Critical Angles for Channeling of 1- to 25-keV ${\mathrm{H}}^{+}$, ${\mathrm{D}}^{+}$, and ${\mathrm{He}}^{+}$ Ions in Gold Crystals

The critical angle for channeling in the low-energy region is measured for ${\mathrm{H}}^{+}$, ${\mathrm{D}}^{+}$, and ${\mathrm{He}}^{+}$ ions transmitted through single-crystal gold foils. It is found that the theoretical calculation by Lindhard fits the experimental points within the experimental errors if the constant $C$ is given the value 2.15. No difference is found between ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ ions. The critical angle for ${\mathrm{He}}^{+}$ ions is found to be 1.13±0.04 times larger than for ${\mathrm{D}}^{+}$ or ${\mathrm{H}}^{+}$ ions of the same energy.