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QUANTUM PHYSICS: CONFIRMATION OF THE EFIMOV EFFECT

The following points are made by B.D. Esry and C.H. Greene (Nature 2006 440:289):

1) In 1970, Vitaly Efimov, with a new Russian PhD in theoretical nuclear physics, predicted a bizarre quantum-mechanical effect[1]: a system consisting of three particles, none of whose two-particle subsystems is stable, can, under certain circumstances, produce an infinite number of bound energy levels. That prediction has been a source of concern for theorists ever since. Yet time and again, attempts to disprove the "Efimov effect" have only verified its existence, albeit -- until now --purely theoretically. New work[2], more than 35 years after the initial prediction, presents the first convincing experimental evidence for the effect.

2) The question explored by Efimov was simple: if each possible pair of particles in a three-particle system is just shy of binding (so there are no bound states), what is the nature of the energy spectrum of the three particles? The answer, that the number of bound states in which the three particles can exist is infinite, is initially surprising. But it can be rationalized by noting that if two particles are already infinitesimally close to forming a bound state, just the faintest whiff of an additional attraction will be sufficient to push them over the edge to confederation. A third attracting particle accomplishes precisely that, no matter how far away from the other two it may roam, or how weak its additional attraction may be. Unsurprisingly, given this qualitative argument, three-body Efimov states have been theoretically found[3] to be extremely "floppy", with all imaginable triangular shapes -- equilateral, isosceles, scalene -- and even linear configurations being comparably probable.

3) The Efimov effect is distantly related to Llewellyn Hilleth Thomas's 1935 proof[4] that, in its ground state, a system of three particles that interact only within a vanishingly small range collapses to an infinitely small size, and its binding energy becomes infinitely large. Efimov discussed the link particularly clearly in a 1971 article[5] that derived an effective potential-energy curve for such a system as a function of a three-particle "hyperradius", R, which is proportional to the root-mean-square distance of the three particles from their center of mass. The three-body potential-energy function turns out to be proportional to R^(-2), and it has a universal, negative coefficient of proportionality. The properties of such a potential are well known, because a similar form governs the motion of a charged particle in the field of a permanent dipole (where two charges of equal and opposite sign are separated by a small distance).

References (abridged):

1. Efimov, V. Phys. Lett. B 33, 563 564 (1970)

2. Kraemer, T. et al. Nature 440, 315 318 (2006)

3. Esry, B. D. , Lin, C. D. & Greene, C. H. Phys. Rev. A 54, 394 401 (1996)

4. Thomas, L. H. Phys. Rev. 47, 903 909 (1935)

5. Efimov, V. N. Sov. J. Nucl. Phys. 12, 589 595 (1971)

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