell Gaps
8
Tetrahedral Shell Effects
9
Neutron-rich Zr Isotopes
10
Tetrahedral Magic Numbers

• 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
Best candidates proton-rich or neutron-rich
nuclei
11
Experimental signatures (1/2)

• Stable tetrahedral minimum Shape isomer
• Low-spin physics dont expect I gt 10 h
• Possibly high excitation energy
• Static octupole moment Q3
• No dipole moment

12
Experimental signatures (2/2)

• Weak collective rotation
• Yrast traps with parity doublet ? (because of
  parity-breaking)
• Bunch of quasi-particle excitations (because of
  the 4-fold degeneracy of s.p. levels)
• Investigations under way
• RPA (Strasbourg)
• GCM (Warsaw)
• Spectroscopy with point symmetries (Lublin)

13
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 will be found 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)
14
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
15
The Jacobi Shape Transition
Example of the Jacobi shape transition in 152Dy
16
The various forms of the Jacobi transition
Instability of the Jacobi transition leading to
fission
17
Jacobi transition and Hyper-deformation
Liquid drop High-temperature Limit
18
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

19
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

The Jacobi shape transition reflects the
macroscopic, liquid-drop nature of the nucleus
(always competing with the quantal aspects)
20
Collaboration Network

• IReS-ULP, Strasbourg, France
• Institute of Theoretical Physics, Warsaw
  University, Poland
• University Marie Curie-Sklodowska, Lublin, Poland
• University of Notre Dame, USA
• Université Libre de Bruxelles, Bruxelles, Belgium
• University of Surrey, Guildford, UK
• Niels Bohr Institute, Copenhagen, Denmark
• Henrik Niewodniczanski Institute of Nuclear
  Physics, Kraków, Poland

21
Bibliography

• X. Li, J. Dudek, Phys. Rev. C49 (1994) 1250(R)
• S. Takami , K. Yabana, M. Matsuo, Phys. Lett.
  B431 (1998) 242-248
• M. Yamagami, K. Matsuyanagi, M. Matsuo, Nucl.
  Phys. A693 (2001) 579-602
• J. Dudek, A. Gózdz, N. Schunck and M. Miskiewicz,
  Phys. Rev. Lett. 88 (2002) 252502
• J. Dudek, A. Gózdz and N. Schunck, Act. Phys.
  Pol. B34 2491 (2003)
• N. Schunck, J. Dudek, A. Gózdz, P. Regan, Phys.
  Rev. C69 (2004) 061305(R)