Cioslowski Jerzy
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
J Chem Phys. 2008 Apr 28;128(16):164713. doi: 10.1063/1.2905214.
Rigorous equalities and bounds for several properties of Coulomb crystals are presented. The energy e(N) per particle pair is shown to be a nondecreasing function of the particle number N for all clusters described by double-power-law pairwise-additive potentials epsilon(r) that are unbound at both r-->0 and r-->infinity. A lower bound for the ratio of the mean reciprocal crystal radius and e(N) is derived. The leading term in the asymptotic expression for the shell capacity that appears in the recently introduced approximate model of Coulomb crystals is obtained, providing in turn explicit large-N asymptotics for e(N) and the mean crystal radius. In addition, properties of the harmonic vibrational spectra are investigated, producing an upper bound for the zero-point energy.
