Europhys. Lett.
Volume 63, Number 3, August 2003
Page(s) 415 - 418
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 01 November 2003
DOI: 10.1209/epl/i2003-00546-1
Europhys. Lett., 63 (3) , pp. 415-418 (2003)

Why charges go to the surface: A generalized Thomson problem

Y. Levin and J. J. Arenzon

Instituto de Física, Universidade Federal do Rio Grande do Sul Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil

(Received 28 April 2003; accepted in final form 5 June 2003)

We study a variant of the generalized Thomson problem in which n particles are confined to a neutral sphere and interacting by a $1/r^{\gamma}$ potential. It is found that for $\gamma \le 1$ the electrostatic repulsion expels all the charges to the surface of the sphere. However, for $\gamma>1$ and $n>n_{\ab{c}}(\gamma)$ occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes.

71.10.Ca - Electron gas, Fermi gas.
64.60.Cn - Order-disorder transformations; statistical mechanics of model systems.

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