Self-consistent description of $EL$ transitions between one-phonon states in magic nuclei

Transition probabilities between low-lying one-phonon states of magic nuclei are for the first time computed self-consistently within an approach to anharmonic effects based on the quantum theory of many-body systems. In the adopted approach, three-quasiparticle correlations in the ground state are taken into account, and the nuclear mean field is interrelated with the effective nucleon-nucleon interaction. These quantities are derived using the energy density functional method with known parameters of the Fayans functional. The $E1$ and $E2$ transitions in the $^{132}$Sn and $^{208}$Pb nuclei are considered as an example, and a reasonably good agreement with the data on these nuclei is reached. Three-quasiparticle correlations in the ground state are shown to make a significant contribution to the probabilities of the discussed transitions.