The stopping power of slow antiparticles penetrating electron gases ar
e evaluated within a scattering theory approach to the energy-loss pro
blem. The required effective scattering potential is obtained from a s
elf-consistent density-functional calculation. A relationship of the s
topping power S proportional to \Z\(b) (b is in the range of 0.7-0.9)
at low velocities is found, in contrast to the Z(2) dependence predict
ed 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 b
e the main reason for the monotonic increment of the stopping power as
a function of \Z\.