Low-energy three-body dynamics in binary quantum gases

The universal three-body dynamics in ultra-cold binary Fermi and Fermi-Bose mixtures is studied. Two identical fermions of mass m and a particle of mass m(1) with the zero-range two-body interaction in states of total angular momentum L = 1 are considered. Using the boundary condition model for the s-wave interaction of different particles, both eigenvalue and scattering problems are treated by solving hyper-radial equations, whose terms are derived analytically. The dependences of the three-body binding energies on the mass-ratio m/m(1) for the positive two-body scattering length are calculated; it is shown that the ground and excited states arise at m/m(1) >= lambda(1) approximate to 8.172 60 and m/m(1) >= lambda(2) approximate to 12.917 43, respectively. For m/m(1) less than or similar to lambda(1) and m/m(1) less than or similar to lambda(2), the relevant bound states turn to narrow resonances, whose positions and widths are calculated. The 2 + 1 elastic scattering and the three-body recombination near the three-body threshold are studied, and it is shown that a two-hump structure in the mass-ratio dependences of the cross sections is connected with the rise of the bound states.