  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.
