Symmetries and collective Nuclear excitations PRESENT AND FUTURE EXOTICS IN NUCLEAR PHYSICS In honor of Geirr Sletten at his 70 th birthday Stefan Frauendorf, Y. Gu, Daniel Almehed Department of Physics University of Notre Dame, USA Institut für Strahlenphysik, Forschungszentrum Rossendorf Dresden, Germany

Rotation of Molecules 2

Weak spontaneous symmetry breaking Hamiltonian has a symmetry  approximate eigenstate breaks it  collective mode/doubling Twofold discrete: Dynamic chirality Continuous orientation : Condensation of quadrupole phonons -Tidal waves Combination of the two: Condensation of octupole phonons 3

Yrast line Mean field: rigid sphericalrigid deformed soft irregular multi p-h regular w proportional to I regular w weakly increases with I -condensation of quadrupole phonons -very soft rotor Tidal wave 1.Weakly oriented nuclei – tidal waves 4

E I qp. excitations Tidal waves 5 Angular velocity Deformation Rotor increases stays constant Tidal wave Vibrator stays constant increases Generation of angular momentum

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Quadrupole waves: Theoretical method Cranking model: semiclassical treatment of angular momentum Micro-macro method (Nilsson+fixed pairing). Find the equilibrium shape for the rotating mean field. Minimizing at fixed frequency problematic: Minimizing 7 S. Frauendorf, Y. Gu, arXiv , PRL, in preparation

g-factors Even for I=2 the angular velocity is so high that nucleons respond non-perturbativly.

Above I=4 collective and single particle motion interwoven B(E2) more regular than energies. Z=48, N=60-66: after neutron alignment, smaller deformation -> approach of antimagnetic rotation Z=46, N=56,60 and Z=44, N=62,64 angular velocity nearly constant during neutron alignment – tidal wave with quasiparticle degrees of freedom More B(E2) values to check theory Strongly anharmonic TW in “vibrational nuclei” 10 Details: Treating the yrast states of vibrational or transitional nuclei as running tidal waves makes microscopic calculations simple.

H H H H H H H H C C N N F F Rotational frequency: 100meV Chirality of molecules COOH rightleft 11

H H H H H H H H C C N N F F Rotational frequency: 100meV meV 6000 GHz Chirality of molecules 11

Consequence of static chirality: Two identical rotational bands. Chiral Vibration Tunneling 2. Dynamic chirality of nuclei 12

Chiral vibration 2D - TAC+RPA 3D - TAC 2D - TAC+RPA Nuclear chirality - a transient phenomenon Large amplitude collective motion - tough Triaxial Rotor+ particle+hole Frauendorf,Meng, NPA 617, 131 (1997 ) 13

3D-TAC with spherical Woods-Saxon [Dimitrov et al PRL 84 (2000)] Modified QQ-force N-dependent  in 2 N-shells [Baranger, Kumar NPA 110 (1968)] Parameters fitted to reproduce Strutinsky results Pair field  adjusted to 80% of odd-even mass difference RPA - Small amplitude harmonic vibrations around the mean field minimum Tilted Axis Cranking + RPA orientation shape 14

Best case of chirality so far: S. Zhu et al. Phys. Rev. Lett. 91, (2003) 15

Chiral vibrations in 135-Nd TAC+RPA calculations Same inband transition rates - Good agreement with experiment Mukhopadhyay, Almehed et al. PRL 99, (2007) Phonon is mainly orientation fluctuations 16

135-Nd Transition rates in-band cross band 17

135-Nd Transition rates in-band cross band 18

Small  Dripline Almehed and Frauendorf PRC, in review TAC+RPA in Odd-odd nuclei 19

Orientation amplitudes Harmonic approximation but ‘large’ amplitude. Shape amplitudes few % 134-Pr  = keV 20

Rotating triaxial nuclei do become chiral But chirality is weakly broken. The observed pairs of bands are manifest of slow motion of angular momentum through the two chiral sectors. The chiral mode is transitional: strongly anharmonic – strong tunneling The chiral mode well decouples from the shape modes I=14 I=10I=12 J1J1 J2J2 J3J3 21