  The isotopic dependence of the excitation energies of the pygmy dipole
resonance (PDR) is analyzed in the framework of the self-consistent
relativistic Hartree-Bogoliubov (RHB) model and the relativistic quasiparticle
random-phase approximation (RQRPA). The DD-ME1 density-dependent meson-exchange
interaction is used in the effective mean-field Lagrangian, and pairing
correlations are described by the pairing part of the finite-range Gogny
interaction D1S. Model calculations reproduce available experimental data on
charge radii, the neutron skin, neutron separation energies, and excitation
energies of isovector giant dipole resonances in Ni, Sn and Pb nuclei. In all
three isotopic chains the one-neutron separation energies decrease with mass
number much faster than the excitation energies of the PDR. As a result,
already at moderate proton-neutron asymmetry the PDR peak energy is calculated
above the neutron emission threshold. This result has important implications
for the observation of the PDR in (gamma,gamma') experiments.
