  We study the inverse scattering problem of determining a magnetic field and
electric potential from scattering measurements corresponding to finitely many
plane waves. The main result shows that the coefficients are uniquely
determined by $2n$ measurements up to a natural gauge. We also show that one
can recover the full first order term for a related equation having no gauge
invariance, and that it is possible to reduce the number of measurements if the
coefficients have certain symmetries. This work extends the fixed angle
scattering results of Rakesh and M. Salo to Hamiltonians with first order
perturbations, and it is based on wave equation methods and Carleman estimates.
