A model of an ion embedded in jellium is presented. The static charge state of a heavy ion is determined self-consistently. The effective charge of a heavy ion at low velocities is calculated, which is incorporated with the Brandt-Kitagawa effective charge theory to take the velocity dependence of the effective charge into account. The quantal harmonic oscillator model is generalized to calculate the electronic energy loss of heavy ions colliding with a carbon target. The results are compared with available experimental data.

The stopping power of slow antiparticles penetrating electron gases are evaluated within a scattering theory approach to the energy-loss problem. The required effective scattering potential is obtained from a selfconsistent density-functional calculation. A relationship of the stopping power Sα|Z|b (b is in the range of 0.7-0.9) at low velocities is found, in contrast to the Z2 dependence predicted by the linear-response theory. The diffuse distribution of partial wave contributions of screening electrons in the case of antiparticles is quite different from that for normal particles and is thought to be the main reason for the monotonic increment of the stopping power as a function of |Z|.