Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Prediction of a weakly bound excited state of Efimov character in a Li7He24 system

M.-S. Wu, Hui-Li Han, Chengbin Li, Ting-Yun Shi

Published Dec 8, 2014• 16 citations
Publisher

Abstract

We carry out calculations on the van der Waals trimer $^{7}\mathrm{Li}^{4}\mathrm{He}_{2}$ using the mapping method within the frame of hyperspherical coordinates, which allows us to give accurate binding energies and wave functions for both the ground and excited state of the system. When the realistic two-body potentials are adopted, the system presents an excited state which shows Efimov character. We study the range of the interaction strength in which the excited state could exist and find that the state persists within the experiment error band for binding energy of LiHe molecule. We also study the three-body parameter (3BP) of $^{7}\mathrm{Li}^{4}\mathrm{He}_{2}$ system and its relationship with the background scattering length ${a}_{\text{HeHe}}$. Our calculations demonstrate that the 3BP of $^{7}\mathrm{Li}^{4}\mathrm{He}_{2}$ system is dependent on the value of the scattering length ${a}_{\text{HeHe}}$, independent of the short-range details of the He-He interaction. The results confirm the prediction of Wang et al. [Phys. Rev. Lett. 109, 243201 (2012)] that the 3BP for a heteronuclear atomic system is universally determined from the van der Waals lengths and the homonuclear scattering length.

DOI
10.1103/physreva.90.062506

Related papers

Universality in Efimov-associated tetramers in He4

Emiko Hiyama, M. Kamimura

We calculated, using seven realistic $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ potentials in the literature, the Efimov spectra of the $^{4}\mathrm{He}$ trimer and tetramer and analyzed the universality of the systems. The three-(four-)body Schr\"odinger equations were solved fully nonadiabatically with the high-precision calculation method employed in our previous work on the $^{4}\mathrm{He}$ trimer and tetramer [Phys. Rev. A 85, 022502 (2012); Phys. Rev. A 85, 062505 (2012)]. We found the following universality in the four-boson system: (i) The critical scattering lengths at which the tetramer ground and excited states couple to the four-body threshold are independent of the choice of the two-body realistic potentials in spite of the difference in the short-range details and do not contradict the corresponding values observed in the experiments in ultracold alkali-metal atoms when scaled with the van der Waals length ${r}_{\mathrm{vdW}}$, and (ii) the four-body hyperradial potential has a repulsive barrier at the four-body hyperradius ${R}_{4}\ensuremath{\approx}3\phantom{\rule{0.16em}{0ex}}{r}_{\mathrm{vdW}}$, which prevents the four particles from getting close together to explore nonuniversal features of the interactions at short distances. This result is an extension of the universality in Efimov trimers that the appearance of the repulsive barrier at the three-body hyperradius ${R}_{3}\ensuremath{\approx}2\phantom{\rule{0.16em}{0ex}}{r}_{\mathrm{vdW}}$ makes the critical scattering lengths independent of the short-range details of the interactions as reported in the literature and also in the present work for the $^{4}\mathrm{He}$ trimer with the realistic potentials.

arXiv:1409.2501•Physical Review A•Nov 18, 2014•30 citations

Efimov states in asymmetric three-body atomic clusters

Elena A. Kolganova

The work is devoted to the investigation of the weakly bound three-body atomic clusters. The calculations on the van der Waals trimer 7 Li 4 He 2 are carried out using the differential Faddeev equations, which allows us to give accurate binding energies for both the ground and the exited state of the system. The results obtained indicate the Efimov nature of the excited state in this system.

Physics of Particles and Nuclei•Nov 1, 2017•0 citations

Efimov states near a Feshbach resonance and the limits of van der Waals universality at finite background scattering length

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.

arXiv:1709.00749•Physical Review A•Mar 27, 2018•30 citations

Universal three-body parameter of heavy-heavy-light systems with a negative intraspecies scattering length

Caiyun Zhao, Hui-Li Han, M.-S. Wu +1 more

The three-body parameter (3BP) ${a}_{\ensuremath{-}}^{(1)}$ is crucial for understanding Efimov physics, and a universal 3BP has been shown in experiments and theory in ultracold homonuclear gases. The 3BP of heteronuclear systems has been predicted to possess much richer properties than its homonuclear counterparts due to the larger parameter space. In this work, we investigate the universal properties of ${a}_{\ensuremath{-}}^{(1)}$ for heavy-heavy-light (HHL) systems with a negative intraspecies scattering length ${a}_{HH}$. We find that ${a}_{\ensuremath{-}}^{(1)}$ follows a universal behavior determined by the van der Waals (vdW) interaction and the mass ratio. A linear fit of ${a}_{\ensuremath{-}}^{(1)}$ for large $|{a}_{HH}|$ leads to a simple formula, which gives the general dependence of ${a}_{\ensuremath{-}}^{(1)}$ on the mass ratio and the vdW length ${r}_{vdW}$. In a special case, when the two heavy atoms are in resonance, ${a}_{\ensuremath{-}}^{(1)}$ is approximately constant: ${a}_{\ensuremath{-}}^{(1)}=\ensuremath{-}(6.3\ifmmode\pm\else\textpm\fi{}0.6){r}_{vdW,HL}$.

arXiv:1903.09565•Physical Review A•Nov 12, 2019•6 citations

Searching for Efimov states in triatomic systems: The case of LiHe 2

I. Baccarelli, Gerardo Delgado-Barrio, Franco Antonio Gianturco +3 more

The possible presence of Efimov-type states in isotopic variants of triatomic molecules composed of one Li and two boson He atoms is investigated. Firstly, through the study of two-body interactions in the frame of the effective range theory, it is shown that, at least with the present choice of dimer potentials, the system containing 7 Li unlikely presents any Efimov state, while the 6 Li isotopic variant would be a better candidate in this regard. Then, triatomic bound states are searched through variational calculations in terms of pair inter-atomic distances and distributed Gaussian functions (DGF). The calculations were performed at several values of a parameter λ controlling the strength of the potential. Each system presents two bound levels at the “physical” situation λ = 1. By increasing lambda, the excited levels become “ghost” states as their energies are above the helium dimer energy and present, therefore, an Efimov character. Hence, we conclude that three-body (3B) predictions coming only from two-body (2B) calculations do not have, at least for the systems studied here, any great relevance. Such predictions are not in fact fulfilled for LiHe 2 , as shown by the greatly reduced relevance of isotopic effects in our actual 3B calculations.

Europhysics Letters (EPL)•Jun 1, 2000•31 citations

Zero-energy scattering and bound states in the He4 trimer and tetramer

S. Nakaichi-Maeda, T. K. Lim

Using the HFDHE2 He-He potential of Aziz et al. [J. Chem. Phys. 90, 4330 (1979)] with the Faddeev-Yakubovsky theory, we have calculated the $^{4}\mathrm{He}$ atom-triatom scattering length and found it to be - 116 \AA{}. We reduced the $s$-wave two-body $t$ matrix to a separable form through the unitary-pole approximation and did the same for the $s$-wave [3+1] and [2+2] subamplitudes with the energy-dependent-pole approximation in our work. Also, the binding energies of all the states in the trimer and tetramer, and the atom-diatom scattering length, already determined in our previous work with other potentials, were recalculated for the new interaction. We found an excited trimer bound state, apparently not an Efimov state, near the atom-diatom threshold and an atom-diatom scattering length of 195 \AA{}. A feature of our results was the absence of an excited state in the tetramer, but in its place, was a resonancelike state which led to the large atom-triatom scattering length.

Physical Review A•Aug 1, 1983•46 citations
We carry out calculations on the van der Waals trimer 7Li4He2^{7}\mathrm{Li}^{4}\mathrm{He}_{2}7Li4He2​ using the mapping method within the frame of hyperspherical coordinates, which allows us to give accurate binding energies and wave functions for both the ground and excited state of the system. When the realistic two-body potentials are adopted, the system presents an excited state which shows Efimov character. We study the range of the interaction strength in which the excited state could exist and find that the state persists within the experiment error band for binding energy of LiHe molecule. We also study the three-body parameter (3BP) of 7Li4He2^{7}\mathrm{Li}^{4}\mathrm{He}_{2}7Li4He2​ system and its relationship with the background scattering length aHeHe{a}_{\text{HeHe}}aHeHe​. Our calculations demonstrate that the 3BP of 7Li4He2^{7}\mathrm{Li}^{4}\mathrm{He}_{2}7Li4He2​ system is dependent on the value of the scattering length aHeHe{a}_{\text{HeHe}}aHeHe​, independent of the short-range details of the He-He interaction. The results confirm the prediction of Wang et al. [Phys. Rev. Lett. 109, 243201 (2012)] that the 3BP for a heteronuclear atomic system is universally determined from the van der Waals lengths and the homonuclear scattering length.
We calculated, using seven realistic $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}$ potentials in the literature, the Efimov spectra of the 4He^{4}\mathrm{He}4He trimer and tetramer and analyzed the universality of the systems. The three-(four-)body Schr\"odinger equations were solved fully nonadiabatically with the high-precision calculation method employed in our previous work on the 4He^{4}\mathrm{He}4He trimer and tetramer [Phys. Rev. A 85, 022502 (2012); Phys. Rev. A 85, 062505 (2012)]. We found the following universality in the four-boson system: (i) The critical scattering lengths at which the tetramer ground and excited states couple to the four-body threshold are independent of the choice of the two-body realistic potentials in spite of the difference in the short-range details and do not contradict the corresponding values observed in the experiments in ultracold alkali-metal atoms when scaled with the van der Waals length rvdW{r}_{\mathrm{vdW}}rvdW​, and (ii) the four-body hyperradial potential has a repulsive barrier at the four-body hyperradius ${R}_{4}\ensuremath{\approx}3\phantom{\rule{0.16em}{0ex}}{r}_{\mathrm{vdW}}$, which prevents the four particles from getting close together to explore nonuniversal features of the interactions at short distances. This result is an extension of the universality in Efimov trimers that the appearance of the repulsive barrier at the three-body hyperradius ${R}_{3}\ensuremath{\approx}2\phantom{\rule{0.16em}{0ex}}{r}_{\mathrm{vdW}}$ makes the critical scattering lengths independent of the short-range details of the interactions as reported in the literature and also in the present work for the 4He^{4}\mathrm{He}4He trimer with the realistic potentials.
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 39K^{39}\mathrm{K}39K. 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.
The three-body parameter (3BP) ${a}_{\ensuremath{-}}^{(1)}$ is crucial for understanding Efimov physics, and a universal 3BP has been shown in experiments and theory in ultracold homonuclear gases. The 3BP of heteronuclear systems has been predicted to possess much richer properties than its homonuclear counterparts due to the larger parameter space. In this work, we investigate the universal properties of ${a}_{\ensuremath{-}}^{(1)}$ for heavy-heavy-light (HHL) systems with a negative intraspecies scattering length aHH{a}_{HH}aHH​. We find that ${a}_{\ensuremath{-}}^{(1)}$ follows a universal behavior determined by the van der Waals (vdW) interaction and the mass ratio. A linear fit of ${a}_{\ensuremath{-}}^{(1)}$ for large ∣aHH∣|{a}_{HH}|∣aHH​∣ leads to a simple formula, which gives the general dependence of ${a}_{\ensuremath{-}}^{(1)}$ on the mass ratio and the vdW length rvdW{r}_{vdW}rvdW​. In a special case, when the two heavy atoms are in resonance, ${a}_{\ensuremath{-}}^{(1)}$ is approximately constant: ${a}_{\ensuremath{-}}^{(1)}=\ensuremath{-}(6.3\ifmmode\pm\else\textpm\fi{}0.6){r}_{vdW,HL}$.
The possible presence of Efimov-type states in isotopic variants of triatomic molecules composed of one Li and two boson He atoms is investigated. Firstly, through the study of two-body interactions in the frame of the effective range theory, it is shown that, at least with the present choice of dimer potentials, the system containing 7 Li unlikely presents any Efimov state, while the 6 Li isotopic variant would be a better candidate in this regard. Then, triatomic bound states are searched through variational calculations in terms of pair inter-atomic distances and distributed Gaussian functions (DGF). The calculations were performed at several values of a parameter λ controlling the strength of the potential. Each system presents two bound levels at the “physical” situation λ = 1. By increasing lambda, the excited levels become “ghost” states as their energies are above the helium dimer energy and present, therefore, an Efimov character. Hence, we conclude that three-body (3B) predictions coming only from two-body (2B) calculations do not have, at least for the systems studied here, any great relevance. Such predictions are not in fact fulfilled for LiHe 2 , as shown by the greatly reduced relevance of isotopic effects in our actual 3B calculations.
Using the HFDHE2 He-He potential of Aziz et al. [J. Chem. Phys. 90, 4330 (1979)] with the Faddeev-Yakubovsky theory, we have calculated the 4He^{4}\mathrm{He}4He atom-triatom scattering length and found it to be - 116 \AA{}. We reduced the sss-wave two-body ttt matrix to a separable form through the unitary-pole approximation and did the same for the sss-wave [3+1] and [2+2] subamplitudes with the energy-dependent-pole approximation in our work. Also, the binding energies of all the states in the trimer and tetramer, and the atom-diatom scattering length, already determined in our previous work with other potentials, were recalculated for the new interaction. We found an excited trimer bound state, apparently not an Efimov state, near the atom-diatom threshold and an atom-diatom scattering length of 195 \AA{}. A feature of our results was the absence of an excited state in the tetramer, but in its place, was a resonancelike state which led to the large atom-triatom scattering length.