  We examine the energy spectrum of a charged particle in the presence of a
{\it non-rotating} finite electric dipole. For {\emph{any}} value of the dipole
moment $p$ above a certain critical value p_{\mathrm{c}}$ an infinite series of
bound states arises of which the energy eigenvalues obey an Efimov-like
geometric scaling law with an accumulation point at zero energy. These
properties are largely destroyed in a realistic situation when rotations are
included. Nevertheless, our analysis of the idealised case is of interest
because it may possibly be realised using quantum dots as artificial atoms.
