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

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

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

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 Susceptibility Moment of inertia Normal persistent currents

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)

Experimental moments of inertia

Imax>15,16,17 for N<50, 50<N<82, N>82 resp.

Imax>20

Microscopic calculations Shell correction method, using Woods Saxon potential Mimimize

Periodic orbit theory L length of orbit, k wave number damping factor

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).

super oscillation basic oscillation

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

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

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

Meridian ridge Equator ridge

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

Modulation factor equator meridian sphere

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

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

spikes

Superdeformed nuclei equator meridian + -

Shell energy at high spin equator meridian sphere

parallel N perpendicular

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.

Oblate parallel

Prolate parallel

Oblate pependicular

Prolate perpendicular

optimal