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Symmetries and collective Nuclear excitations PRESENT AND FUTURE EXOTICS

This paper discusses the various symmetries and collective excitations in nuclear physics, including the rotation of molecules, weak spontaneous symmetry breaking, tidal waves, and chiral vibrations. It explores the theoretical methods for studying these phenomena and presents experimental data on transition rates in nuclei. The paper also discusses the concept of chirality in nuclear physics and its implications for rotational and shape dynamics.

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Symmetries and collective Nuclear excitations PRESENT AND FUTURE EXOTICS

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

  2. Rotation of Molecules 2

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

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

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

  6. 6

  7. Quadrupole waves: Theoretical method S. Frauendorf, Y. Gu, arXiv 0709.0254, PRL, in preparation 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

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

  9. Treating the yrast states of vibrational or transitional nuclei as running tidal waves makes microscopic calculations simple. Strongly anharmonic TW in “vibrational nuclei” Above I=4 collective and single particle motion interwoven B(E2) more regular than energies. Details: 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 10 More B(E2) values to check theory

  10. Chirality of molecules right left COOH COOH H H H H H C C H N H N H F F 11 Rotational frequency: 100meV

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

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

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

  14. Tilted Axis Cranking + RPA • 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 orientation shape RPA - Small amplitude harmonic vibrations around the mean field minimum 14

  15. Best case of chirality so far: S. Zhu et al. Phys. Rev. Lett. 91, 132501 (2003) 15

  16. Chiral vibrations in 135-Nd TAC+RPA calculations Mukhopadhyay, Almehed et al. PRL 99, 172501 (2007) Phonon is mainly orientation fluctuations Same inband transition rates - Good agreement with experiment 16

  17. 135-Nd Transition rates in-band cross band 17

  18. 135-Nd Transition rates in-band cross band 18

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

  20. Shape amplitudes few % Orientation amplitudes 25 keV 134-Pr =0.4 Harmonic approximation but ‘large’ amplitude. 20

  21. I=14 I=10 I=12 J2 J3 J1 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 well decouples from the shape modes The chiral mode is transitional: strongly anharmonic – strong tunneling 21

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