Approches fonctionnelles pour les systèmes finis appariés

GANIL Guest House - Tuesday 6th September - 9h30

The combination of functional theory where the energy is written as a functional of the density, and the conguration mixing method, provides an efficient description of nuclear ground and excited state properties. The specic pathologies that have been recently observed, show the lack of a clear underlying justication associated to the breaking and the restoration of symmetries within density functional theory. This thesis focuses on alternative treatments of pairing correlations in finite many body systems that consider the breaking and the restoration of the particle number conservation. The energy is written as a functional of a projected quasi-particle vacuum and can be linked to the one obtained within the conguration mixing framework[1]. This approach has been applied to make the projection either before or after the application of the variational principle. It is more flexible than the usual conguration mixing method since it can handle more general effective interactions than the latter. The application to the Krypton isotopes shows the feasibility and the efficiency of the method to describe pairing near closed shell nuclei. Following a parallel path, a theory where the energy is written as a functional of the occupation number and natural orbitals is proposed. The new functional is benchmarked in an exactly solvable model, the pairing Hamiltonian. The efficiency and the applicability of the new theory have been tested for various pairing strengths, single particle energy spectra and numbers of particles[2, 3].
 

Références
[1] G. Hupin, D. Lacroix, and M. Bender, Phys. Rev. C , 014309 (2011).
[2] D. Lacroix and G. Hupin, Phys. Rev. B 82, 144509 (2010).
[3] G. Hupin and D. Lacroix, Phys. Rev. C 83, 024317 (2011).