We develop a self-consistent relativistic second random-phase approximation (RSRPA) based on a covariant energy density functional with density-dependent point-coupling interaction. The formalism extends the conventional simple configuration space composed of particle-hole transitions by including two-particle–two-hole (2p-2h) configurations through a generalized Thouless ansatz and a time-dependent variational principle. To ensure consistency with the underlying mean-field ground state and avoid the double counting of correlations, we implement the subtraction method, in which the static contribution is removed from the residual interaction. The first applications of the RSRPA include studies of isoscalar and isovector giant monopole (ISGMR and IVGMR) and quadrupole resonances (ISGQR and IVGQR) in ${}^{16}\mathrm{O}$, which demonstrate the importance of 2p-2h couplings to describe the fragmentation of the transition strength and the stabilizing role of the subtraction method.

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• Collective levels
• Nuclear density functional theory
• Nuclear many-body theory