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 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.
We carry out calculations on the van der Waals trimer
7Li4He2 using the mapping method within the frame of hyperspherical coordinates, which allows us to give accurate binding energies and wave functions for both the ground and excited state of the system. When the realistic two-body potentials are adopted, the system presents an excited state which shows Efimov character. We study the range of the interaction strength in which the excited state could exist and find that the state persists within the experiment error band for binding energy of LiHe molecule. We also study the three-body parameter (3BP) of
7Li4He2 system and its relationship with the background scattering length
aHeHe. Our calculations demonstrate that the 3BP of
7Li4He2 system is dependent on the value of the scattering length
aHeHe, independent of the short-range details of the He-He interaction. The results confirm the prediction of Wang et al. [Phys. Rev. Lett. 109, 243201 (2012)] that the 3BP for a heteronuclear atomic system is universally determined from the van der Waals lengths and the homonuclear scattering length.
Atom-dimer exchange and dissociation reaction rates are predicted for different combinations of two
4He atoms and one of the alkaline species among
6Li,7Li, and
23Na, by using three-body scattering formalism with short-range two-body interactions. Our study was concerned with low-energy reaction rates in which the
s-,
p-, and
d-wave contributions are the relevant ones. The
4He is chosen as one of the atoms in the binary mixture, in view of available previous investigations and laboratory accessibilities. Focusing on possible experimental cold-atom realizations with two-atomic mixtures, in which information on atom-dimer reaction rates can be extracted, we predict the occurrence of a dip in the elastic reaction rate for colliding energies smaller than 20 mK, when the dimer is the
4He23Na molecule. We are also anticipating a zero in the elastic
p-wave contribution for the
4He+4He7Li and
4He+4He23Na reaction processes. With weakly bound molecules reacting with atoms at very low colliding energies, we interpret our results in the light of Efimov physics which supports model independence and robustness of our predictions. Specific sensitivities on the effective range were evidenced, highlighted by the particular inversion role of the
p- and
d-waves in the atom exchange and dissociation processes.
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.
The usefulness of a scale-independent approach to identify Efimov states in three-body systems is shown by comparing such an approach with a realistic calculation in the case of three helium atoms. We show that the scaling limit is realized in practice in this case, and suggest its application to study other similar systems, including the case where two kinds of atoms are mixed. We also consider the observed large scattering length of
the87Rb dimer to estimate the critical value of the ground-state energy of the corresponding trimer
(> 1.5mK), in order to allow for one Efimov state above the ground state.