Dynamical correlations in the ground state: transitions between one-phonon nuclear states

The probabilities of the $E1$ transition between the first ${{2}^{ + }}$ and ${{3}^{ - }}$ excited levels in nuclei with pairing have been calculated within the self-consistent many-body nuclear theory and Green's function method. Calculations for a long chain of even-even tin isotopes have been performed for the first time. The known Fayans energy density functional has been used to calculate the characteristics of phonons and $E1$ transitions between excited states. A good description has been achieved for existing experimental data for the reduced probabilities of $E1$ transitions between the first one-phonon states for the $^{116-124}$Sn isotopes but not for the $^{112}$Sn and $^{114}$Sn isotopes. Possible reasons for this discrepancy have been discussed; the most probable reason is the deformation in the ground or excited states. It has been shown that new dynamical three-quasiparticle correlations in the ground state should be taken into account to explain the experimental data for $^{116-124}$Sn.