Electronic Stopping and Momentum Density of Diamond Obtained from First-Principles Calculations

We calculate the "head" element or the (0,0)-element of the wave-vector and frequency-dependent dielectric matrix of bulk crystals via first-principles, all-electron Kohn-Sham states in the integral of the irreducible polarizability in the random phase approximation. We approximate the macroscopic "head" element of the inverse matrix by its reciprocal value, and integrate over frequencies and momenta to obtain the electronic energy loss of protons at low velocities. Numerical evaluation for diamond targets predicts that the band gap causes a strong non-linear reduction of the electronic stopping power at ion velocities below 0.2 atomic units.