Antihydrogen atoms may rarely be produced by the collision of antiprotons with ions. At relativistic velocities, the antiproton may pass around the Coulomb field of the nucleus and the electronpositron pairs can be produced electromagnetically. After this pair production, not so often, positron can be captured by the antiproton and as a result, antihydrogen atoms may be produced. In this work, we have calculated the antihydrogen production cross section in the framework of perturbation theory, by applying Monte-Carlo integration techniques. In order to compute the lowest-order Feynman diagrams amplitudes, we used Darwin wave functions for the bound states of the positrons and SommerfeldMaue wave functions for the continuum states of the electrons. © 2012 Elsevier B.V. All rights reserved.