Shell structure and semiclassics

In the early history of quantum physics, classicalmechanics was modified with certain rules, in orderto obtain agreement with new experiments. Animportant example is themodel of thehydrogen atom by Niels Bohr in 1913,which could explainmeasured absorption lines. Some hundred years later,methods based onclassical mechanics, still turn out to bevery powerful tools in understanding experiments withmany quantum systems.In a fermionic many-body system, treated in themean-field approximation,the single-particle spectrum determines theshell-structure i.e. theordered bunching of individual energy levels. Animportant example is theelectronic shell-structure for atoms, which forms thebasis of theperiodic table.For systems with a larger number of particles,super-shell structures,i.e. long range order of the shell-structure, mayemerge. Observations of this effect have beenachieved e.g.in clusters ofmetallic atoms. Within a semiclassical approach, the(super-)shell-structure can be explained in an elegant way interms of different classical periodic orbits.Here this concept is further developed and applied tosystems being close to a harmonic oscillator.