On the maximal ionization for the atomic Pauli operator

Within the Born-Oppenheimer approximation Lieb proved that the number of non-relativistic, spin-$\frac{1}{2}$ particles that can be bound to an atom of nuclear charge $Z$ in the presence of an external magnetic field satisfies $N_{\max} < 2Z+1$, provided the magnetic field tends to zero at infinity and the coupling between the magnetic field and the spin is ignored. Assuming that the magnetic field is generic, we prove an upper bound which holds when the spin-field coupling is included; the set of generic magnetic fields contains an open, dense subset of $[L^{3/2}(\R^{3})]^{3}$.