We simulate the behavior of two weakly attractive atoms, either spin-polarized hydrogen atoms or ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms, on a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ cluster by examining the angular correlation of the atoms as they move on the surface of a sphere. We have calculated converged energy levels, wave functions, and reduced densities ${\mathrm{\rho }}^{\left(\mathit{J}\right)}$(${\mathrm{\theta }}_{12}$) for the low-lying states of these two systems. We also give the oscillator strengths for several transitions between low-lying states for the case of spin-polarized hydrogen. The energy levels can be arranged in patterns reminiscent of the rovibrational levels of a linear triatomic molecule, but the reduced densities differ significantly from those predicted by the molecular model. The lowest state for two ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ atoms on a sphere of radius 13.0 bohr is bound, with E=-0.031 90 ${\mathrm{cm}}^{\mathrm{-}1}$.

• Received 19 March 1990

DOI:https://doi.org/10.1103/PhysRevA.42.2259