Phonon-particle coupling effects in odd-even double mass differences of magic nuclei

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. In addition to the usual pole diagram, the phonon “tadpole” diagram is taken into account approximately. Results for double-magic $^{132}$Sn and $^{208}$Pb nuclei show that the PC corrections make agreement with the experimental data better.