  A method is developed to consider the particle-phonon coupling (PC) effects
in the problem of finding odd-even double mass differences (DMD) of magic
nuclei within the approach starting from the free $NN$-potential. Three PC
effects are taken into account, the phonon induced interaction, the
renormalization of the "ends" due to the $Z$-factors and the change of the
single-particle energies. We use the perturbation theory in $g^2_L$, where
$g_L$ is the vertex of the $L$-phonon creation. PC corrections to
single-particle energies are found self-consistently with an approximate
account for the so-called tadpole diagram. Results for double-magic $^{132}$Sn
and $^{208}$Pb nuclei show that the PC corrections make agreement with the
experimental data better.
