Classical Scattering Cross Section for a Cut-Off Coulomb Potential

The penetration of matter by charged particles and of transport coefficients for ionized gases are often calculated by the method of impact parameters wherein the Coulomb scattering cross section is set equal to zero for orbits with impact parameters larger than the range of the force. The method does not correspond to a reasonable assumption on the interaction, however, and it is sometimes difficult for students in classical mechanics and plasma physics to accept. It is therefore interesting that the cross section for scattering by a Coulomb force which is zero beyond a certain radius of interaction can easily be calculated by the methods usually presented in junior-senior level courses in classical mechanics. The result provides a simple basis for the method of impact parameters.