Scattering from the charge radius of a neutral particle

In the physics curriculum, students normally learn about Rutherford scattering from charged particles in classical mechanics, quantum mechanics, and quantum field theory. This paper provides a pedagogical introduction to the problem of scattering from neutral particles, characterizing an effective charge distribution by a charge radius. Using the Born approximation, the quantum mechanical and field theoretic calculations agree to leading order in the long-wavelength limit but disagree with the classical calculation.