  Elastic charge-exchange in relativistic heavy ion collisions is responsible
for the non-disruptive change of the charge state of the nuclei. We show that
it can be reliably calculated within the eikonal approximation for the reaction
part. The formalism is applied to the charge-pickup cross sections of 158
GeV/nucleon Pb projectiles on several targets. The relative contributions of
pion- and rho-exchange are determined, using a single-particle model for the
internal structure of the nuclei. The calculated cross sections are
non-negligible for heavy targets. It is shown that these cross sections can be
useful to obtain information on the Gamow-Teller transition strengths of the
nuclei.
