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

Abstract

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 Schrodinger equation, in which the Schrodinger 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 JΠ = 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.