Asymptotic equivalence of the shell-model and local-density descriptions of Coulombic systems confined by radially symmetric potentials in two and three dimensions.
Asymptotic equivalence of the shell-model and local-density (LDA) descriptions of Coulombic systems confined by radially symmetric potentials in two and three dimensions is demonstrated. Tight upper bounds to the numerical constants that enter the LDA expressions for the Madelung energy are derived and found to differ by less than 0.5% from the previously known approximate values. Thanks to the variational nature of the shell-model approximate energies, asymptotic expressions for other properties, such as mean radial positions of the particles and number densities, are also obtained. A conjecture that generalizes the present results to confining potentials with arbitrary symmetries is formulated.
Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
Jerzy
J
Cioslowski
Joanna
J
Albin