Binary-encounter stopping cross sections. III. Straggling and screening

Abstract

A previously developed binary-encounter model describing the slowing down of energetic heavy charged particles over a broad range of incident-particle energies is employed to calculate energy straggling as a function of target ${Z}_{2}$ for incident helium and hydrogen. This model seriously overestimates the measured stopping cross sections at high incident-particle energy for helium on heavy target atoms, but appears to yield more reasonable results for energy straggling. The large results in the stopping calculation are attributed to the neglect of the distortion of the electron charge cloud during the collision. A screened interaction, based on screening in a free-electron gas, is employed to estimate the size of the effect on both the stopping and straggling results for 10-MeV incident ${\mathrm{He}}^{++}$ on target atoms $1\ensuremath{\le}{Z}_{2}\ensuremath{\le}36$, and for equilibrium-charge-state beams of hydrogen at energies 1 keV to 1 MeV on a number of targets. It was found that the neglect of distortion may result in errors equivalent to or greater than those due to the neglect of the long-range dipole interactions when estimating $S$, particularly at higher energies. For the straggling calculation both of these effects result in considerably smaller correction to the binary-encounter method.