Universal nature and finite-range corrections in elastic atom-dimer scattering below the dimer breakup threshold

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We investigate universal behavior in elastic atom-dimer scattering below the dimer breakup threshold calculating the atom-dimer effective-range function akδ. Using the He-He system as a reference, we solve the Schrödinger equation for a family of potentials having different values of the two-body scattering length a and we compare our results to the universal zero-range form deduced by Efimov, akδ=c₁(ka)+c₂(ka)[s₀(κ*a)+ϕ(ka)], for selected values of the three-body parameter κ*. Using the parametrization of the universal functions c₁,c₂,ϕ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter κ*.