Quasiparticle-vibration coupling in a relativistic framework: Shell structure of Z=120 isotopes

For the first time, the shell structure of open-shell nuclei is described in a fully self-consistent extension of the covariant energy density functional theory. The approach implies quasiparticle-vibration coupling for superfluid systems. A one-body Dyson equation formulated in the doubled quasiparticle space of Dirac spinors is solved for nucleonic propagators in tin isotopes which represent the reference case: The obtained energies of the single-quasiparticle levels and their spectroscopic amplitudes are in agreement with data. The model is applied to describe the shell evolution in a chain of superheavy isotopes (292,296,300,304)120 and finds a rather stable proton spherical shell closure at Z = 120. An interplay of the pairing correlations and the quasiparticle-phonon coupling gives rise to a smooth evolution of the neutron shell gap between N = 172 and N = 184 neutron numbers. Vibrational corrections to the alpha-decay energies reach several hundred keV and can be either positive or negative, thus also smearing out the shell effects.