  Inelastic $\alpha$-scattering excitation cross sections are calculated for
electric dipole excitations in $^{124}$Sn based on the transition densities
obtained from the relativistic quasiparticle time-blocking approximation
(RQTBA) in the framework of a semiclassical model. The calculation provides the
missing link to directly compare the results from the microscopic RQTBA
calculations to recent experimental data measured via the $(\alpha ,\alpha
'\gamma)$ reaction, which show a structural splitting of the low-lying E1
strength often denoted as pygmy dipole resonance (PDR). The experimentally
observed splitting is reproduced by the cross section calculations, which
allows to draw conclusion on the structure of the PDR.
