Parameter-free shell model of spherical Coulomb crystals.
An accurate shell model of spherical Coulomb crystals is presented. Employing intrashell angular particle positions that correspond to the global energy minima of the pertinent Thomson problems, it yields rigorous upper bounds to the exact energies that are accurate to within 0.03%, which constitutes an improvement of two orders of magnitude over its predecessors based upon continuous intrashell distributions. In addition, the present model faithfully reproduces mean crystal radii and shell occupancies without recourse to any empirical parameters. Thanks to its simple form and the well-known asymptotics of the Thomson problem at the bulk limit, it affords analytical formulas for energies and mean crystal radii of very large spherical Coulomb crystals. Moreover, it rigorously accounts for certain features of the less accurate models published previously.
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
Jerzy
J
Cioslowski
Ewa
E
Grzebielucha