  Density Functional Theory (DFT) is a powerful and accurate tool exploited in
Nuclear Physics to investigate the ground-state and some collective properties
of nuclei along the whole nuclear chart. Models based on DFT are, however, not
suitable for the description of single-particle dynamics in nuclei. Following
the field theoretical approach by A. Bohr and B. R. Mottelson to describe
nuclear interactions between single-particle and vibrational degrees of
freedom, we have undertaken important steps to build a microscopic dynamic
nuclear model. In connection to that, one important issue that needs to be
better understood is the renormalization of the effective interaction in the
particle-vibration approach. One possible way to renormalize the interaction is
the so called {\it subtraction method}. In this contribution we will implement
the {\it subtraction method} for the first time in our model and study its
consequences.
