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Molecular Physics

Searching for many-body effects and Efimov states in very weakly bound triatomics: HeNeH−and HeNeH

Sergio Orlandini, I. Baccarelli, Franco Antonio Gianturco

Published Feb 1, 2008• 4 citations
Publisher

Abstract

The rotationless, vibrational states of two weakly bound triatomic species are calculated using a variational expansion over multicentred Gaussian functions (the DGF method described in the main text) and corrections are introduced by using the three-body potentials vis à vis the sum-of-potentials approximation. The effects are seen to be very small and isotopic substitution is further introduced to evaluate changes on the vibrational structures of both systems, aiming at possibly detecting Efimov behaviour in such special trimers: no Efimov states are found with the available potentials and when the two-body potential strengths are varied. An additional study on the effects of isotopic substitutions for H atoms is also presented.

DOI
10.1080/00268970801939001

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The rotationless, vibrational states of two weakly bound triatomic species are calculated using a variational expansion over multicentred Gaussian functions (the DGF method described in the main text) and corrections are introduced by using the three-body potentials vis à vis the sum-of-potentials approximation. The effects are seen to be very small and isotopic substitution is further introduced to evaluate changes on the vibrational structures of both systems, aiming at possibly detecting Efimov behaviour in such special trimers: no Efimov states are found with the available potentials and when the two-body potential strengths are varied. An additional study on the effects of isotopic substitutions for H atoms is also presented.
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.
The weakly bound diatomic systems He24 and HeH−4 have been found able to support only one bound state for J=0, although the latter also supports an additional bound state for J=1. In the present paper we, therefore, study the structure of the bound states which might exist for the weakly bound triatomic He24H−, in its J=0 state, by describing the full potential as a simple addition of two-body (2B) interactions. We carry out bound state calculations using both Jacobi coordinates within a discrete variable representation (DVR) and pair coordinates with a distributed Gaussian function (DGF) expansion. The system is shown to possess two bound states with respect to its lower dissociation threshold and two further “ghost” states before the complete break-up threshold. The spatial structures of such states and of the floppy complex are analyzed in detail, as is the possibility of detecting Efimov-type states in such a weakly bound aggregate. Finally, the inclusion of three-body (3B) forces in the description of the full interaction and its effect on the number of possible bound states is also discussed.
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.
Helium trimer bound states are calculated with a variational method described in terms of pair atom coordinates and distributed Gaussian functions by assuming zero total angular momentum. With the two-body interaction potential used, a weakly bound state for the dimer and only two bound states for the trimer are found. Although strictly speaking the first excited trimer state is not an Efimov state, we show that this state presents several characteristics of the Efimov behavior which are extensively discussed in the present work. Special emphasis is placed on the main geometrical configurations contributing to the two bound trimer states, and suggestions are made on the possible ways of experimentally detecting the Efimov-type state.
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.
We confirm the existence of and study the location and spatial shape for the ground bound state of the triatomic system that contains one lithium (6Li or 7Li) atom and two boson helium partners. The computational method employed involves a variationally determined multi-center expansion over Gaussian functions of variable width, as discussed in our previous recent work. The overall behavior of this very diffuse, bound wave-function with zero angular momentum is analyzed in detail to extract specific indicators on its spatial features. The strength of the available three-particle interaction is arbitrarily scaled in order to investigate the possible appearance of either halo or Efimov states in the present system.