  The production of antihydrogen in flight in antiproton-nucleus collisions is
calculated theoretically in the Plane Wave Born Approximation (which is
equivalent to the straight line semiclassical approximation). Antihydrogen has
been produced in this way at LEAR/CERN and is presently studied at FERMILAB at
various antiproton energies. Dirac wave functions for the leptons are used,
taking first order (Z.alpha) corrections into account. Analytical results are
obtained for differential cross-sections. Total cross sections are obtained by
numerical integration. The dependence on the transverse momentum transfer is
studied and the accuracy of the equivalent photon approximation and a recent
variant by Munger, Brodsky,and Schmidt is discussed as a function of beam
energy.
