Recombination rates from potential models close to the unitary limit

Abstract

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≈67.1sin2[s0ln(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. 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. © 2013 American Physical Society.