Phonon-Particle Coupling Effects in the Single-Particle Energies of Semi-Magic Nuclei

摘要

A method is presented to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies (SPEs) in semi-magic nuclei. In such nuclei always there is a collective low-lying 2(+) phonon, and a strong mixture of single-particle and particle-phonon states often occurs. As in magic nuclei, the so-called g(L)(2) approximation, where g(L) is the vertex of the L-phonon creation, can be used for finding the PC correction delta Sigma(PC)(epsilon) to the initial mass operator Sigma(0). In addition to the usual pole diagram, the phonon "tadpole" diagram is also taken into account. In semi-magic nuclei, the perturbation theory in delta Sigma(PC)(epsilon) with respect to Sigma(0) is often invalid for finding the PC corrected SPEs. Instead, the Dyson equation with the mass operator Sigma(epsilon)=Sigma(0)+delta Sigma(PC)(epsilon) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.