  Electrons in strong magnetic fields can be described by one-dimensional
models in which the Coulomb potential and interactions are replaced by
regularizations associated with the lowest Landau band. For a large class of
models of these type, we show that the maximum number of electrons that can be
bound is less than a Z + Z f(Z). The function f(Z) represents a small
non-linear growth which is quadratic in log Z when the magnetic field strength
grows polynomially with the nuclear charge Z. In contrast to earlier work, the
models considered here include those arising from realistic cases in which the
full trial wave function for N-electrons is the product of an N-electron trial
function in one-dimension and an antisymmetric product of states in the lowest
Landau level.
