Self-Consistent Calculations of Probabilities for the \({E}\)1 Transition between the Ground State and the \({[3_{1}^{-}\times 2_{1}^{+}]_{1^{-}}}\) Two-Phonon State in Tin Isotopes

A self-consistent method for studying second-order anharmonic effects on the basis of many-body quantum field theory is applied for the first time in calculating probabilities for \(E\)1 transitions between the ground state and the \([3_{1}^{-}\times 2_{1}^{+}]_{1^{-}}\) two-phonon state in the semimagic tin isotopes \({}^{104-124}\)Sn. The approach used involves taking into account (i) self-consistency of the nuclear mean field and effective interaction on the basis of the energy density functional method with the parameters of the Fayans functional DF3-a, which were earlier found to provide good results; (ii) ground-state three-quasiparticle correlations; and (iii) nuclear-polarizablility effects. Good agreement with available experimental data, including those for \({}^{112}\)Sn, is obtained. Values of \(B\)(\(E\)1) are predicted for \({}^{104{-}110,114}\)Sn even–even nuclei. It is shown that dynamical ground-state three-quasiparticle correlations make a substantial contribution to the reduced probabilities for the \(E\)1 transitions in question, so that their inclusion is necessary for explaining experimental data.