Relativistic two-phonon model for low-energy nuclear response

A two-phonon version of the relativistic quasiparticle time blocking approximation introduces as a new class of many-body models for nuclear structure calculations based on the covariant energy density functional. As a fully consistent extension of the relativistic quasiparticle random phase approximation, the relativistic two-phonon model implies fragmentation of nuclear states over two-quasiparticle and two-phonon configurations coupled to each other. In particular, we show how the lowest two-phonon $1^-$ state, identified as a member of the $[2^+\otimes 3^-]$ quintuplet, emerges from the coherent two-quasiparticle pygmy dipole mode in vibrational nuclei. The inclusion of the two-phonon configurations into the model space allows a quantitative description of the positions and the reduced transition probabilities of the lowest 1$^-$ states in tin isotopes $^{112,116,120,124}$Sn as well as the low-energy fraction of the dipole strength below the giant dipole resonance without any adjustment procedures. The model is applied to the low-lying dipole strength in neutron-rich $^{68,70,72}$Ni isotopes. Recent experimental data for $^{68}$Ni are reproduced fairly well.