  We use the numerical renormalization group method to investigate the spectral
properties of a single-impurity Anderson model with a gap {\delta} across the
Fermi level in the conduction-electron spectrum. For any finite {\delta} > 0,
at half filling the ground state of the system is always a doublet. Away from
half filling a quantum phase transition (QPT) occurs as function of the gap
value {\delta}, and the system evolves from the strong-coupling (SC) Kondo-type
state, corresponding to {\delta} <{\delta}_C toward a localized moment (LM)
regime for {\delta} > {\delta}_C. The opening of the gap leads to the formation
of one (two) bound states when the system is in the SC (LM) regime. The
evolution across the QPT of their positions and the corresponding weights
together with the dynamic properties of the model are investigated.
