Nonlinear hydrodynamic theory of electronic stopping power

Abstract

We have formulated a fully nonlinear hydrodynamic theory of the electronic stopping power of charged particles in matter. In the zero velocity limit, our theory reduces to a Thomas-Fermi-Dirac-von Weiszäcker description of the electronic screening around an external point charge. With increasing velocity, the dynamic screening charge is obtained from a numerical solution of the hydrodynamic equations. We also introduce a fluid viscosity which allows one to simulate the single-particle excitations responsible for the low velocity stopping power. A comparison of our results for protons and antiprotons with linear response theory shows that nonlinearities in the screening are important for all velocities up to the stopping power maximum. In addition, comparison with earlier nonlinear quantum-mechanical calculations at low velocities shows that the hydrodynamic theory provides a realistic and accurate description of the stopping power phenomenon.