Product-State Distributions of Three-Body Recombination in Zero-Collision-Energy ⁴He₂-Alkaline-Earth-Metal Systems

The distributions of product states after three-body recombination (TBR) of zero-collision-energy ⁴He₂X systems, with X being ⁹Be, ²⁴Mg, ⁴⁰Ca, ⁸⁸Sr, or ¹³⁸Ba, are investigated in the hyperspherical representation by quantum mechanically solving the Schrödinger equation. It is found that the weakly bound (dimer) product states are preferentially populated for all of these cases, which could be understood from the joint effects of the lowest incident channel and the relatively long-range behavior of the corresponding nonadiabatic couplings among these lowest incident and shallow recombination channels. For the strongly bound products, since the flow is accessible in the small hyperradial region, their distributions are closely related to the behavior of the nonadiabatic couplings among the corresponding deep recombination channels. Particularly, our results indicate that the products are not always formed exclusively in the most weakly bound state when the scattering lengths among the reactants are relatively large and that there may exist a large fluctuation of the strongly bound products versus their binding energies in the universal region. In addition, the total TBR rates of these nonuniversal systems are also accounted for by the joint effects of the main adiabatic potentials and nonadiabatic couplings.