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

I. Baccarelli ^1,3 - G. Delgado-Barrio ¹ - F. A. Gianturco ² -
T. Gonzalez-Lezana ¹ - S. Miret-Artés ¹ - P. Villarreal ¹

¹ Instituto de Matemáticas y Física Fundamental
Consejo Superior de Investigaciones Científicas
Serrano, 123, 28006 Madrid, Spain
² Department of Chemistry, The University of Rome
Città Universitaria, I-00185 Roma, Italy
³ Laboratoire de Dynamique des Ions, Atomes et Molecules
Universitè Pierre et Marie Curie
4 Place Jussieu, 75252 Paris Cedex, France

PACS :
03.65.Ge - Solutions of wave equations: bound states
21.45.+v - Few-body systems
21.60.Gx - Cluster models

Abstract:

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 unlikely presents any Efimov state, while the 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 controlling the strength of the potential. Each system presents two bound levels at the "physical'' situation . 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 , as shown by the greatly reduced relevance of isotopic effects in our actual 3B calculations.

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