Scaling predictions for radii of weakly bound triatomic molecules

Abstract

The mean-square radii of the molecules ${}^4$He${}_3$, ${}^4$He${}_2{-}^6$Li, ${}^4$He${}_2{-}^7$Li and ${}^4$He${}_2{-}^{23}$Na are calculated using a three-body model with contact interactions. They are obtained from a universal scaling function calculated within a renormalized scheme for three particles interacting through pairwise Dirac-delta interaction. The root-mean-square distance between two atoms of mass $m_A$ in a triatomic molecule are estimated to be of de order of $\mathcal{C}\sqrt{{\hslash }^2/[m_A(E_3-E_2)]}$, where $E_2$ is the dimer and $E_3$ the trimer binding energies, and $\mathcal{C}$ is a constant (varying from $\sim 0.6$ to $\sim 1$) that depends on the ratio between $E_2$ and $E_3$. Considering previous estimates for the trimer energies, we also predict the sizes of Rubidium and Sodium trimers in atomic traps.

7 pages, 2 figures