  We investigate higher order effects in electromagnetic dissociation of
neutron halo nuclei using a simple and realistic zero range model for the
neutron-core interaction. In the sudden (or Glauber) approximation all orders
in the target-core interaction are taken into account. Small deviations from
the sudden approximation are readily calculated. We obtain very simple
analytical results for the next-to-leading order effects, which have a simple
physical interpretation. For intermediate energy electromagnetic dissociation,
higher order effects are generally small. We apply our model to Coulomb
dissociation of $^{19}$C at 67 A MeV. The analytical results are compared to
numerical results from the integration of the time-dependent Schroedinger
equation. Good agreement is obtained. We conclude that higher order
electromagnetic effects are well under control.
