We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length ${a}_{\mathrm{o}\mathrm{s}\mathrm{c}}$ . The atoms are assumed to interact through a short-range potential with a scattering length $a$ , and the short-distance behavior of the three-body wave function is characterized by a parameter $\ensuremath{\theta}$. For large positive $a/{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}$ , the energies of states that, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\ensuremath{\theta}$. For other states, the $\ensuremath{\theta}$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}|\ensuremath{\gg}1$.We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length ${a}_{\mathrm{o}\mathrm{s}\mathrm{c}}$. The atoms are assumed to interact through a short-range potential with a scattering length $a$, and the short-distance behavior of the three-body wave function is characterized by a parameter $\ensuremath{\theta}$. For large positive $a/{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}$, the energies of states that, in the absence of the trap, correspond to three free atoms approach values independent of $a$ and $\ensuremath{\theta}$. For other states, the $\ensuremath{\theta}$ dependence of the energy is strong, but the energy is independent of $a$ for $|a/{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}|\ensuremath{\gg}1$.

arXiv:cond-mat/0203014Physical Review LettersNov 27, 200265 citations

Long-range scattering of two- and three-body quantum systems

Volker Enß

Journées Équations aux dérivées partiellesJan 1, 198919 citations

LARGE ATOMIC AND NUCLEAR THREE-BODY SYSTEMS: SCATTERING AND BINDING

Lauro Tomio, Marcelo Takeshi Yamashita, T. Frederico

The universal character of non-relativistic large three-body bosonic systems is addressed, with focus on highly interesting situations that occur in low-energy nuclear and atomic physics. Investigations on the trajectory of the first excited Efimov state, in a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems, are reported. The approach is applied to n-n-18C, where the n - n virtual energy and the three-body ground state are kept fixed. It is shown that the real part of the elastic s-wave phase-shift ([Formula: see text]) presents a zero, or a pole in [Formula: see text], when the system has an Efimov excited or virtual state. A brief discussion is given on the relevance of the approach for ultracold atom physics with tunable scattering lengths.The universal character of non-relativistic large three-body bosonic systems is addressed, with focus on highly interesting situations that occur in low-energy nuclear and atomic physics. Investigations on the trajectory of the first excited Efimov state, in a renormalized zero-range three-body model for a system with two bound and one virtual two-body subsystems, are reported. The approach is applied to n-n-18C, where the n - n virtual energy and the three-body ground state are kept fixed. It is shown that the real part of the elastic s-wave phase-shift ([Formula: see text]) presents a zero, or a pole in [Formula: see text], when the system has an Efimov excited or virtual state. A brief discussion is given on the relevance of the approach for ultracold atom physics with tunable scattering lengths.

Modern Physics Letters AApr 30, 20090 citations

Ultra-low energy elastic scattering in a system of three He atoms

Vladimir Roudnev

arXiv:physics/0206058Chemical Physics LettersJan 1, 200342 citations

Three-Body Recombination of Li6 Atoms with Large Negative Scattering Lengths

Eric Braaten, H.‐W. Hammer, Daekyoung Kang +1 more

The three-body recombination rate at threshold for distinguishable atoms with large negative pair scattering lengths is calculated in the zero-range approximation. The only parameters in this limit are the 3 scattering lengths and the Efimov parameter, which can be complex-valued. We provide semianalytic expressions for the cases of 2 or 3 equal scattering lengths, and we obtain numerical results for the general case of 3 different scattering lengths. Our general result is applied to the three lowest hyperfine states of 6Li atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.The three-body recombination rate at threshold for distinguishable atoms with large negative pair scattering lengths is calculated in the zero-range approximation. The only parameters in this limit are the 3 scattering lengths and the Efimov parameter, which can be complex-valued. We provide semianalytic expressions for the cases of 2 or 3 equal scattering lengths, and we obtain numerical results for the general case of 3 different scattering lengths. Our general result is applied to the three lowest hyperfine states of 6Li atoms. Comparisons with recent experiments provide indications of loss features associated with Efimov trimers near the 3-atom threshold.

arXiv:0811.3578Physical Review LettersAug 13, 200956 citations

THEORY OF RESONANCE SCATTERING ON ATOMIC SYSTEMS

M.V. Kazarnovski, Alexander V. Stepanov

Acta Physica Academiae Scientiarum HungaricaeJan 1, 19622 citations

We calculate energy levels of two and three bosons trapped in a harmonic oscillator potential with oscillator length

{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}

. The atoms are assumed to interact through a short-range potential with a scattering length

a

, and the short-distance behavior of the three-body wave function is characterized by a parameter $\ensuremath{\theta}$. For large positive

a/{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}

, the energies of states that, in the absence of the trap, correspond to three free atoms approach values independent of

a

and $\ensuremath{\theta}$. For other states, the $\ensuremath{\theta}$ dependence of the energy is strong, but the energy is independent of

a

for $|a/{a}_{\mathrm{o}\mathrm{s}\mathrm{c}}|\ensuremath{\gg}1$.