D- energy spectrum in toroidal quantum ring

The structure of energy spectrum of the negative donor centre in a toroidal-shaped quantum ring with two different morphologies of the cross-section is analyzed. By using the adiabatic procedure we have deduced a one-dimensional wave equation with periodic conditions which describes the low-lying energy levels related to the electrons rotation around the symmetry axis. Our results are in good agreement with those previously obtained as the size of the ring cross-section tends to zero.