Theoretical Calculations For Weakly Bound States Of He-he-mg Complex Using Hyperspherical Coordinates

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.Since ⁴He 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.In this thesis,we calculated the L=0 ground and excited state energies for the He₂Mg 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 He₂Mg.And then,by employing the best empirical interaction between each pair of particles,we solved the Schrodinger equation for the He₂Mg systems at a series of fixed hyper-radii using B-splines.As a result,the upper bounds of the ground states binding energies of ⁴He₂²⁴Mg,³He⁴He²⁴Mg and ³He₂²⁴Mg are -3.5501K,-1.0858K and -1.2171K respectively;and the lower bounds of the binding energies are -5.0405K,-3.6844K and -3.1490K respectively.We found no evidence of the existence of halo states or Efimov states for this complex.