The energy spectrum and the wave functions of a shaflow donor placed at the center of a spherical quantum antidot are computed within the effective mass approximation. The wave functions for discrete bound states and for continuum states are obtained in a closed form. We show that, due to the local potential of the microstructure, resonaτιces occur in the continuum. Tleir energies are close to those of hydrogen-like levels lying under the top of the barrier when the quantum antidot radius is

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... ge as compared to the effective Bohr radius. The lifetimes of the resonant states and the oscillator strengths for optical transitions from the ground state are computed. We show how the energy spectrum and the oscillator strengths depend on the antidot parameters. PACS numbers: 73.20. Dx, Zero-dimensional microstructures, known as quantum dots (QDs) confine electrons and (or) holes inside a small region. The lack of translational symmetry produces atom-like discrete levels, whose energies can be varied just by changing the QD diameter. Like for real atoms, one can expect to obtain information about these energy levels by studying the optical transitions. In a previous paper [1] we have presented theoretical results of electron states in a spherical QD. We have shown that QD structures produce not only discrete levels but also resonant states in the continuum. Their positions and energy widths depend on the well size and on the values of the confining potential. There is a correspondence between bound and resonant states. As the radius of the QD decreases, the bound states continuously transform into resonant states and a crítical value of the radius for this transition can be found for each state. The Coulomb potential alone does not produce any resonances in the continuum. however, if it is complemented with the potential of the dot, resonant states appear. In the case of superimposed Coulomb repulsive potential (which can be given, for example, by a compensated acceptor), the resonances are very narrow (743)