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_s ^-3/4 me⁴/Latin small letter h with stroke² in this limit, where r_s = (3/4πρ)^1/3 e² m/Latin small letter h with stroke². 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.