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Recombination rates from potential models close to the unitary limit

We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schrödinger equation above the dimer threshold for different potentials having large values of the two-body scattering length $a$. To this aim we use the hyperspherical adiabatic expansion and we extract the $S$-matrix through the integral relations recently derived. The results are compared to the universal form, $α\approx 67.1\sin^2[s_0\ln(κ_*a)+γ]$, for different values of $a$ and selected values of the three-body parameter $κ_*$. A good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections, which have been recently proposed by two of the authors in Ref.[1]. Furthermore, we analyze the validity of the above formula in the description of a very different system: neutron-neutron-proton recombination. Our analysis confirms the universal character of the process in systems of very different scales having a large two-body scattering length.