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2008

Analytical solution of the bosonic three-body problem

Gogolin, Alexander O., Mora, Christophe, Egger, Reinhold

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We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers).

Modelling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schr\"odinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained.
We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate.

Analytical solution of the bosonic three-body problem · Around

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The exact solution can be fully justified in the framework of the theory of generalized hypergeometric functions

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The Efimov trimer disappears into the atom-dimer continuum at the scattering length a ∗ > 0 a_{*}>0 given by a ∗ κ ∗ ≃ 0.070764 a_{*}\kappa_{*}\simeq 0.070764 [ 5 ] . By numerical solution of Eq. ( 5

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