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The influence of particle-phonon coupling on pairing correlations in nucleiis studied by solving the Dyson equation including the anomalous (pairing)Green function. We develop the formalism for solving the equation with theminimum of approximations. The solution of the Dyson equation is compared withthe diagonalization of particle-phonon coupled Hamiltonian in a small space.This comparison reveals that the effect of many-phonon states is incorporatedin the Dyson equation. We calculate the pairing gap of the neutron in 120Sn. Wecompare analytically the present method with a simpler treatment based onBloch-Horowitz perturbation theory.Comment: 39 pages, 18 figure

Effect of Particle-Phonon Coupling on Pairing Correlations in Finite Systems: The Atomic Nucleus