Workshop Spiral II - Caen 4-6th October 2005 Exotic Nuclear Shapes I >> 1 T > 0 I = 0 T = 0 Nicolas Schunck Departamento de Fisica Teorica, Universidad Autonoma de Madrid Cantoblanco 28049, Madrid, Spain Workshop Spiral II - Caen 4-6th October 2005

Standard Nuclear Shapes Types of nuclear shapes: Spherical Prolate Oblate Tri-axial Pear-shape Workshop Spiral II - Caen 4-6th October 2005

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. Workshop Spiral II - Caen 4-6th October 2005

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. 88 252502 (2002) Workshop Spiral II - Caen 4-6th October 2005

Point Groups and Level Degeneracy 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 Spiral II - Caen 4-6th October 2005

Symmetry Groups Td and Oh Parameterization of the shape symmetries: Tetrahedral: α32 ≠ 0 Octahedral: α40, α44 ≠ 0 Other possibilities involving higher order multipoles αλμ J. Dudek, A. Góźdź and N. Schunck Act. Phys. Pol. B34 2491 (2003) Workshop Spiral II - Caen 4-6th October 2005

Tetrahedral Shell Gaps Td Spherical J. Dudek, A. Góźdź and N. Schunck Act. Phys. Pol. B34 2491 (2003) Workshop Spiral II - Caen 4-6th October 2005

Tetrahedral Shell Effects Shell Correction [MeV] Tetrahedral Deformation (Rank 7) Workshop Spiral II - Caen 4-6th October 2005

Neutron-rich Zr Isotopes N. Schunck, J. Dudek, A. Góźdź, P. Regan Phys. Rev. C69 061305(R) (2004) Workshop Spiral II - Caen 4-6th October 2005

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… J. Dudek, A. Góźdź, N. Schunck and M. Miskiewicz Phys. Rev. Lett. 88 252502 (2002) Workshop Spiral II - Caen 4-6th October 2005

Experimental signatures (1/2) Stable tetrahedral minimum: Shape isomer Low-spin physics: don’t expect I > 10 ħ… Possibly high excitation energy Static octupole moment Q3 No dipole moment Schematic illustrations of where to look for tetrahedral states Workshop Spiral II - Caen 4-6th October 2005

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) Four-fold degenerate single-particle levels should give rise to multiple quasi-particle excitations Workshop Spiral II - Caen 4-6th October 2005

Workshop Spiral II - Caen 4-6th October 2005 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) Workshop Spiral II - Caen 4-6th October 2005

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 Spiral II - Caen 4-6th October 2005

The Jacobi Shape Transition Example of the Jacobi shape transition in 152Dy Workshop Spiral II - Caen 4-6th October 2005

The various forms of the Jacobi transition Instability of the Jacobi transition leading to fission Workshop Spiral II - Caen 4-6th October 2005

Jacobi transition and Hyper-deformation Liquid drop = High-temperature Limit Workshop Spiral II - Caen 4-6th October 2005

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 N=8 orbital in N=5 shell Workshop Spiral II - Caen 4-6th October 2005

Workshop Spiral II - Caen 4-6th October 2005 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) Workshop Spiral II - Caen 4-6th October 2005

Collaboration Network IReS-ULP, Strasbourg, France Institute of Theoretical Physics, Warsaw University, Poland University Marie Curie-Skłodowska, 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 Workshop Spiral II - Caen 4-6th October 2005

Workshop Spiral II - Caen 4-6th October 2005 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. Góźdź, N. Schunck and M. Miskiewicz, Phys. Rev. Lett. 88 (2002) 252502 J. Dudek, A. Góźdź and N. Schunck, Act. Phys. Pol. B34 2491 (2003) N. Schunck, J. Dudek, A. Góźdź, P. Regan, Phys. Rev. C69 (2004) 061305(R) Workshop Spiral II - Caen 4-6th October 2005