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We study the fermionic Matsubara Green functions in medium-mass nuclei atfinite temperature. The single-fermion Dyson equation with the dynamical kernelof the particle-vibration-coupling (PVC) origin is formulated and solved in thebasis of Dirac spinors, which minimize the grand canonical potential with themeson-nucleon covariant energy density functional. The PVC correlations beyondmean field are taken into account in the leading approximation for theenergy-dependent self-energy, and the full solution of the finite-temperatureDyson equation is obtained for the fermionic propagators. Within this approach,we investigate the fragmentation of the single-particle states and itsevolution with temperature for the nuclear systems $^{56,68}$Ni and $^{56}$Ferelevant for the core-collapse supernova. The energy-dependent, or dynamical,nucleon effective mass is extracted from the PVC self-energy at varioustemperatures.

Temperature evolution of the nuclear shell structure and the dynamical nucleon effective mass