The higher Tamm-Dancoff approximation: Theoretical context and phenomenological aspects

We present the key aspects of the theoretical foundations of the Higher Tamm-Dancoff Approximation which can be interpreted as a truncated shell-model approach based on a Hartree Fock solution, ensuring the conservation of the particle number. Then we discuss some phenomenological aspects of the residual interactions used, namely the delta interaction to describe the neutron neutron and proton proton pairing correlations and the quadrupole-quadrupole interaction to describe vibrational correlations.