  We calculate the grand canonical partition function at the one-loop level for
scalar quantum electrodynamics at finite temperature and chemical potential. A
classical background charge density with a charge opposite that of the scalars
ensures the neutrality of the system. For low density systems we find evidence
of a first order phase transition. We find upper and lower bounds on the
transition temperature below which the charged scalars form a condensate. A
first order phase transition may have consequences for helium-core white dwarf
stars in which it has been argued that such a condensate of charged helium-4
nuclei could exist.
