Bose condensation in supercritical external fields

We study the relativistic field theory of a charged spin-zero boson field in the presence of an external field, such as the Coulomb field of a prescribed charge distribution. It is shown that for a sufficiently intense field the ground state is unstable against the formation of a Bose-Einstein condensate of charged boson pairs. A consistent quantum theory can be formulated when known nonlinear couplings such as the Coulomb interactions of the bosons are properly included in the Hamiltonian. Speculations are offered concerning the possible stability of nuclei with charge number $Z\gtrsim {10}^3$.