Perturbation expansion in Dynamical Nuclear Field Theory and its relation with Boson expansion theory

With the Dynamical Nuclear Field Theory (DNFT) in the Tamm-Dancoff representation we examine higher order corrections in the vibrational mode of a spherical nuclear system. Due to the effects of bubble diagrams, the perturbation expansion in terms of the unrenormalized coupling strength and boson energy fails at full self-consistency. On the other hand, it becomes applicable in the form of linked-cluster expansion when we use these constants renormalized by the effect of bubble diagrams, in the schematic model. However, in comparison with the boson expansion theory, serious defects are found in higher order DNFT. (author)