  A new relativistic method based on the Dirac equation for calculating fully
differential cross sections for ionization in ion-atom collisions is developed.
The method is applied to ionization of the atomic hydrogen by antiproton
impact, as a non-relativistic benchmark. The fully differential, as well as
various doubly and singly differential cross sections for ionization are
presented. The role of the interaction between the projectile and the target
nucleus is discussed. Several discrepancies in available theoretical
predictions are resolved. The relativistic effects are studied for ionization
of hydrogenlike xenon ion under the impact of carbon nuclei.
