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Two-point fermionic propagators in strongly-correlated media are considered with an emphasis on the dynamical interaction kernels of their equations of motion (EOM). With the many-body Hamiltonian confined by a two-body interaction, the EOMs for the two-point fermionic propagators acquire the Dyson form and, before taking any approximation, the interaction kernels decompose into the static and dynamical (time-dependent) contributions. The latter translate to the energy-dependent and the former map to the energy-independent terms in the energy domain. We dwell particularly on the energy-dependent terms, which generate long-range correlations while making feedback on their short-range static counterparts. The origin, forms, and various approximations for the dynamical kernels of one-fermion and two-fermion propagators, most relevant in the intermediate-coupling regime, are discussed. Applications to the electromagnetic dipole response of 68,70-Ni and low-energy quadrupole response of 114,116,124-Sn are presented. 

β -decay rates of neutron-rich nuclei, in particular those located at neutron shell closures, play a central role in simulations of the heavy-element nucleosynthesis and resulting abundance distributions. We present β -decay half-lives of even-even N = 82 and N = 126 r -process waiting-point nuclei calculated in the approach based on relativistic quasiparticle random phase approximation with quasiparticle-vibration coupling. The calculations include both allowed and first-forbidden transitions. In the N = 82 chain, the quasiparticlevibration coupling has an important impact close to stability, as it increases the contribution of Gamow-Teller modes and improves the agreement with the available data. In the N = 126 chain, we find the decay to proceed dominantly via first-forbidden transitions, even when the coupling to vibrations is included.