Shell structure and semiclassics

In the early history of quantum physics, classical§mechanics was modified with certain rules, in order§to obtain agreement with new experiments. An§important example is the§model of the§hydrogen atom by Niels Bohr in 1913,§which could explain§measured absorption lines. Some hundred years later,§methods based on§classical mechanics, still turn out to be§very powerful tools in understanding experiments with§many quantum systems.§In a fermionic many-body system, treated in the§mean-field approximation,§the single-particle spectrum determines the§shell-structure i.e. the§ordered bunching of individual energy levels. An§important example is the§electronic shell-structure for atoms, which forms the§basis of the§periodic table.§For systems with a larger number of particles,§super-shell structures,§i.e. long range order of the shell-structure, may§emerge. Observations of this effect have been§achieved e.g.§in clusters of§metallic atoms. Within a semiclassical approach, the§(super-)§shell-structure can be explained in an elegant way in§terms of different classical periodic orbits.§Here this concept is further developed and applied to§systems being close to a harmonic oscillator.