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.