The first applications of the relativistic Second Tamm-Damncoff approximation in doubly-magic nuclei

Understanding nuclear collective excitations and processes relevant for astrophysics requires theoretical frameworks that extend beyond the lim­itations of the Random Phase Approximation (RPA). The RPA, confined to a simple 1 particle - 1 hole (1 p-1h) configuration space, cannot fully cap­ture the fragmentation and the spreading width of excitation spectra. Re­cently, a fully self-consistent relativistic Second Tamm-Dancoff Approximation (RSTDA) has been developed in the framework of covariant density functional theory, incorporating two-particle-two-hole (2p-2h) configurations. Here we focus on the RSTDA with diagonal approximation and the application of the subtraction method, in the cases of monopole and quadrupole transitions in 16O and 40Ca. By employing the subtraction method, double-counting effects and infrared divergence are eliminated from the calculated excitation spectra. Using the relativistic contact interaction with DD-PC1 parametrization, in the particle-hole channel, we have analyzed the influence of energy cutoff for the 2p-2h on the excitation spectra. We have calculated transition strength distribution of the giant resonances and the corresponding energy and inverse-energy weighted strengths, the centroid energies and widths. We have investigated the impact of the subtraction method in the diagonal approximation by comparing spectra ob­tained with and without its application. This dual comparison provides insight into the role of complex configurations and the elimination of double-counting effects in shaping the spectral characteristics.