Relativistic RPA plus phonon-coupling analysis of pygmy dipole resonances

The relativistic random-phase approximation (RRPA) plus phonon-coupling (PC) model is applied in the analysis of E1 strength distributions in $^{208}$Pb and $^{132}$Sn, for which data on pygmy dipole resonances (PDR) have recently been reported. The covariant response theory is fully consistent: the effective nuclear interaction NL3 is used both to determine the spectrum of single-nucleon Dirac states, and as the residual interaction which determines the collective phonon states in the relativistic RPA. It is shown that the picture of the PDR as a resonant oscillation of the neutron skin against the isospin saturated proton-neutron core, and with the corresponding RRPA state characterized by a coherent superposition of many neutron particle-hole configurations, remains essentially unchanged when particle-vibration coupling is included. The effect of two-phonon admixtures is a weak fragmentation and a small shift of PDR states to lower excitation energy. Even though the PDR calculated in the extended model space of $ph \otimes$phonon configurations contains sizeable two-phonon admixtures, it basically retains a one-phonon character and its dynamics is not modified by the coupling to low-lying surface vibrations.