The screening and stopping coefficients of slow light ions

We present a theoretical approach to study the screening charge density n(s)(r) and the respective stopping coefficient Q for hydrogen and helium at the low velocity limit. An electron gas, with electronic density n(e), is used to represent the conduction or valence electrons of the target material. Solving numerically the Schrödinger radial equation, for a given potential V (r), the phase shifts δ(l) and the corresponding stopping coefficient Q are calculated as a function of n(e). The cusp condition and the Friedel sum rule are imposed on the charge density n(r) = n(s)(r)+n(e) at the origin and to the phase shifts, respectively. The results are compared with density functional calculations and with available experimental results.