Self-consistent calculations of the quadrupole moments of the lowest $3^{-}$ states in Sn and Pb isotopes

self-consistent approach to anharmonic effects based on the quantum many-body theory is for the first time used to calculate the quadrupole moments of the lowest $3^{-}$ states in Sn and Pb isotopes, including the $^{100}$Sn, $^{132}$Sn, and $^{208}$Pb doubly magic ones. The consistency between the mean nuclear field and the effective interaction is maintained using the energy-density-functional method with known parameters of the Fayans functional. Thereby, the quadrupole moments of the lowest $3^{-}$ states of isotopes with nucleon pairing are reliably predicted, and the existing data for the $^{208}$Pb isotope are reproduced. It has been shown that the new three-quasiparticle correlations are responsible for slightly more than half of the observed effect and the remaining part is due to the quadrupole polarizability of the nucleus.