Contribution from close and distant collisions to $K$-shell excitation in Ge measured using the channeling technique for relativistic protons, ${\pi }^{+}$, and ${\pi }^{-}$

For the first time, the impact-parameter dependence for $K$-shell ionization was measured for relativistic projectiles, although in an indirect way. Experimentally, channeling of GeV projectiles was used to gradually exclude close-encounter processes. In the present experiment, the Lorentz $\gamma$ factor varied between ∼2 and ∼100; in this region, the contribution from distant collisions becomes increasingly important and amounts to about 50% of the total yield for $\gamma \sim 100$. The experimental data are compared to theoretical calculations of impact-parameter distributions, and the agreement is fair for both positive and negative particles.