1. Normal persistent currents and gross shell structure at high spin S. Frauendorf Department of Physics University of Notre Dame

3. Interested in 3D system that adjust its shape – quantum droplets: Nuclei and metal clusters Collaborators: M. Deleplanque V.V. Pashkevich A. Sanzhur

4. Relation between rotation and magnetism Hamiltonian in the rotating frame Hamiltonian with external magnetic field Larmor frequency For small frequency the quadratic term can be neglected, and Larmor’s theorem holds. Will be considered: Magnetic length (cyclotron radius) >> size

5. Induced currents give the magnetic response of the electron system Currents in the rotating frame give the deviation from rigid rotation. Large system : unmagnetic/rigid rotation Small systems: shell effects Strong magnetic response/deviation from rigid rotation Normal persistent currents SusceptibilityMoment of inertia

6. Magnetism and shapes are difficult to measure for clusters. Moments of inertia and shapes of rotating are nuclei well known. Look at high spin. At low spin there are pair correlations Harmonic oscillator is misleading. Phys. Rev. C 69 044309 (2004)

7. Experimental moments of inertia

8. Imax>15,16,17 for N 82 resp.

9. Imax>20

10. Microscopic calculations Shell correction method, using Woods Saxon potential Mimimize

12. Periodic orbit theory L length of orbit, k wave numberdamping factor

13. Basic and supershell structure Square and triangle are the dominant orbits. The difference of their lengths causes the supershell beat. Basic shell structure determined by one orbit (square).

14. super oscillation basic oscillation

16. Classical periodic orbits in a spheroidal cavity with small-moderate deformation Equator plane Meridian plane one fold degenerate two fold degenerate

17. Shell energy of a spheroidal cavity L meridian =const L equator =const

18. L meridian =const Shell energy of a Woods-Saxon potential

19. Meridian ridge Equator ridge

20. Influence of rotation 1 st order perturbation theory: Change of action: integrate the perturbation over the unperturbed orbit S. C. Craegh, Ann. Phys. (N.Y.) 248, 60 (1996) rotational flux Area field

22. equator meridian sphere Modulation factor

24. Moments of inertia and energies classical angular momentum of the orbit For each term

26. rotational alignment Backbends Meridian ridge spikes right scale K-isomers equator ridge

27. spikes

28. Superdeformed nuclei equator meridian +-

29. Shell energy at high spin equator meridian sphere

30. parallel perpendicular N

31. Summary Far-reaching analogy between magnetic susceptibility and deviation from rigid body moment of inertia Shell structure leads to normal persistent currents. Basic shell structure qualitatively described by one family of periodic orbits (triangle or four angle). Supershells are due to the interference of two (triangle and four angle). Rotational/magnetic flux through the orbit controls the shell oscillations as functions of the rotational/Larmor frequency Length of the orbit controls the shell oscillations as functions Of the particle number. Shell structure of ground state energy and moment of inertia strongly correlated.

34. Oblate parallel

35. Prolate parallel

36. Oblate pependicular

37. Prolate perpendicular

40. optimal