The Higher Tamm-Dancoff Approximation and the treatment of pairing and vibrational correlations in atomic nuclei

A review of a consistent microscopic treatment of correlations, both of a pairing nd of a vibrational nature, will be presented. This approach dubbed as the Higher Tamm-Dancoff Approximation, consists in performing iteratively highly truncated shell-model type calculations using self consistent single particle states. The latter are defined as eigenstates of a hartree-Fock Hamiltonian associated to, e.g., a Skryme effective force and to the one body density matrix of the correlated solution. The method will be illustrated with selected examples concerning pairing correlations in magic nuclei, in N-Z nuclei, in K-isomeric states or in fast rotational states as well as to describe quantal flucuations around a classical equilibrium shape (RPA-like correlations). The relevance of this approach to study isospin mixing will be discussed.