Ground state energy of the one-component charged Bose gas

The model considered here is the "jellium" model in which there is a uniform, fixed background with charge density - eρ in a large volume V and in which N = ρV 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 ρ limit. He found that the energy per particle is - 0.402r^-3/4_s me⁴/ℏ² in this limit, where r_s = (3/4πρ)^1/3e²m/ℏ². 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.