A Theoretical Study of Pure and Mixed Spin-Polarized Tritium and Helium Triatomic Systems Using Hyperspherical Coordinates

Pure and mixed spin-polarized tritium ( ${{rm T}uparrow}$ ) and helium (He) triatomic systems are studied using hyperspherical coordinates. A slow variable discretization approach is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed FEM-DVR hyperradii. By using the best empirical interaction potentials, we study comparatively the bound states of ( ${{rm T}uparrow}$ )₃, ⁴He( ${{rm T}uparrow}$ )₂, ${^4{rm He}_2{rm T}uparrow}$ , ⁴He₃ and ${^4{rm He}_2^3{rm He}}$ in the J ^Π = 0⁺ symmetry. The bound state energy levels are calculated for all these molecular species except ⁴He( ${{rm T}uparrow}$ )₂, for which we have found no bound state. The calculated wave functions of these species are found all to exhibit a very large spatial extension, indicating the diffuse nature of these bound states. The molecular structure of these species will also be calculated and analyzed in detail.