Mean field based calculations with the Gogny force: Some theoretical tools to explore the nuclear structure

We present a review of several works using the finite-range Gogny interaction in mean field approaches and beyond to explore the most striking nuclear structure features. Shell evolution along the N = 16, 20, 28, 40 isotopic chains is investigated. The static deformation obtained in the mean field description are shown to be often in disagreement with the one experimentally determined. Dynamics is addressed in a GCM-like method, including rotational degrees of freedom, namely the five-dimension collective Hamiltonian (5DCH). This framework allows the description of the low-energy collective excitations. Nevertheless, some data cannot be reproduced with the collective Hamiltonian approach. Thus the QRPA formalism is introduced and used to simultaneously describe high-and low-energy spectroscopy as well as collective and individual excitations. After the description of giant resonances in doubly magic exotic nuclei, the role of the intrinsic deformation in giant resonances is presented. The appearance of low-energy dipole resonances in light nuclei is also discussed. In particular the isoscalar or isovector nature of Pygmy states is debated. Then, the first microscopic fully coherent description of the multipole spectrum of heavy deformed nucleus U-238 is presented. Finally, a comparison of the low-energy spectrum obtained within the two extensions of the static mean field, namely QRPA and 5DCH, is performed for 2(+) states in N = 16 isotones, nickel and tin isotopes. For the first time the different static and dynamic factors involved in the generation of the 2(+) states in the nickel isotopic chain, from drip line to drip line, can be analysed in only one set of coherent approaches, free of adjustable parameters, using the same two-body interaction D1S and the resulting HFB mean field.