Scaling predictions for radii of weakly bound triatomic molecules

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The mean-square radii of the molecules ⁴He₃, ⁴He₂-⁶Li, ⁴He₂-⁷Li and ⁴He₂-²³Na 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 mₐ in a triatomic molecule are estimated to be of de order of C√ℏ²/[mₐ(E₃-E₂)], where E₂ is the dimer and E₃ the trimer binding energies, and C is a constant (varying from 0.6 to 1) that depends on the ratio between E₂ and E₃. Considering previous estimates for the trimer energies, we also predict the sizes of Rubidium and Sodium trimers in atomic traps.