Stability of coulomb systems with magnetic fields

The ground state energy of an atom in the presence of an external magnetic filedB (with the electron spin-field interaction included) can be arbitrarity negative whenB is arbitrarily large. We inquire whether stability can be restored by adding the self energy of the field, B². For a hydrogenic like atom we prove that there is a critical nuclear charge,z_c, such that the atom is stable forz<z_c and unstable forz>z_c.Work partically supported by U.S. National Scinece Foundation grant DMS-8405264 during the author's stay at the Institute for Advanced Study, Princeton, NJ, USAWork partially supported by U.S. National Science Foundation grant PHY-8116101-A03Work partially supported by U.S. and Swiss National Science Foundation Cooperative Science Program INT-8503858. Current address: Institut f. Mathematik, FU Berlin, Arnimallee 3, D-1000 Berlin 33