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

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

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 Isolde - CERN 10-12nd February 2007

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

Tetrahedral Shell Gaps Spherical Td J. Dudek, A. Góźdź and N. Schunck Act. Phys. Pol. B34 2491 (2003) Workshop Isolde - CERN 10-12nd February 2007

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. 88 252502 (2002) Workshop Isolde - CERN 10-12nd February 2007

Neutron-rich Zr Isotopes Shell Gaps and Real Minima N. Schunck, J. Dudek, A. Góźdź, P. Regan Phys. Rev. C69 061305(R) (2004) Workshop Isolde - CERN 10-12nd February 2007

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

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. 97 072501 (2006) Workshop Isolde - CERN 10-12nd February 2007

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

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

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

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

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

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

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

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

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

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

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. 97 072501 (2006) Workshop Isolde - CERN 10-12nd February 2007

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

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