Inelastic cross-sections and energy loss properties by non-relativistic heavy ions in zirconium dioxide

A formalism for the inelastic cross-section for electronic collisions of protons and heavier ions in a material is developed based on a quadratic extrapolation of the experimentally based dipole oscillator strength distribution (DOSD) of the material into the energy momentum plane. The approach is tested by calculating various energy loss properties in zirconium dioxide. Mean free path, stopping power and continuous slowing down approximation (csda) range are predicted as a function of ion energy for various incident ions, with the stopping powers compared to experimental data to assess the effectiveness of the methodology. The DOSD is straightforwardly obtained from the experimentally measured energy loss function data below 80 eV and atomic photo-absorption cross-section data above 100 eV. Agreement between the results of the calculation for stopping power and the experimental data is within 10% for all ions when compared for energies greater than the Bragg peak. The discrepancy is larger below the peak due to limitations in the methodology, especially the failure to make corrections for the Barkas and higher order effects and the lack of charge cycling cross-section data.