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

Abstract

The possible presence of Efimov-type states in isotopic variants of triatomic molecules composed of one Liand two boson He atoms is investigated. Firstly, through the study oftwo-body interactions in the frame of the effective range theory,it is shown that, at least with the present choice of dimerpotentials, the system containing 7Li unlikely presents any Efimov state, while the 6Li isotopic variant would be a better candidate in this regard.Then,triatomic bound states are searched through variational calculations in termsof pair inter-atomic distances and distributed Gaussian functions (DGF).The calculations were performed at several values of a parameter λcontrolling the strength of the potential. Each system presents two boundlevels at the “physical” situation λ = 1. By increasing lambda, theexcited levels become “ghost” states as their energies areabove the helium dimer energyand present, therefore, an Efimov character.Hence, we conclude that three-body (3B) predictions coming only fromtwo-body (2B) calculations do not have, at least for the systems studied here, any great relevance. Such predictions are notin fact fulfilled for LiHe2, as shown by the greatly reduced relevance of isotopic effects in our actual 3B calculations.