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

Search for weakly bound states of the He-He-Be triatomic system

Yong Li, Hongwei Song, Qingdong Gou, Hui-Li Han, Ting-Yun Shi

Published Feb 5, 2009• 8 citations
Publisher

Abstract

We search for the existence of weakly bound He-He-Be molecules. The He-He-Be molecule is treated as a three-body system. By using hyperspherical coordinates, the Schr\"odinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$, $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$, and $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}$ trimers.

DOI
10.1103/physreva.79.024501

Related papers

Search for Borromean states in the He-He-Rb triatomic system

Yong Li, Wenjuan Zhang, Qingdong Gou +2 more

We search for the existence of weakly bound He-He-Rb molecules. The He-He-Rb molecule is treated as a three-body system. By using hyperspherical coordinates, the Schr\"odinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the $^{3}\mathrm{He}$-$^{3}\mathrm{He}$-$^{85}\mathrm{Rb}$, $^{3}\mathrm{He}$-$^{4}\mathrm{He}$-$^{85}\mathrm{Rb}$, and $^{4}\mathrm{He}$-$^{4}\mathrm{He}$-$^{85}\mathrm{Rb}$ trimers, respectively. The bound state for the $^{3}\mathrm{He}$-$^{3}\mathrm{He}$-$^{85}\mathrm{Rb}$ molecule is a Borromean state found in a realistic molecular systems because there are no bound states in both the $^{3}\mathrm{He}$-$^{3}\mathrm{He}$ and $^{3}\mathrm{He}$-$^{85}\mathrm{Rb}$ dimers.

Physical Review A•Aug 30, 2010•19 citations

Weakly bound states of the He-He-Mg trimer

Yong Li, Deping Huang, Qingdong Gou +2 more

We search for the existence of the weakly bound He-He-Mg molecules. The He-He-Mg molecule is treated as a three-body system. By using hyperspherical coordinates, the Schr\"odinger equation for the triatomic system is solved in the adiabatic approximation. We obtain that the binding of the three atoms is possible. The binding energies of such molecules are estimated.

Physical Review A•Jul 13, 2011•8 citations

Weakly bound states of the He-He-Ca triatomic system

Qingdong Gou, Yong Li

We investigate for the existence of the weakly bound He-He-Ca molecules. By employing the best empirical interaction between each pair of particles, the Schr\"odinger equation for the triatomic system is solved using hyperspherical coordinates in the adiabatic approximation. The bound states are found for each of the ${}^{3}$He-${}^{3}$He-${}^{40}$Ca, ${}^{3}$He-${}^{4}$He-${}^{40}$Ca, and ${}^{4}$He-${}^{4}$He-${}^{40}$Ca trimers, respectively. The binding energies of such molecules are estimated. We discuss the features of the channel functions associated with the hyperspherical potential curves of each system to obtain insight into the geometry of the molecules.

Physical Review A•Jan 13, 2012•9 citations

Halo state in realistic molecular systems

Yong Li, Qingdong Gou, Ting-Yun Shi

We search for the existence of the weakly bound He-He-K molecules where the binding energies are expected to be of the order of degrees Kelvin. By employing the best empirical interaction between each pair of particles, the Schr\"odinger equation for the triatomic systems is solved using hyperspherical coordinates in the adiabatic approximation. A bound state is found for each of the $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$, $^{4}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$, and $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ trimers, respectively. The bound state for the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ molecule is the halo state found in realistic molecular systems for there are no bound states in both the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}$ and $^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ dimers.

Physical Review A•Sep 1, 2006•26 citations

Calculations of the binding energies of weakly bound He-He-H, He-He-H-and He-H-H molecules

Yong Li, C. D. Lin

We searched for the existence of weakly bound He-He-H, He-He-H - and He-H-H molecules where the binding energies are expected to be of the order of degrees Kelvin. By employing the best empirical interaction between each pair of particles, we solved the Schrödinger equation for the triatomic systems using hyperspherical coordinates in the adiabatic approximation. We found no bound states for 4 He- 4 He- 1 H, three bound states for 4 He- 4 He- 1 H - and one bound state for 4 He- 1 H- 1 H. Bound states for other isotope combinations are also examined.

Journal of Physics B Atomic Molecular and Optical Physics•Oct 7, 1999•22 citations

The weakly bound states and resonances of the BeHe2 triatomic system

Hui-Li Han, Yong Li, Ting-Yun Shi

In the present study, we carry out a full search of the bound states and resonances of the He(2)Be triatomic system, with its isotopic variants (3)He(2)(9)Be, (3)He(4)He(9)Be, and (4)He(2)(9)Be using the hyperspherical method. Three-body long-range effects are also included in the computation by adding to the additive potential the Axilrod-Teller triple-dipole term. In addition, the possibility of the occurrence of Efimov-type states in these systems is discussed. We have found a bound state for each of the (3)He(2)(9)Be and (3)He(4)He(9)Be trimers, while one weakly bound excited state is also found to exist for the (4)He(2)(9)Be system.

The Journal of Chemical Physics•May 18, 2011•7 citations
We search for the existence of weakly bound He-He-Be molecules. The He-He-Be molecule is treated as a three-body system. By using hyperspherical coordinates, the Schr"odinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the 3He\ensuremath-3He\ensuremath-9Be^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}3He\ensuremath-3He\ensuremath-9Be, 3He\ensuremath-4He\ensuremath-9Be^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}3He\ensuremath-4He\ensuremath-9Be, and 4He\ensuremath-4He\ensuremath-9Be^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{9}\mathrm{Be}4He\ensuremath-4He\ensuremath-9Be trimers.
We search for the existence of weakly bound He-He-Rb molecules. The He-He-Rb molecule is treated as a three-body system. By using hyperspherical coordinates, the Schr\"odinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the 3He^{3}\mathrm{He}3He-3He^{3}\mathrm{He}3He-85Rb^{85}\mathrm{Rb}85Rb, 3He^{3}\mathrm{He}3He-4He^{4}\mathrm{He}4He-85Rb^{85}\mathrm{Rb}85Rb, and 4He^{4}\mathrm{He}4He-4He^{4}\mathrm{He}4He-85Rb^{85}\mathrm{Rb}85Rb trimers, respectively. The bound state for the 3He^{3}\mathrm{He}3He-3He^{3}\mathrm{He}3He-85Rb^{85}\mathrm{Rb}85Rb molecule is a Borromean state found in a realistic molecular systems because there are no bound states in both the 3He^{3}\mathrm{He}3He-3He^{3}\mathrm{He}3He and 3He^{3}\mathrm{He}3He-85Rb^{85}\mathrm{Rb}85Rb dimers.
We investigate for the existence of the weakly bound He-He-Ca molecules. By employing the best empirical interaction between each pair of particles, the Schr\"odinger equation for the triatomic system is solved using hyperspherical coordinates in the adiabatic approximation. The bound states are found for each of the 3{}^{3}3He-3{}^{3}3He-40{}^{40}40Ca, 3{}^{3}3He-4{}^{4}4He-40{}^{40}40Ca, and 4{}^{4}4He-4{}^{4}4He-40{}^{40}40Ca trimers, respectively. The binding energies of such molecules are estimated. We discuss the features of the channel functions associated with the hyperspherical potential curves of each system to obtain insight into the geometry of the molecules.
We search for the existence of the weakly bound He-He-K molecules where the binding energies are expected to be of the order of degrees Kelvin. By employing the best empirical interaction between each pair of particles, the Schr\"odinger equation for the triatomic systems is solved using hyperspherical coordinates in the adiabatic approximation. A bound state is found for each of the $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$, $^{4}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$, and $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ trimers, respectively. The bound state for the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ molecule is the halo state found in realistic molecular systems for there are no bound states in both the $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}$ and $^{3}\mathrm{He}\text{\ensuremath{-}}^{39}\mathrm{K}$ dimers.
We searched for the existence of weakly bound He-He-H, He-He-H - and He-H-H molecules where the binding energies are expected to be of the order of degrees Kelvin. By employing the best empirical interaction between each pair of particles, we solved the Schrödinger equation for the triatomic systems using hyperspherical coordinates in the adiabatic approximation. We found no bound states for 4 He- 4 He- 1 H, three bound states for 4 He- 4 He- 1 H - and one bound state for 4 He- 1 H- 1 H. Bound states for other isotope combinations are also examined.
In the present study, we carry out a full search of the bound states and resonances of the He(2)Be triatomic system, with its isotopic variants (3)He(2)(9)Be, (3)He(4)He(9)Be, and (4)He(2)(9)Be using the hyperspherical method. Three-body long-range effects are also included in the computation by adding to the additive potential the Axilrod-Teller triple-dipole term. In addition, the possibility of the occurrence of Efimov-type states in these systems is discussed. We have found a bound state for each of the (3)He(2)(9)Be and (3)He(4)He(9)Be trimers, while one weakly bound excited state is also found to exist for the (4)He(2)(9)Be system.