Towards a non empirical description of heavy nuclei

Since the defence of my Ph.D. thesis in September 2002, I have essentially devoted nine years of research activity to advancing the formal understanding and enhancing the predictive power of SR and MR EDF approaches to structure and reaction properties of medium-to-heavy mass nuclei. In the most recent years, I have engaged myself into developing innovative ab-initio many-body methods applicable to medium-mass open-shell nuclei. On the long term, my two main objectives are (i) to advancing many-body methods and the understanding of many-fermion systems in general and (ii) to reducing decisively the phenomenological character of methods applicable to systems made out of a few tens to a few hundreds of fermions by addressing the points raised in the above introduction. The present document does not aim at summarizing those ten years of research activity. Rather, I made the choice to report in some details on three selected topics that are somewhat representative of my overall contribution to the field. The first part (Sec. II) describes an in-depth re-analysis of the concept of single-nucleon shell structure in the context of many-fermion systems. The second part (Sec. III) summarizes recent advances towards a more rigorous formulation of the MR-EDF method and discusses the corresponding remaining difficulties as well as ways under current development to overcome them. The third part (Sec. IV) discusses the on-going quest towards a microscopic description of superfluidity in nuclei and reports on the first-ever ab-initio calculations of open-shell medium-mass nuclei based on Self-consistent Gorkov Green's function theory. Although representative, the three above topics only cover a fraction of my research activity since my Ph.D. thesis defence. Consequently several other studies I have been involved with are briefly summarized in apps. A-E. For completeness, my publication list is also provided as an appendix. Last but not least, it is essential to stress that many results reported in the present document have been obtained through collaborative work as the corresponding publication list illustrate. (author)