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, $\rho$, and of energy, $\epsilon$, 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.

• Received 19 May 1961

DOI:https://doi.org/10.1103/PhysRev.124.128