Interaction of the single-particle and collective degrees of freedom in   non-magic nuclei: the role of phonon tadpole terms
  A method of a consistent consideration of the phonon contributions to mass and gap operators in non-magic nuclei is developed in the so-called g^2 approximation, where g is the low-lying phonon creation amplitude. It includes simultaneous accounting for both the usual non-local terms and the phonon tadpole ones. The relations which allow the tadpoles to be calculated without any new parameters are derived. As an application of the results, the role of the phonon tadpoles in the single-particle strength distribution and in the single-particle energies and gap values has been considered. Relation to the problem of the surface nature of pairing is discussed. 
S. Kamerdzhiev, E.E. Saperstein