# Functional renormalization group for nuclear structure theory

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.

# Evolution of ISAAC and Xpn codes for an extension of the QRPA method to the complete processing of odd nuclei; towards a database without interpolation for odd nuclei

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.

# Crystal plasticity in classical molecular dynamics and mesoscopic upscaling

Thanks to new supercomputer architectures, classical molecular dynamics simulations will soon enter the realm of a thousand billion atoms, never before achieved, thus becoming capable of representing the plasticity of metals at the micron scale. However, such simulations generate a considerable amount of data, and the difficulty now lies in their exploitation in order to extract the statistical ingredients relevant to the scale of "mesoscopic" plasticity (the scale of continuous models).

The evolution of a material is complex, as it depends on lines of crystalline defects (dislocations) whose evolution is governed by numerous mechanisms. In order to feed models at higher scales, the quantities to be extracted are the velocities and lengths of dislocations, as well as their evolution over time. These data can be extracted using specific analysis techniques based on characterization of the local environment ('distortion score', 'local deformation'), a posteriori or in situ during simulation. Finally, machine learning tools can be used to analyze the statistics obtained and extract and synthesize (by model reduction) a minimal description of plasticity for models at higher scales.

# Numerical studies of laser plasma interaction in intermediate field on Laser Megajoule

In the Inertial Confinement Fusion experiments (ICF), intense laser beams cross a gas filled hohlraum. The gas is fully ionized and laser beams then propagate into a sub-critical plasma where laser plasma instabilites can develop. Optical smoothing techniques enable to break both spatial and temporal coherences so that both spatial and temporal scales of the beam become smaller than those required for the development of the instabilites. The breaking of spatial coherence is done thanks to the use of a phase plate which spreads the laser energy in a multitude of light grains called speckles. The breaking of temporal coherence is done by using a phase modulator which widens the spectrum and by dispersing each frequency with a grating. It is essential to know the statistical properties of speckles (width, lenght, contrast, coherence time, velocities ...) to be able to predict the instabilities levels which can depend on time and on the distance of propagation of the beam. .

For the sake of simplicity, the laser plasma instabilities are very often studied at the best focus of the beam. However, in the FCI experiments, laser beams are focused near the laser entrance hole of the hohlraum whose length is about 1 cm. The development of instabilities can then occur before the best focus (outside the hohlraum) and mainly beyond the best focus (far inside the hohlraum). The goal of this post-doctoral contract is to study the development of instabilities when it occurs in the intermediate field (far from the best focus of the beam) and to assess the efficiency of different smoothing options on Lase MagaJoule (LMJ) to limit these instabilities. We will especially study propagation instabilities (self-focusing, forward stimulated Brillouin scattering) and stimulated Brillouin backscattering. This work will be done thanks to numerous existing numerical codes and diagnostic tolls.