  The Lorentz-Dirac radiation reaction formula predicts that the position shift
of a charged particle due to the radiation reaction is of first order in
acceleration if it undergoes a small acceleration. A semi-classical calculation
shows that this is impossible at least if the acceleration is due to a
time-independent potential. Thus, the Lorentz-Dirac formula gives an incorrect
classical limit in this situation. The correct classical limit of the position
shift at the lowest order in acceleration is obtained by assuming that the
energy loss at each time is given by the Larmor formula.
