Theoretical description of collective nuclear excitations and astrophysically relevant processes require methods going beyond the random phase approximation (RPA) or Tamm-Dancoff approximation (TDA), which are limited to one-particle–one-hole (1p-1h) configurations. In this work, we introduce the second Tamm-Dancoff approximation (STDA) based on the relativistic nuclear energy density functional, which also incorporates two-particle–two-hole (2p-2h) configurations, providing a more comprehensive description of nuclear excitations. Within the relativistic STDA (RSTDA), we implement the subtraction method, which is essential to avoid double counting of correlations and provide realistic description of excited states. Using the DD-PC1 parametrization of the relativistic point-coupling interaction, in the first application of the RSTDA we investigate the properties of isoscalar monopole and quadrupole transitions in ${}^{16}\mathrm{O}$. The analysis reveals the important role of complex configurations in centroid energies, transition strength distributions, and the fine structure of nuclear response. By resolving the fragmentation and spreading of excitation strength, the RSTDA enables accurate description of experimental spectra.

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• Collective models
• Electromagnetic transitions
• Nuclear many-body theory
• Nuclear density functional theory