Classical motion of an electron in an electric-dipole field II. Point dipole case

The classical motion of an electron in the field of a point electric dipole is analysed. It is shown that the only motion for which the distance γ from the dipole to the electron does not either increase without limit or decrease to and remain at zero is that for which γ is constant and the total energy E is zero. A necessary condition for such bound motion is D > 3 surd 3 p ϕ 2 /4 me , where D is the dipole moment, p ϕ is the component of angular momentum along the dipole axis, and m and e are the electronic mass and charge. It follows that any point dipole can bind an electron classically.