Energy Dissipation by Ions in the kev Region

TLDR

At low energies ionic collisions with atoms are largely elastic, and the derived range‑energy curve shows that electronic excitation becomes increasingly important at higher ion energies. The authors derive simple theoretical approximations for scattering cross sections, ranges, and straggling using power potentials and a Thomas‑Fermi universal potential, yielding a forward‑peaked scattering distribution and a natural range–energy measure, and provide an approximate formula for electronic stopping that rises proportionally with ion velocity at low to moderate speeds. The resulting approximations produce a forward‑peaked scattering distribution, a range‑energy curve highlighting increasing electronic excitation at higher energies, and an electronic stopping formula proportional to ion velocity, which the authors use to explain observed isotope effects in range measurements.

Abstract

At low energies ionic collisions with atoms are largely elastic. Simple theoretical approximations to scattering cross sections, ranges and straggling are derived for power potentials, showing that the scattering is peaked in the forward direction rather than isotropic. Using an approximate universal potential of Thomas-Fermi type a natural measure of range, $\ensuremath{\rho}$, and of energy, $\ensuremath{\epsilon}$, is obtained for all ions in all substances. The corresponding range-energy curve is computed.At higher ion energies the electronic excitation becomes increasingly important. An approximate formula is given for the electronic stopping contribution, increasing proportional to ion velocity at low and moderate velocities. These results are applied in the interpretation of a few isotope effects, observed in range measurements.