Geometric scaling in the spectrum of an electron captured by a stationary finite dipole

Abstract

We examine the energy spectrum of a charged particle in the presence of a non-rotating finite electric dipole. For any value of the dipole moment p above a certain critical value pc 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.