The atomic nucleus is the epitome of complexity : it is a strongly correlated system of nucleons (which are themselves composite degrees of freedom) coupled via the strong and electroweak interactions which features a wealth of emergent behaviors (deformation, supefluidity, clustering, ...). The long term endeavor of nuclear structure theory is to understand and predict how an arbitrary number of nucleons self-organize and become disorganized in nuclei. Among the various theoretical frames, the energy density functional (EDF) method, close, yet different from the density functional theory, provides the best compromise between the robustness of the description and its numerical complexity. However, the phenomenological ingredients entering the formulation of standard EDFs affect their predictive power.
The postdoctoral project aims at formulating the EDF approach from first principles, in order to benefit from a theoretical frame with both a maximal predictive power and a favorable numerical cost. The supervising team has identified the functional renormalization group (FRG) as the most relevant language for such a non empirical reformulation of the EDF method.
The present projet aims at formulating the EDF method from first principles via the FRG.

The treatment of odd-isospin nuclei in microscopic approaches is currently limited to the so-called «blocking» approximation. In the Hartree-Fock Bogolyubov (HFB) approach, the ground state of an odd-mass nucleus is described as a one-particle excitation (qp) on its reference vacuum. Thus, in the QRPA approach, where the basic excitations are states «with 2 quasi-particles», the blocked qp is excluded from the valence space under the Pauli exclusion principle. As a result, the chosen qp is a spectator and is not involved in the QRPA collective states. If the single nucleon should have a significant contribution some levels will not be reproduced. The development in the QRPA codes (ISAAC and Xpn) of a procedure that allows all nucleons to participate in collective states is mandatory for a microscopic description of odd nuclei. Moreover, recent Xpn developments have allowed the description of forbidden ß- first decays improving the estimation of half-life time of fission fragments. This could be extended to address ß+ and electronic captures and could be adapted to large-scale calculations useful for nuclear astrophysics.