Presented is a study of the charge-state evolution of relativistic lead ions passing through a thin aluminum stripper foil. It was motivated by the Gamma Factory project at CERN, where optical laser pulses will be converted into intense gamma-ray beams with energies up to a few hundred MeV via excitation of atomic transitions in few-electron heavy-ions at highly relativistic velocities. In this study all charge-states starting from Pb$^{54+}$ up to bare ions are considered at kinetic projectile energies of 4.2 and 5.9 GeV/u. To this purpose the BREIT code is employed together with theoretical cross-sections for single-electron loss and capture of the projectile ions. To verify the predicted charge-state evolution, the results are compared to the very few experimental data being available for highly-relativistic lead beams. Reasonable agreement is found, in particular for the yields of Pb$^{80+}$ and Pb$^{81+}$ ions that were recently measured using an aluminum stripper foil located in the transfer beam line between the PS and SPS synchrotron accelerators at CERN. The present study lays the groundwork to optimize the yields of charge states of interest for experiments within the scientific program of the future Gamma Factory project.
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