Weakly Bound Alkaline-earth-helium Three-atom Systems

Micro-few-body systems are the fundamentals of many-body and macroscopic systems in the quamtum world. Calculations and experiments on few-body systems can help us understand the complicated phenomenons of many-body systems. Studies of the weakly bound system have deepened our understanding of Efimov physics and halo effect, low-energy three-body scattering, the sympathetic cooling of Bose-Einstein Condensate, and the intrinsic nature of the interaction between two atoms in the helium nanodroplets experiments.The existence of the weakly bound alkaline-earth-helium and alkali-helium three-atom molecules are investigated. By employing the best empirical interaction potentials between each pair of particles, the Schrrodinger equation for the trimers is solved by using B-splines in the adiabatic hyperspherical approximation.Using the flexible and highly localized properties of B-splines, schemes for optimizing basis sets according to the distributions of different weakly bound three-atom systems have been suggested. And the high accurate hypersphercial potentials and channel functions for each triatomic systems were obtained. We got the upper bounds and lower bounds of the binding energies for each of the weakly bound systems respectively. There is no evidence of the existence of halo states or Efimov states for the complexs. The channel functions, the sum of three pairwise potentials and geometry structures are analysed at fixed hyperradius R.For the three-atom systems:3He-3He-40Ca、4He-4He-40Ca、4He-3He-40Ca、3He-3He-88Sr、4He-4He-88Sr.4He-3He-88Sr.3He-3He-138Ba、4He-4He-138Ba、4He-3He-138Ba、4He-3He-133Cs,4He-4He-133Cs, there is only one bound state for each of these molecules. And no bound state is supported by the3He-3He-133Cs system.