Ground State Energy of the One-Component Charged Bose Gas

Abstract

The model considered here is the `jellium' model in which there is a uniform, fixed background with charge density $-e\rho$ in a large volume $V$ and in which $N=\rho V$ particles of electric charge $+e$ and mass $m$ move --- the whole system being neutral. In 1961 Foldy used Bogolubov's 1947 method to investigate the ground state energy of this system for bosonic particles in the large $\rho$ limit. He found that the energy per particle is $-0.402r_s^{-3/4}m{e}^4/{\hslash }^2$ in this limit, where $r_s=(3/4\pi \rho {)}^{1/3}{e}^{2}m/{\hslash }^2$. Here we prove that this formula is correct, thereby validating, for the first time, at least one aspect of Bogolubov's pairing theory of the Bose gas

38 pages latex. Typos corrected.Lemma 6.2 changed

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