Numerical solutions to two-body problems in classical electrodynamics: Head-on collisions with retarded fields and radiation reaction. II. Attractive case

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Abstract
Head-on collisions of oppositely charged particles obeying the Lorentz-Dirac equation with retarded fields have been investigated both numerically and analytically. We show, in agreement with Eliezer for this case, that no physical solutions exist with finite initial values of position, energy, and acceleration and that Clavier's contention to the contrary is flawed. If the electric field is everywhere finite, a physical solution does exist, but in the limit as the field becomes singular, one or more of the initial values of the physical solution must become infinite. Thus, difficulties with the "physical solution" of the Lorentz-Dirac equation for this problem occur not just when the particles are close together, but as soon as they are released from rest at large separations.