In this Rapid Communication an ab initio approach to the inner-shell c
harge-transfer process in heavy-ion-solid-target collisions is present
ed. Unlike the extensively studied ion-gas-target systems heavy-ion-so
lid-target measurements showed systematic deviations from available th
eories. These deviations were interpreted as revealing a fundamental d
ifference between collisions with gas and those with solid targets. Wi
thin the framework of our relativistic formalism a quantitative descri
ption of heavy-ion-solid-target charge-transfer processes is reached,
thus laying to rest the old problem of solid-target effects. As an exa
mple, the results for Cu on a Ni solid target are discussed.