V. Efimov [1] proposed in 1970 that a threebody system with very weak twoparticle interactions can form strongly bound states if the twoparticle scattering length becomes much larger than the range of the potential. In fact, if the twobody interactions approach zero, the number of resonant threebody states can approach infinity. The helium trimer , first identified in 1977, has been believed to be such a threebody system. In the past two or three years, the field has exploded, with several heavier lowtemperature atomic trimers, notably those containing , , , and , having been verified to exhibit the Efimov effect [2]. Given an interatomic potential of the form , let the coupling constant be reduced below , either in concept or by means of some newly developed lowtemperature techniques involving Feshbach resonances. It is then found that Efimov trimers are created with binding energies in the millikelvin (mK) range. The green lines represent the energies of these Efimov states as a function of coupling constant. As the temperature is raised these dissociate directly into three free atoms. If, however, is increased, while maintaining the low temperature, the trimers are found to dissociate into dimers+monomers, which occupy the solid green region of the graphic. The author, in collaboration with L. L. Lohr [3], derived exact solutions for dimers and trimers based on a model in which the interatomic interaction has the form of a Dirac bubble potential, . As shown by Efimov, the precise form of the interatomic potential is not important, only its resonant character. The results derived to construct the graphic can therefore be considered to be of general validity.
[1] V. Efimov, "Energy Levels Arising from Resonant TwoBody Forces in a ThreeBody System," Physics Letters, 33B(8), 1970 pp. 563–564. [3] L. L. Lohr and S. M. Blinder, "Analytic Representation of the Efimov Effect in the Helium Trimer," Physical Review A 69(6) , 2004 064102 pp. 1–4.
