Channeling ofH+1,D+2, andHe++3Ions in Germanium: A Diffraction Calculation

Abstract

The channeling properties of ${}_{}{}^1{}_{}{}^{}\mathrm{H}_{}^{+}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{}^{+}{}_{}{}^{}$, and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{++}{}_{}{}^{}$ ions in germanium have been examined, using a diffraction model for the interaction between the lattice and the channeled ions. The stopping power ($-\frac{\mathrm{dE}}{\mathrm{dx}}$) and the differential mean-square energy spread ($\frac{d{\sigma }^2}{\mathrm{dE}}$) of the channeling energy spectrum have been calculated for each of the above ions in the energy range 3 to 8 MeV for three incident directions in the lattice. The energy states of the electrons in the lattice are approximated by using a shell model of the lattice atoms. $Z$ electrons per atom are assumed to occupy a rigid, negatively charged shell surrounding an atomic core, where $Z$ is an adjustable parameter in the calculation. An harmonic approximation to the shell-core and shell-shell interactions in the lattice then leads to phononlike excitations in which the shell and atomic core are moving out of phase. This introduces a time-dependent polarization in the lattice which interacts strongly with the incident ions. The lower-energy portion of this excitation spectrum is indetified with the plasmon spectrum of the solid, and the known properties of the plasmons are included in the calculation. The parameter $Z$ is adjusted to give agreement between the theoretical and experimental channeling energy losses. No experimental data are presently available for comparison with the calculations for ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{++}{}_{}{}^{}$. The results indicate that each of the three directions considered in the calculations can be characterized by a reasonable value of $Z$, which is expected to be $\gtrsim 4$ depending on the degree to which the valence electrons shielded the inner electrons. For ions incident near the directions indicated these values are $〈1,1,0〉$, $Z=5.6\mathrm{}\pm 0.3$; $〈1,1,1〉$, $Z=8.6\mathrm{}\pm 0.4$; $〈1,1,2〉$, $Z=7.2\mathrm{}\pm 0.3$.