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

¹  Jack Dodd Centre for Quantum Technology, Department of Physics, University of Otago 730 Cumberland St, Dunedin 9016, New Zealand
²  Department of Physics, St. Francis Xavier University - Antigonish, Nova Scotia B2G 2W5, Canada
³  Department of Physics & Astronomy, McMaster University - 1280 Main St. West, Hamilton, Ontario K2H 4C3, Canada

Corresponding author: daniel.schumayer@gmail.com

Received: 3 November 2009
Accepted: 14 December 2009

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 p_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.