Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model

The relativistic quasiparticle random phase approximation (RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov (RHB) model. For the interaction in the particle-hole channel effective Lagrangians with nonlinear meson self-interactions are used, and pairing correlations are described by the pairing part of the finite-range Gogny interaction. The RQRPA configuration space includes the Dirac sea of negative-energy states. Both in the particle-hole and particle-particle channels, the same interactions are used in the RHB calculation of the ground state and in the matrix equations of the RQRPA. The RHB+RQRPA approach is tested in the example of multipole excitations of neutron-rich oxygen isotopes. The RQRPA is applied in the analysis of the evolution of the low-lying isovector dipole strength in Sn isotopes and $N=82$ isotones.