Searching for Efimov states in triatomic systems:: The case of LiHe2

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 Li-7 unlikely presents any Efimov state, while the Li-6 isotopic variant would be a better candidate in this regard. Then, triatomic bound states are searched through variational calculations in terms of pair intel-atomic distances and distributed Gaussian functions (DGF). The calculations were performed at several values of a parameter lambda controlling the strength of the potential. Each system presents two bound levels at the "physical" situation lambda = 1. By increasing lambda, the excited levels become "ghost" stales as their energies are above the helium dimer energy and present, therefore, an Efimov character. Hence, Ne 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 LiHe2, as shown by the greatly reduced relevance of isotopic effects in our actual 3B calculations.