Three-Body van der Waals Forces in Quartet State Alkali Trimers.

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Published Mar 17, 1997• 0 citations

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Published Mar 17, 1997• 0 citations

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Christian B. Langmack, Richard Schmidt, W. Zwerger

We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in $^{39}\mathrm{K}$ . Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $\ensuremath{-}8$ and $\ensuremath{-}10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in $^{39}\mathrm{K}$. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $\ensuremath{-}8$ and $\ensuremath{-}10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.

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We construct a simple model to calculate the trimer bound state energy ${E}_{T}^{(n)}$ and three-body recombination rate ${K}_{3}^{0}$ of three identical bosons with van der Waals interaction without using any two- or three-body fitting parameter. Using this simple model, we investigate the influence of the van der Waals finite-range effect on ${E}_{T}^{(n)}$ and ${K}_{3}^{0}$ . Our calculation shows that the finite-range effect leads to the ground trimer state energy ${E}_{T}^{(0)}$ not crossing the atom-dimer threshold, and the scaled three-body recombination rate ${K}_{3}^{0}/{a}^{4}$ deviating from the universal three-body theory. The results of our simple model agree within a few percent with other theoretical works with van der Waals interaction and also the experimental data.We construct a simple model to calculate the trimer bound state energy ${E}_{T}^{(n)}$ and three-body recombination rate ${K}_{3}^{0}$ of three identical bosons with van der Waals interaction without using any two- or three-body fitting parameter. Using this simple model, we investigate the influence of the van der Waals finite-range effect on ${E}_{T}^{(n)}$ and ${K}_{3}^{0}$. Our calculation shows that the finite-range effect leads to the ground trimer state energy ${E}_{T}^{(0)}$ not crossing the atom-dimer threshold, and the scaled three-body recombination rate ${K}_{3}^{0}/{a}^{4}$ deviating from the universal three-body theory. The results of our simple model agree within a few percent with other theoretical works with van der Waals interaction and also the experimental data.

Physical Review ASep 8, 20168 citations

^{39}\mathrm{K}

. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $\ensuremath{-}8$ and $\ensuremath{-}10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.

We construct a simple model to calculate the trimer bound state energy

{E}_{T}^{(n)}

and three-body recombination rate

{K}_{3}^{0}

of three identical bosons with van der Waals interaction without using any two- or three-body fitting parameter. Using this simple model, we investigate the influence of the van der Waals finite-range effect on

{E}_{T}^{(n)}

and

{K}_{3}^{0}

. Our calculation shows that the finite-range effect leads to the ground trimer state energy

{E}_{T}^{(0)}

not crossing the atom-dimer threshold, and the scaled three-body recombination rate

{K}_{3}^{0}/{a}^{4}

deviating from the universal three-body theory. The results of our simple model agree within a few percent with other theoretical works with van der Waals interaction and also the experimental data.