Weakly Bound Triatomic He₂²¹ Na And Molecules

The study for weakly bound states of simple molecules is an important subject both in atomic and molecular physics and quantum chemistry, among them, the weakly bound three-body systems correlating with He attract many interests in theoretical and experimental research[1]. Since4He is a boson, it obeys the Bose-Einstein statistics, and this research is related to ultracold atomic physics and Bose-Einstein condensate. Further more, these three-body systems have more abundant physical phenomenas then the two-body systems, the curious quantum properties of the three-body systems may be found, just like the halo (or Borromean) states or Efimov states[2].In this paper, we calculated the L=0ground and excited state energies for the He221Na system using hyperspherical coordinates. First, we calculate the vibrational energies of alkaline-earth-helium diatoms using different potential models, and compared with different results, we choose the reasonable potential model for He221Na And then, by employing the best empirical interaction between each pair of particles, we solved the Schrodinger equation for the He221Na systems at a series of fixed hyper-radii using B-splines [2]. As a result, the upper bounds of the ground states binding energies of4He221Na,3He4He21Na and3He221Na ar e-259.7720mK,-81.0599mK and-20.1052mK respectively; and the lower bounds of the binding energies are-383.6293mK,-160.8173mK and-50.7535mK respectively. We found no evidence of the existence of halo states or Efimov n states for this complex.