[en] In this study we have built the quadrupolar collective Bohr Hamiltonian in a purely microscopic way by using an approximation of the time-dependant Hartree-Fock adiabatic approach. The purpose of this work was to obtain a quantitative description of the collective properties in the low energy range of intermediate and heavy nuclei by using a 2-body effective interaction of Skyrme-type. We consider low energy processes as dynamic regimes in which the collective movement is adiabatic when compared with modes associated to individual freedom. In the N-body solution we propose, we have assumed that: -) a mean field exists at any moment, -) some collective variables exist whose temporal variations include all the dynamics, and -) the collective movement is adiabatic. This work is a microscopic formulation and an efficient approach to resolve the Bohr and Mottelson unified model. Low energy spectra have been computed for 4 nuclei: Ge"7"4, Se"7"6, Cd"1"1"0 and Pt"1"8"6 and they agree well with experimental data