Particle-vibration coupling within covariant density functional theory

Abstract

Covariant density functional theory, which has so far been applied only within the framework of static and time-dependent mean-field theory, is extended to include particle-vibration coupling (PVC) in a consistent way. Starting from a conventional energy functional, we calculate the low-lying collective vibrations in the relativistic random phase approximation (RRPA) and construct an energy-dependent self-energy for the Dyson equation. The resulting Bethe-Salpeter equation in the particle-hole (p-h) channel is solved in the time blocking approximation (TBA). No additional parameters are used, and double counting is avoided by a proper subtraction method. The same energy functional, i.e., the same set of coupling constants, generates the Dirac-Hartree single-particle spectrum, the static part of the residual p-h interaction, and the particle-phonon coupling vertices. Therefore, a fully consistent description of nuclear excited states is developed. This method is applied for an investigation of damping phenomena in the spherical nuclei with closed shells $^{208}\mathrm{Pb}$ and $^{132}\mathrm{Sn}$. Since the phonon coupling terms enrich the RRPA spectrum with a multitude of p-h\ensuremath{\bigotimes}phonon components, a noticeable fragmentation of the giant resonances is found, which is in full agreement with experimental data and with results of the semiphenomenological nonrelativistic approach.