WKB level spectra in two inhomogeneous electron liquids : Na clusters and C cages
Faculty of Sciences. Physics
Physics and chemistry of liquids. - London
, p. 123-133
University of Antwerp
After a brief summary of known magic numbers and eigenvalue sums for (a) the hydrogenic potential - Ze(2)/r and (b) the three-dimensional isotropic harmonic oscillator potential, approximate semi-classical scaling laws are presented relating to WKB eigenvalues for two more complex central potentials V(r). The first is the so-called Woods-Saxon potential, used in early work to calculate electronic magic numbers in clusters of Na atoms. The second potential V(r) chosen arises from a simple surface charge model of almost-spherical carbon cages such as C-60. For these last two potentials, semi-classical theory is shown to lead to qualitative insight, without very lengthy mathematical calculations.