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Pré-Publication, Document De Travail Année : 2011

Trimers in the resonant 2+1 fermionic problem on a narrow Feshbach resonance : From Efimovian Dawn to Hydrogenoid Twilight

Yvan Castin

Résumé

We study the quantum three-body free space problem of two same-spin-state fermions of mass $m$ interacting with a different particle of mass $M$, on a narrow Feshbach resonance with infinite $s$-wave scattering length. This problem is made interesting by the existence of a tunable parameter, the mass ratio $\alpha=m/M$. By a combination of analytical and numerical techniques, we obtain a detailed picture of the spectrum of three-body bound states, within {\sl each} sector of fixed total angular momentum $l$. For $\alpha$ increasing from $0$, we find that the trimer states first appear at the Efimovian threshold $\alpha_c$, where the Efimov exponent $s$ vanishes, and that the {\sl entire} trimer spectrum (starting from the ground trimer state) is geometric for $\alpha\to \alpha_c^+$, with a global energy scale that has a finite and non-zero limit. For further increasing values of $\alpha$, the least bound trimer states still form a geometric spectrum, with an energy ratio $\exp(2\pi/|s|)$ that becomes closer and closer to unity, but the most bound trimer states deviate more and more from that geometric spectrum and eventually form a hydrogenoid spectrum.
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Dates et versions

hal-00607657 , version 1 (10-07-2011)
hal-00607657 , version 2 (08-12-2011)
hal-00607657 , version 3 (06-01-2015)

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Yvan Castin, Edoardo Tignone. Trimers in the resonant 2+1 fermionic problem on a narrow Feshbach resonance : From Efimovian Dawn to Hydrogenoid Twilight. 2011. ⟨hal-00607657v1⟩
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