  A semi-microscopic model to study the neutron and proton induced backbending
phenomena in some deformed even-even nuclei from the rare earth region, is
proposed. The space of particle-core states is defined by the angular momentum
projection of a quadrupole deformed product state. The backbending phenomena
are described by mixing four rotational bands, defined by a set of angular
momentum projected states, and a model Hamiltonian describing a set of paired
particles moving in a deformed mean field and interacting with a
phenomenological deformed core. The ground band corresponds to the
configuration where all particles are paired while the other rotational bands
are built on one neutron or/and one proton broken pair. Four rare earth
even-even nuclei which present the second anomaly in the observed moments of
inertia are successfully treated within the proposed model.
