  We continue the study of the two-component charged Bose gas initiated by
Dyson in 1967. He showed that the ground state energy for $N$ particles is at
least as negative as $-CN^{7/5}$ for large $N$ and this power law was verified
by a lower bound found by Conlon, Lieb and Yau in 1988. Dyson conjectured that
the exact constant $C$ was given by a mean-field minimization problem that
used, as input, Foldy's calculation (using Bogolubov's 1947 formalism) for the
one-component gas. Earlier we showed that Foldy's calculation is exact insofar
as a lower bound of his form was obtained. In this paper we do the same thing
for Dyson's conjecture. The two-component case is considerably more difficult
because the gas is very non-homogeneous in its ground state.
