An elementary exposition of the Efimov Effect

Abstract

Two particles that are just shy of binding may develop an infinite number of shallow bound states when a third particle is added. This counter intuitive quantum mechanical result was first predicted by V. Efimov for identical bosons interacting with a short-range pair-wise potential. The so-called Efimov effect persists even for non-identical particles, provided at least two of the three bonds are almost bound. The Efimov effect has recently been verified experimentally using ultra-cold atoms. In this article, we explain the origin of this effect using only elementary quantum mechanics, and summarize the experimental evidence for the Efimov effect. A new, simple derivation for the number of Efimov states is given in the Appendix.

4 figures. Version to appear in American Journal of Physics. Minor typos fixed

References in corpus (7)

• Observation of an Efimov spectrum in an atomic system
• Universality in Three- and Four-Body Bound States of Ultracold Atoms
• Observation of universality in ultracold 7Li three-body recombination
• Observation of heteronuclear atomic Efimov resonances
• Efimov Physics in Cold Atoms
• Analytical solution of the bosonic three-body problem
• Efimov states and their Fano resonances in a neutron-rich nucleus

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• Fermions meet two bosons -- the heteronuclear Efimov effect revisited
• Efimov effect for two particles on a semi-infinite line
• Fall-to-the-centre as a $\mathcal{P}\mathcal{T}$ symmetry breaking transition
• A semiclassical analysis of the Efimov energy spectrum in the unitary limit
• Efimov Trimers : Analytic Solution Via Separable Potentials