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Physical Review A

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

David López‐Durán, Tomás González‐Lezana, Gerardo Delgado-Barrio, Pablo Villarreal, Francesco Antonio Gianturco

Published Jul 25, 2012• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.86.016501

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Reply to ``Comment on `Weakly bound states of the He-He-Ca triatomic system' ''

Qingdong Gou, Yong Li

There are three points in the preceding Comment. We agree with the first point, and we point out that the second and third points are due to a misunderstanding.Received 10 June 2012DOI:https://doi.org/10.1103/PhysRevA.86.016502©2012 American Physical Society

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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.
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 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 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.
The interactions between alkali atoms and 4 He, as well as those between H - and 4 He, are known to be even weaker than those between two helium atoms. In this work we show that when the three-particle potential energy surface is obtained as a sum of two-body functions, the ensuing ground state configurations are indeed very weakly bound and acquire spatial shapes difficult to describe in simple configurational terms. We have employed the quantum diffusion Monte Carlo method to analyse the He 2 Li, He 2 Na and He 2 H - systems, for which possible molecular `shapes' are extracted from the final DMC distributions by defining within them conventional chemical structures with varying degree of `stiffness' attached to the nuclear positions.
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.