Pygmy and giant dipole resonances in neutron-rich nuclei within the quasiparticle representation of the phonon damping model

The quasiparticle representation of the phonon damping model (PDM) is developed to include the superfluid pairing correlations microscopically. The formalism is applied to calculate the photoabsorption and the electromagnetic (EM) differential cross sections of $E1\mathrm{}$ excitations in neutron-rich oxygen and calcium isotopes. The calculated photoabsorption cross sections agree reasonably well with the available data for ${}^{16,18}\mathrm{O}$ and ${}^{40,48}\mathrm{Ca}.$ The fractions of energy-weighted sum of strength in the region of the pygmy dipole resonance (PDR) ${(E}_{\gamma }<~15–16$ MeV) and the PDR peaks in the EM cross sections for ${}^{20,22}\mathrm{O}$ are also found in reasonable agreement with experimental systematics. The deviation from the prediction given by the cluster model’s sum rule shows the importance of the effect of coupling to noncollective degrees of freedom in the damping of pygmy and giant dipole resonances.