Description of Excitations in Odd Non-magic Nuclei by the Green's Function Method

General equations for one- particle Green function in non- magic nuclei have been derived where a pairing mechanism, which is analogous to the Bardeen- Cooper- Schrieffer one, has been singled out explicitely. A "refining" procedure for the phenomenological single- particle energies and pairing gaps is formulated to avoid double counting of the phonon mixing if the initial data of the problem are these phenomenological quantities. The general equations obtained have been written in the squared phonon creation amplitude approximation. This corresponds to taking quasiparticle$\otimes$phonon configurations into account and, as shown in the work, is a good approximation for semi- magic nuclei. Using this approximation the secular equation to calculate excitations of odd non- magic nuclei has been obtained. The equation takes ground state correlations into account completely and contains only the squared energy variable. Distributions of single- particle strength in 119Sn and 121}Sn have been calculated and reasonable agreement with the available experiment has been obtained.