  Energy spectra and electromagnetic transitions of nuclei are strongly
depending from the correlations of the bound nucleons. Two particle
correlations are responsible for the scattering of model particles either to
low momentum- or to high momentum-states. The low momentum states form the
model space while the high momentum states are used to calculate the G-matrix.
The three and higher order particle correlations do not play a role in the
latter calculation especially if the correlations induced by the scattering
operator are of sufficient short range. They modify however, via the long tail
of the nuclear potential, the Slater determinant of the A particles by
generating excited Slater's determinants. In this work the influence of the
correlations on the level structure and ground state distributions of even open
shell nuclei is analyzed via the boson dynamic correlation model BDCM. The
model is based on the unitary operator $e^S$ ({\it S} is the correlation
operator) formalism which in this paper is presented within a non perturbative
approximation. The low lying spectrum calculated for $^6$Li reproduce very well
the experimental spectrum while for $^6$He a charge radius slightly larger than
that obtained within the isotopic-shift (IS) theory has been calculated. Good
agreement between theoretical and experimental results has been obtained
without the introduction of a genuine three body force.
