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.

Autorentext

Magnus Ögren, Dr studies in Physics at Lund University in Sweden,later working in the field of fermionic quantum atom optics at theUniversity of Queensland, Australia.

Klappentext

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.