Study on nuclear breathing modes within QRPA formalism: a challenge for modern effective interactions

Giant resonances are privileged modes of vibration. They make it possible to understand aspects of the structure of the atomic nucleus (energy levels, clustering, and so on) thanks to their decays and their excitation energies. They can also be used to test the validity of a theoretical model and constrain phenomenological interactions. Among these modes, the Isoscalar Giant Monopole Resonance (ISGMR) is noticeable as it is related by its main excitation energy to the incompressibility of nuclear matter and therefore to its equation of state. Studied for decades, the ISGMR is still subject to debate. Over all the nuclei, no theoretical model manages to reproduce all the experimental values, which are sometimes themselves not compatible with each other, depending on the set-up used and the data analyzes carried out. In particular, the theoretical models giving a good reproduction of Lead isotopes fail to reproduce the chains of Nickel, Cadmium and Tin, and vice versa. The whole objective of this thesis work is to try to understand why and to provide some answers to this problem. First, we will review the characteristics of ISGMR. We will present the key points of experimental data analysis techniques and point out in particular the unavoidable iso-vectorial component of any isoscalar excitation, which sometimes seems neglected. We will discuss the problem studied, namely the theory-experiment difference on the reproduction of the ISGMR of many isotopes. We will afterwards describe the Hartree-Fock-Bogoliubov (HFB) + Quasi-particle Random Phase Approximation (QRPA) theoretical framework with Gogny interaction in which we place ourselves to describe ISGMR. We will then show the convergence tests carried out, necessary for a good estimation of the excitation energies of the ISGMR and will present the state-of-the-art results associated with this theoretical framework in the even-even nuclei of ^56-60Ni, ^90,92Zr, ^{106,110,114,116}Cd, ^112-124Sn, ^204-208Pb and which will serve as points of comparison in the following. We will come back to the iso-vectorial component of our isoscalar excitation mode and will show how taking it into account can be useful in the specific study of Zirconium and Molybdenum isotopic chains. We will develop in the following chapter the studies carried out on the expression of the monopolar transition operator taking into account the kinematics data of inelastic diffusions used to probe the ISGMR and the impact of a new operator on high excitation energies. In particular, we will present the new ability to reproduce the high-energy components of monopolar spectra. We will then discuss the impact of the 2-body center of mass correction as a corrective term to our effective Hamiltonian in ¹²C and ²⁴Mg nuclei in addition to the main isotopic chains studied. Finally, we will expose the work done on the fitting procedure of a new three-ranged Gogny interaction in the central two-body term and detail some of the results associated with the new D3G3 parametrization. (author)