Channeling of fast protons, deuterons, andαparticles

The ratios of channeled to random stopping powers have been obtained for light ions with $Z_1^2\frac{E}{M}\simeq 160$ MeV travelling along the $〈110〉$ and $〈111〉$ axial directions, using a coincidence technique in which a silicon $\frac{\mathrm{dE}}{\mathrm{dx}}$ detector was used as the channeling crystal. Dechanneling lengths $x_{\frac{1}{2}}$ and the trajectory spread contribution to energy loss straggling were also deduced from the $\frac{\mathrm{dE}}{\mathrm{dx}}$ spectra. The concept of "best-channeled "particles is not applicable to experimental data obtained with targets of thickness $x\gtrsim x_{\frac{1}{2}}$. To compare experiment and theory, a first-order correction is made by averaging the valence-electron density distribution over the spread of trajectories permitted within the channel. Simple calculations are made which successfully reproduce the dechanneling lengths, trajectory spreads, and the stopping-power ratios for silicon. The simple formula for stopping-power ratios is then applied with equal success to the available high-energy data for germanium and is used to relate both silicon and germanium data to the existing quantum-theoretical treatments for "best-channeled" particles. The theory of Golovchenko and Esbensen gives good agreement with our deduced stopping powers for "best-channeled" particles.