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

References in corpus (8)

• Atom--Molecule Coherence in a Bose-Einstein Condensate
• Photoassociation of sodium in a Bose-Einstein condensate
• Microscopic Dynamics in a Strongly Interacting Bose-Einstein Condensate
• Universal aspects of Efimov states and light halo nuclei
• Variational description of the Helium trimer using correlated hyperspherycal harmonic basis functions
• Investigation of ${}^{4}H{e}_3$ trimer on the base of Faddeev equations in configuration space
• Scaling limit of virtual states of triatomic systems
• Classification of three-body quantum halos

Cited by in corpus (12)

• Universality in Few-body Systems with Large Scattering Length
• Radii in weakly-bound light halo nuclei
• Triatomic continuum resonances for large negative scattering lengths
• Production of three-body Efimov molecules in an optical lattice
• Universality of Brunnian ($N$-body Borromean) four and five-body systems
• Nucleon-nucleon scattering within a multiple subtractive renormalization approach
• Efimov physics and the three-body parameter for shallow van der Waals potentials
• Neutron-neutron correlation in the halo dissociation of light exotic nuclei
• Structure of exotic three-body systems
• Mean-square radii in mixed-species systems in two dimensions
• Matter diffraction at oblique incidence: Higher resolution and the Helium Trimer Efimov state
• Dimensional effects in Efimov physics