Angular distribution of ions axially channeled in a very thin crystal: Experimental and theoretical results

We have studied the angular distributions for 6--30-MeV ${\mathrm{C}}^{\mathit{q}+}$ (q=4--6) and 2--9-MeV ${\mathrm{H}}^{+}$ ions axially channeled in the [001] direction of a thin silicon crystal (1792 and 1900 \AA{}). We report highly structured two-dimensional angular distributions that depend sensitively on the projectile's velocity and incident charge state and the target's thickness and azimuthal orientation. Some structure in the angular contour maps is the result of a rainbow effect in axial channeling (i.e., extrema in the classical deflection function). State-to-state charge-state distributions, which are required to interpret the data accurately, have also been measured. All measured angular distributions have been explained via Monte Carlo trajectory calculations using Moliere's approximation to the Thomas-Fermi screening function and a screening length given by target electrons alone. The calculations indicate that all projectile velocity and charge-state effects and the target-thickness effects observed are the result of the projectile's transverse oscillatory motion in the channel. Using this information, we show that swift heavy-ion and proton angular distributions are simply related using a scaling law that depends only on the projectile's velocity and charge-to-mass ratio and on the crystal thickness.