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

Binding energies and structures of Ca-He 2 weakly bound triatomic complexes

David López‐Durán, Rocío Rodríguez‐Cantano, Tomás González‐Lezana, Gerardo Delgado-Barrio, Pablo Villarreal, Franco Antonio Gianturco

Published Aug 1, 2012• 10 citations
Publisher

Abstract

Bound states of ${}^{40}$Ca-${}^{n}$He${}_{2}$, $n=3,4$, triatomic complexes are investigated. The potential-energy surface, represented as the addition of atomic-pair interactions, is that recently used to study these systems by Gou and Li, Phys. Rev. A 85, 012510 (2012). The results obtained from three different methods, in fair agreement, profoundly disagree with those reported in the reference above. In addition, we address the feasibility of two Ca-He interactions existing in the literature by analyzing the characteristics of their ground and excited vibrorotational states. To this end, simulated absorption spectra in the region of microwaves are also presented and discussed.

DOI
10.1103/physreva.86.022501

Related papers

Comment on “Weakly bound states of the He-He-Ca triatomic system”

David López‐Durán, Tomás González‐Lezana, Gerardo Delgado-Barrio +2 more

We discuss the computational results on the energetics and features of the bound states of one and two He atoms attached to a Ca atom, which have been presented by Gou and Li in a recently published paper in Phys. Rev. A 85, 012510 (2012). We show that, given their choice for the interaction potential-energy surface, the energy they found for the three-particle complex's ground state must be incorrect. We also point out that a large number of their excited states for the same system do not really exist since they are located above either of the two-atom components' bound-state energies.

Physical Review A•Jul 25, 2012•3 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

Structure of the weakly bound triatomic He2Li and He2Na molecules

Hiroya Suno

We study the structure of triatomic molecules containing two helium atoms and one alkali-metal atom X (X = Li, Na). The three-body Schr\"odinger equation is solved in hyperspherical coordinates using the He-He and He-X pair van der Waals potentials available in the literature. We calculate the structural properties of the ${\mathrm{He}}_{2}\mathrm{Li}$ and ${\mathrm{He}}_{2}\mathrm{Na}$ bound states, and analyze one-dimensional pair and angle distribution functions as well as two-dimensional pair-pair and angle-angle distribution functions. These bound states are characterized by so peculiar weakly bound structures that classifying them into particular sizes and geometrical shapes appears to be elusive. Particularly, the ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+}$ excited states of $^{4}\mathrm{He}_{2}^{6}\mathrm{Li}$ and $^{4}\mathrm{He}_{2}^{7}\mathrm{Li}$ are found to constitute giant triatomic molecules with their size amounting to several hundred bohrs.

Physical Review A•Jul 11, 2017•14 citations

Ground- and excited-rovibrational-state properties of weakly bound helium-silver triatomic molecules

Hiroya Suno

Ground and excited-rovibrational states of weakly bound triatomic molecules containing two helium and one silver atoms are investigated. We consider three systems, $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{Ag}$, $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{Ag}$, and $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{Ag}$. The three-atom Schr\"odinger equation is solved in hyperspherical coordinates using the potential-energy surface represented as the addition of He-He and He-Ag pair interaction potentials. We compute the energy levels and analyze the structural properties by considering averaged pair distances and bond angles, one-dimensional pair and angle distribution functions, and two-dimensional pair-pair and angle-angle distribution functions. All the He-He-Ag bound states are found to possess similar characteristics, displaying obtuse isosceles ($^{4}\mathrm{He}_{2}\mathrm{Ag}$ and $^{3}\mathrm{He}_{2}\mathrm{Ag}$) or scalene ($^{3}\mathrm{He}^{4}\mathrm{He}\mathrm{Ag}$) triangle configurations where the He-Ag distances are nearly fixed and the Ag bond angle is variable.

Physical Review A•Sep 6, 2022•1 citation

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

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
Bound states of 40{}^{40}40Ca-n{}^{n}nHe2{}_{2}2​, n=3,4n=3,4n=3,4, triatomic complexes are investigated. The potential-energy surface, represented as the addition of atomic-pair interactions, is that recently used to study these systems by Gou and Li, Phys. Rev. A 85, 012510 (2012). The results obtained from three different methods, in fair agreement, profoundly disagree with those reported in the reference above. In addition, we address the feasibility of two Ca-He interactions existing in the literature by analyzing the characteristics of their ground and excited vibrorotational states. To this end, simulated absorption spectra in the region of microwaves are also presented and discussed.
We discuss the computational results on the energetics and features of the bound states of one and two He atoms attached to a Ca atom, which have been presented by Gou and Li in a recently published paper in Phys. Rev. A 85, 012510 (2012). We show that, given their choice for the interaction potential-energy surface, the energy they found for the three-particle complex's ground state must be incorrect. We also point out that a large number of their excited states for the same system do not really exist since they are located above either of the two-atom components' bound-state energies.
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 study the structure of triatomic molecules containing two helium atoms and one alkali-metal atom X (X = Li, Na). The three-body Schr\"odinger equation is solved in hyperspherical coordinates using the He-He and He-X pair van der Waals potentials available in the literature. We calculate the structural properties of the He2Li{\mathrm{He}}_{2}\mathrm{Li}He2​Li and He2Na{\mathrm{He}}_{2}\mathrm{Na}He2​Na bound states, and analyze one-dimensional pair and angle distribution functions as well as two-dimensional pair-pair and angle-angle distribution functions. These bound states are characterized by so peculiar weakly bound structures that classifying them into particular sizes and geometrical shapes appears to be elusive. Particularly, the ${J}^{\mathrm{\ensuremath{\Pi}}}={0}^{+}$ excited states of 4He26Li^{4}\mathrm{He}_{2}^{6}\mathrm{Li}4He26​Li and 4He27Li^{4}\mathrm{He}_{2}^{7}\mathrm{Li}4He27​Li are found to constitute giant triatomic molecules with their size amounting to several hundred bohrs.
Ground and excited-rovibrational states of weakly bound triatomic molecules containing two helium and one silver atoms are investigated. We consider three systems, $^{4}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{Ag}$, $^{3}\mathrm{He}\text{\ensuremath{-}}^{4}\mathrm{He}\text{\ensuremath{-}}\mathrm{Ag}$, and $^{3}\mathrm{He}\text{\ensuremath{-}}^{3}\mathrm{He}\text{\ensuremath{-}}\mathrm{Ag}$. The three-atom Schr\"odinger equation is solved in hyperspherical coordinates using the potential-energy surface represented as the addition of He-He and He-Ag pair interaction potentials. We compute the energy levels and analyze the structural properties by considering averaged pair distances and bond angles, one-dimensional pair and angle distribution functions, and two-dimensional pair-pair and angle-angle distribution functions. All the He-He-Ag bound states are found to possess similar characteristics, displaying obtuse isosceles (4He2Ag^{4}\mathrm{He}_{2}\mathrm{Ag}4He2​Ag and 3He2Ag^{3}\mathrm{He}_{2}\mathrm{Ag}3He2​Ag) or scalene (3He4HeAg^{3}\mathrm{He}^{4}\mathrm{He}\mathrm{Ag}3He4HeAg) triangle configurations where the He-Ag distances are nearly fixed and the Ag bond angle is variable.
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.
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.