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

Acta Physica Sinica

Calculations of the binding energies of weakly bound He-He-Ba molecules

Gou Qing-Dong, Yong Li

Published Jan 1, 2015• 0 citations
Publisher

Abstract

The three-body Schrdinger equation is approximately solved in the hyperspherical coordinates and the binding energies of the three-body weakly bound systems are calculated with the purpose to find if He-He-Ba trimers could exist. Using the special feature of the B-spline function like the flexible and highly localized properties, hypersphercial potentials are obtained by modifying the knots distribution of the B-spline basis of different weakly bound three-atom systems. Employing the best empirical interaction potentials between each pair of particles, we obtain that in the ground state binding energies of the weakly bound typical three-atom systems, the bindings of the molecules, 4He-4He-138Ba, 4He-3He-138Ba and 3He-3He-138Ba are possible. The binding energies of these systems are shown in the order of 1 Kelvin, each system could support only one bound state. These weakly bound molecules can exist only in a very cold environment. To get insight into the geometry of the molecules, the features of the channel functions associated with the hyperspherical potential curves of each system are investigated.

DOI
10.7498/aps.64.193102

Related papers

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

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

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

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

Weakly bound triatomic He2Li and He2Na molecules

Jianmin Yuan, C. D. Lin

We study the existence of stable bound states of triatomic molecules containing two helium atoms and one alkali atom X (X = Li, Na) and examine the dependence of their binding energies on the mass of the constituent atoms. The three-body systems are solved within the adiabatic approximation in hyperspherical coordinates using the He - He and He - X pair van der Waals interactions that are available in the literature. The binding energies of these systems are shown to be of less than 1 K for some isotope combinations. For the lighter isotopes it is shown that no bound states exist. We found no evidence of the existence of halo states or Efimov states for these systems.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 14, 1998•50 citations

Calculation of loosely bound levels for three-body quantum systems using hyperspherical coordinates with a mapping procedure

Viatcheslav Kokoouline, Françoise Masnou-Seeuws

In view of modelization of experiments involving cold atoms and molecules, we develop a method that allows us to calculate weakly bound levels of triatomic molecules. The method combines (1) the hyperspherical coordinates to describe interparticle motion in the three-body system, (2) the solution of the Schr\"odinger equation in two steps: determination of adiabatic states for a fixed hyper-radius and then solution of a set of coupled hyper-radial equations using the slow variable representation of Tolstikhin et al. [J. Phys. B: At. Mol. Opt. Phys. 29, L389 (1996)], (3) and a mapping procedure that reduces considerably the number of basis functions needed to represent wave functions of weakly bound levels. We apply the method to the three different systems: the helium trimer $^{4}\mathrm{He}_{3}$, isotopomers of the $\mathrm{H}_{3}{}^{+}$ ion, and finally a model three-body problem involving three nucleons. For all these systems, we show that the suggested method provides accurate results.

Physical Review A•Jan 10, 2006•38 citations
The three-body Schrdinger equation is approximately solved in the hyperspherical coordinates and the binding energies of the three-body weakly bound systems are calculated with the purpose to find if He-He-Ba trimers could exist. Using the special feature of the B-spline function like the flexible and highly localized properties, hypersphercial potentials are obtained by modifying the knots distribution of the B-spline basis of different weakly bound three-atom systems. Employing the best empirical interaction potentials between each pair of particles, we obtain that in the ground state binding energies of the weakly bound typical three-atom systems, the bindings of the molecules, 4He-4He-138Ba, 4He-3He-138Ba and 3He-3He-138Ba are possible. The binding energies of these systems are shown in the order of 1 Kelvin, each system could support only one bound state. These weakly bound molecules can exist only in a very cold environment. To get insight into the geometry of the molecules, the features of the channel functions associated with the hyperspherical potential curves of each system are investigated.
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 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.
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 study the existence of stable bound states of triatomic molecules containing two helium atoms and one alkali atom X (X = Li, Na) and examine the dependence of their binding energies on the mass of the constituent atoms. The three-body systems are solved within the adiabatic approximation in hyperspherical coordinates using the He - He and He - X pair van der Waals interactions that are available in the literature. The binding energies of these systems are shown to be of less than 1 K for some isotope combinations. For the lighter isotopes it is shown that no bound states exist. We found no evidence of the existence of halo states or Efimov states for these systems.
In view of modelization of experiments involving cold atoms and molecules, we develop a method that allows us to calculate weakly bound levels of triatomic molecules. The method combines (1) the hyperspherical coordinates to describe interparticle motion in the three-body system, (2) the solution of the Schr\"odinger equation in two steps: determination of adiabatic states for a fixed hyper-radius and then solution of a set of coupled hyper-radial equations using the slow variable representation of Tolstikhin et al. [J. Phys. B: At. Mol. Opt. Phys. 29, L389 (1996)], (3) and a mapping procedure that reduces considerably the number of basis functions needed to represent wave functions of weakly bound levels. We apply the method to the three different systems: the helium trimer 4He3^{4}\mathrm{He}_{3}4He3​, isotopomers of the H3+\mathrm{H}_{3}{}^{+}H3​+ ion, and finally a model three-body problem involving three nucleons. For all these systems, we show that the suggested method provides accurate results.