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Why charges go to the surface: a generalized Thomson problem

By Yan Levin and Jeferson J. Arenzon


PACS. 71.10.C – Electron gas-theories and models. PACS. 64.60.Cn – Order-isorder transformations; statistical mechanics of model systems. Abstract. – 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 γ potential. It is found that for γ ≤ 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However for γ> 1 and n> nc(γ) 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. In a recent paper [1] Bowick et al. studied a system of particles confined to the surface of a sphere and interacting by a repulsive 1/rγ potential with 0 < γ < 2. They called this “the generalized Thomson problem”. It is interesting, however, to recall that the original Thomson problem was posed as a model of a classical atom [2]. Thus, n electrons were supposed to be confined in the interior of a sphere with a uniform neutralizing background, the so called “plum pudding ” model of an atom. The Thomson problem, which is still unsolved, is then to find the ground state of electrons inside the sphere. In the absence of a neutralizing background the electrostatic repulsion between the particle

Year: 2003
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