Stopping Power of a Medium for Heavy, Charged Particles

It is shown that the orbital motion of electrons in the molecules of a medium is important for the stopping power of slow charged particles. This is due to the strong dependence of the momentum transfer in a Coulomb field on the relative velocity. Equations for determining the absolute stopping power of an arbitrary medium are derived on the basis of classical mechanics for the entire nonrelativistic energy range. For the high-energy range this equation corresponds to Bethe's formula, and for low energies, to the Fermi-Teller formula. It is concluded, from this equation and from the experimental data, that electron capture is not important in the slowing down of protons. It starts being important for $\alpha$ particles and is decisive for particles of higher charge. The stopping power of H, ${\mathrm{H}}_2$, and A for protons and of ${\mathrm{H}}_2$ for $\alpha$ particles is calculated. Good agreement with the experimental data is obtained.