Using high-resolution x-ray spectroscopy, we have measured, as a function of target thickness, the relative intensities of the fine-structure components of the Balmer line emitted by fast hydrogen-like krypton ions propagating through thin carbon and copper targets. Our results are in clear disagreement with the predictions of a rate-equation model accounting for collisional l mixing. On the other hand, good agreement is found with a model taking solely into account a wake field-induced Stark mixing of degenerate n,l,j substates. Within this model, the values obtained for the electric field agree well with those deduced from measured total stopping power, which indicates that the effect of core electrons must be considered. Furthermore, off-diagonal density matrix elements of the initial capture process to the n = 3 states are inferred from the experimental intensities. A comparison, for carbon targets, with available (gas-phase) calculations of these matrix elements, reveals important differences.