Calculation of Energies of the Ground and Low Excited States of a Confined Helium Atom in a Spherical Parabolic Well

Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of the confined helium atom in a spherical parabolic well. We find that the energies of a spherical parabolic well are in good agreement with those of an impenetrable spherical box for the larger confined potential radius. However, the energy values of a spherical parabolic well are much lower than those of an impenetrable spherical box for small values of r_c. We also find that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values.