Electrons on a spherical surface: Physical properties and hollow spherical clusters
Abstract
We discuss the physical properties of a noninteracting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential, and its electric static polarizability. All these properties are discussed analytically as functions of the number N of electrons. The trends obtained with increasing N are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasispherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the definition of a scale-invariant distribution of magic numbers which follows a power law with critical exponent -0.5. We conclude that our completely mechanistic and analytically tractable model can be useful for the analysis of self-assembling complex systems.
- Publication:
-
Physical Review A
- Pub Date:
- July 2012
- DOI:
- 10.1103/PhysRevA.86.013201
- Bibcode:
- 2012PhRvA..86a3201C
- Keywords:
-
- 61.48.-c;
- 73.22.-f;
- 89.75.Da;
- Structure of fullerenes and related hollow molecular clusters;
- Electronic structure of nanoscale materials: clusters nanoparticles nanotubes and nanocrystals;
- Systems obeying scaling laws