The free electron model and the electronic energy losses of protons at low velocities interacting with polycrystalline tantalum

In this letter, we report experimental data and theoretical work on the electronic energy loss and energy loss straggling of protons transmitted through self-supported thin films of tantalum in a polycrystalline tetragonal phase (beta-Ta). Low-energy protons with energies below 10 keV and Ta films with nominal thickness of 6, 9 and 12 nm are used. The aim of this work is to understand the unexpected values of the Ta stopping power for low-energy proton backscattering reported recently, which are far from the prediction of the standard free electron gas model and semi-empirical approaches. This had led the authors to conclude the failure of the free electron model. Our transmission measurements confirm these experimental results. In this work, a qualitative discussion and quantitative explanation of our experimental results is given, using an approach based on the density functional theory within the framework of the free electron gas (FEG) model. We performed semiclassical deterministic trajectory simulations and employ the local density approximation model, using an inhomogeneous electron density distribution and the polycrystalline character of Ta samples.