Scattering length scaling rules for atom-atom-anion three-body recombination of zero-energy ⁴He⁴He⁶Li^- system

The scattering length scaling rules for three-body recombination (TBR) of the 4He4He6Li- system in the zero-energy limit (E → 0) are investigated by considering various post-Born-Oppenheimer (post-BO) contributions to the standard BO potential of He-He interaction. It is found that these post-BO effects on the TBR rates that lead to different dimer products could be well fitted by the scattering length scalings Cab with a being the scattering length of the He-He interaction, and b and C the constants. It is interesting to find that the powers b about both the weakly and deeply bound dimer products are quite different from the well-known powers given by the scattering length scaling laws in the fields of ultracold neutral atomic gases. Such difference and the distinct powers associated with various dimer products are qualitatively accounted for by the properties of the major effective potentials and relatively long-range nonadiabatic couplings. Particularly, from these properties, the scaling powers are expected to be dependent on systems, but the power scattering length scaling behaviors to be universal, which has also been checked to apply to a wide range of a by tuning the He-He interaction.