Rutherford scattering with radiation reaction

Numerical solutions of the Lorentz-Dirac equation are presented for the scattering of a spinless point particle in the static Coulomb field of a fixed point of opposite charge. Within the framework of classical electrodynamics, radiation reaction has thus been included exactly. For any initial energy, there is a minimum impact parameter below which the particle is captured. The classical capture cross section is readily found and is presented here as a function of incident energy. Scattering cross sections for a fixed initial energy ($\simeq {10}^{3}m{c}^2$) are also presented and compared with those for relativistic Rutherford scattering. Loss of energy and angular momentum to radiation is calculated, and the total energy (particle plus radiation) is found to be accurately conserved in all cases not involving capture. Radiation reaction is seen frequently to cause the projectile to accelerate away from the attractive scattering center.