• Energy Research
• French National Research Agency (AN... close
• 2010 close

Methods based on the use of Energy Density Functionals (EDFs) are the only ones that can currently be applied to all nuclei but the lightest ones in a systematic manner. Nuclear EDF methods coexist on two distinct levels. On the first one, traditionally call "self-consistent mean-field theory", a single product state provides the density matrix that enters the EDF. We call this method a single-reference (SR) approach. On the second level, often called "beyond mean-field methods", symmetry restoration and configuration mixing in the spirit of the Generator Coordinate Method (GCM) can be achieved. At that level, the many-body energy takes the form of a functional of all transition density matrices that can be constructed from a set of several product states. We call this method a multi-reference (MR) calculation. The project we propose covers the following major steps: 1.The extension of the nuclear energy density functional through higher-order terms in density matrices and derivatives in a systematic manner will lead to a better understanding of the relevant degrees of freedom at play in the parameterization of the energy functional and in its adjustment. The set-up of the generalized analytical functional form of the functionals will be accompanied with the development of a reliable fitting protocol that discriminates the relevant degrees of freedom of the EDF and the data to constrain it, and that provides computed quantities with theoretical error bars. The fitting protocol itself will depart from the well-established Lyon protocol through the incorporation of several new high-level features: (i) the systematic analysis of spurious instabilities against finite- and infinite-size perturbations in the four spin-isospin channels through linear-response calculations of infinite nuclear matter, (ii) the use of new data requiring more involved computations, e.g. of deformed nuclei and (iii) constraints from ab-initio calculations of infinite nuclear matter performed in terms of low-momentum two- and three-nucleon interactions. 2. Systematic full-fledged SR EDF calculations of odd-A nuclei will be performed. 3. MR EDF calculations taking into account one- and two-quasi-particle states as planned here will allow for the description of the coupling between collective and explicit single-particle degrees of freedom in atomic nuclei when restoring symmetries and allowing for fluctuations in collective degrees of freedom. This is a pioneering work that has never been been attempted in the context of EDF-based methods so far. In particular, this will clarify many open questions on the relation between eigenvalues of the single-particle SR Hamiltonian and observable single-particle energies. 4. An improved description of the static and dynamic correlations in low-lying states of odd-A nuclei. This will also have an impact on ongoing and future studies of pairing correlations. Indeed, incorporating such correlations will modify the odd-even staggering of masses that is one of the key observables for pairing correlations. The direct benefits of these developments will be that they provide: 1.) EDFs of spectroscopic quality in the perspective of the production of exotic nuclei by upcoming facilities, overcoming the current impasse faced in the attempts to improve the nuclear EDF. 2.) EDFs that allow MR calculations that are free of the pathologies recently identified. 3.) Calculations of odd-A and even-even nuclei taking the coupling between collective and explicit single-particle degrees into account needed to unambiguously study the evolution of shell structure with N and Z in exotic nuclei, that is a major driving force of current and future experimental efforts.