A one-dimensional model for many-electron atoms in extremely strong magnetic fields: maximum negative ionization

We consider a one-dimensional model for many-electron atoms in strong magne tic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. Fo r this model we show that the maximum number of electrons N-max satisfies a bound of the form N-max < 2Z + 1 + c root B where Z denotes the charge of the nucleus, B the field strength and c is a constant. We follow Lieb's str ategy in which convexity plays a critical role. For the case N = 2 with fra ctional nuclear charge, we also discuss the critical value Z(c) at which th e nuclear charge becomes too weak to bind two electrons.