Anomalous Pauli Electron States for Magnetic Elds with Tails

We consider a two-dimensional electron with an anomalous magnetic moment, g > 2, interacting with a nonzero magnetic eld B perpendicular to the plane which gives rise to a ux F. Recent results about the discrete spectrum of the Pauli operator are extended to elds with the O(r ?2?) decay at innnity: we show that if jFj exceeds an integer N, there is at least N +1 bound states. Furthermore, we prove that weakly coupled bound states exist under mild regularity assumptions also in the zero ux case.