Electronic stopping from orbital mean excitation energies including both projectile and target electronic structure

In this work, we revisit our Bethe theory for the energy deposition of swift charged particles with electronic structure when colliding with atomic targets [Phys. Rev. A, 55 2864 (1997)]. As the projectile ion beam has a mixture of several projectile charge states, the electronic stopping cross section is the sum of contributions from all the Z₁ electrons. We use the independent particle approximation for the mean excitation energies such that the electronic stopping cross section becomes a sum of contributions from all the target electrons, N₂. We use an analytical expression of the generalized oscillator strength based on the Harmonic Oscillator approximation such that the stopping cross section becomes a function of only the orbital mean excitation energy, I_0i. These orbital mean excitation energies determine the atomic mean excitation energy I₀ via the Bragg's rule. The projectile electronic density for a given number of electrons N₁ ≤ Z₁ is derived from the Local Plasma Approximation and we thereby obtain an analytic expression for the total stopping cross section for projectiles with structure in terms of the target orbital mean excitation energies within the First Born Approximation. We compare the results of our calculations for several projectile–target combination to experiment showing an excellent agreement to the experimental data available in the literature.