Calculations of nuclear stopping, ranges, and straggling in the low-energy region

Recent experimental results indicate that existing theories of low-energy nuclear stopping power based upon statistically derived potentials, such as the Thomas-Fermi potential, are in error by over 100%. This paper shows that these errors can be reduced to less than 10% by using more realistic interatomic potentials. We have calculated interatomic potentials from first principles in the free-electron approximation for 14 diatomic interactions representing light particles incident on heavy targets (${M}_{1}\ensuremath{\ll}{M}_{2}$), self-irradiation (${M}_{1}={M}_{2}$), and heavy particles on light targets (${M}_{1}\ensuremath{\gg}{M}_{2}$). The potentials were approximated by a Moli\`ere-like form and the parameters tabulated for general covenience. The classical orbit equation was integrated numerically for bare potentials and the scattering cross section, stopping power, range, and straggling calculated. Simple three-parameter expressions for the stopping power are given which are directly integrable to obtain the range. The results are in reasonable agreement with experiment for a representative Kr-C potential and agree within 10% for an average potential derived from the free-electron calculations.