Geometric scaling in the spectrum of an electron captured by a stationary finite dipole
D. SchumayerJack Dodd Centre for Quantum Technology, Department of Physics, University of Otago 730 Cumberland St, Dunedin 9016, New ZealandB. P. van ZylDepartment of Physics, St. Francis Xavier University - Antigonish, Nova Scotia B2G 2W5, CanadaR. K. BhaduriDepartment of Physics & Astronomy, McMaster University - 1280 Main St. West, Hamilton, Ontario K2H 4C3, CanadaD. A. W. HutchinsonJack Dodd Centre for Quantum Technology, Department of Physics, University of Otago 730 Cumberland St, Dunedin 9016, New Zealand
2010en
ABI
Abstract
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.
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