Bose condensation in supercritical external fields charged condensates

This paper extends a previous one which was applicable only to short range interactions. We study the relativistic field theory of a charged spin-zero boson field in the presence of the Coulomb field of a prescribed (nuclear) 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 negatively charged bosons, positively charged bosons escaping the system. When the effects of weak interaction are included, the instability occurs in a weaker field and positrons are emitted. A consistent quantum theory is formulated after the Coulomb interaction of the bosons is included. Properties of the condensate are examined in the limit of large condensate density, in a mean field approximation, which is also studied numerically. Possible implications concerning the existence of abnormally bound nuclei are presented.