Neutral and positively charged excitons in quantum ring

•Using the series Fourier method, the energy spectra of excitons is calculated.•A comparative analysis of energies dependencies for excitons with those for the donor complexes, is presented.•Energy levels of excitons are split in two groups with different responses to magnetic field.•The increase of the radius produces enhance of the number of the vibrational states.

We study theoretically quantized states of the neutral and positively charged exciton complexes confined within a circular narrow ring in the presence of the magnetic field applied along the symmetry axis. We show that in the structural adiabatic limit, when the width of the pattern of the particles pathways within the ring is much smaller than its radius, the wave equations for both complexes are separable and their exact solutions can be found in a form of the Fourier series of one and two variables, respectively. We present results of calculation of the lower energies of complexes as functions of the ring's radius and the magnetic field strength for different values of the electron-to-hole mass ratio. We found that in the molecular adiabatic limit, when this ratio tends to zero and the model describes the corresponding donor complexes, the physical interpretation of the quantum-size effect and the oscillations of energy levels in threading magnetic field revealed for the excitons spectra becomes more transparent.