  We study the ground state of the Pauli Hamiltonian with a magnetic field in
R^(2d). We consider the case where a scalar potential W is present and the
magnetic field B is given by $B=2i\partial\bar\partial W$. The main result is
that there are no zero modes if the magnetic field decays faster than
quadratically at infinity. If the magnetic field decays quadratically then zero
modes may appear, and we give a lower bound for the number of them. The results
in this paper partly correct a mistake in a paper from 1993.
