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We consider relativistic collisions of heavy hydrogen-like ions with hydrogenand helium atoms in which the ion-atom interaction causes both collidingparticles to undergo transitions between their internal states. Using anapproach enabling one, for the first time, to give a detailed description ofthis important case of the relativistic quantum few-body problem we concentrateon the study of the longitudinal momentum spectrum of the atomic recoil ions.We discuss the role of relativistic and higher order effects, predict asurprisingly strong influence of the projectile's electron on the momentumtransfer, draw the general picture of the recoil ion formation and show thatthe important information about the doubly inelastic collisions could beobtained in experiment merely by measuring the recoil momentum spectrum.

Four-body quantum dynamics of two-center electronic transitions in relativistic ion-atom collisions and target recoil momentum spectroscopy