We extend the self-consistent Green's functions formalism to take into account three-body interactions. We analyze the perturbative expansion in terms of Feynman diagrams and define effective one-and two-body interactions, which allows for a substantial reduction of the number of diagrams. The procedure can be taken as a generalization of the normal ordering of the Hamiltonian to fully correlated density matrices. We give examples up to third order in perturbation theory. To define nonperturbative approximations, we extend the equation of motion method in the presence of three-body interactions. We propose schemes that can provide nonperturbative resummation of three-body interactions. We also discuss two different extensions of the Koltun sum rule to compute the ground state of a many-body system.

We perform a systematic analysis of the density dependence of the nuclear symmetry energy within the microscopic Brueckner-Hartree-Fock (BHF) approach using the realistic Argonne V18 nucleon-nucleon potential plus a phenomenological three body force of Urbana type. Our results are compared thoroughly to those arising from several Skyrme and relativistic effective models.The values of the parameters characterizing the BHF equation of state of isospin asymmetric nuclear matter fall within the trends predicted by those models and are compatible with recent constraints coming from heavy ion collisions, giant monopole resonances or isobaric analog states.In particular we find a value of the slope parameter L = 66.9 MeV, compatible with recent experimental constraints from isospin diffusion, L = 88 ± 25 MeV. The correlation between the neutron skin thickness of neutron-rich isotopes and the slope, L, and curvature, K sym , parameters of the symmetry energy is studied. Our BHF results are in very good agreement with the correlations already predicted by other authors using non-relativistic and relativistic effective models. The correlations of these two parameters and the neutron skin thickness with the transition density from non-uniform to β-stable matter in neutron stars are also analyzed. Our results confirm that there is an inverse correlation between the neutron skin thickness and the transition density.PACS numbers: 21.65.Cd; 21.65.Ef; 21.65.Mn 2 A well-grounded understanding of the properties of isospin-rich nuclear matter is a necessary ingredient for the advancement of both nuclear physics and astrophysics. Isospin asymmetric nuclear matter is present in nuclei, especially in those far away from the stability line, and in astrophysical systems, particularly in neutron stars. A major scientific effort is being carried out at an international level to study experimentally the properties of asymmetric nuclear systems. Laboratory measurements, such as those running or planned to run in the existing or the next-generation, radioactive ion beam facilities at CSR (China), FAIR (Germany), RIKEN (Japan), SPIRAL2/GANIL (France) and the upcoming FRIB (USA), can probe the behavior of the symmetry energy close and above saturation density [1]. Moreover, the 208 Pb Radius Experiment (PREX), scheduled to run at JLab in early 2010, should provide a very accurate measurement of the neutron skin thickness in lead via parity violating electron scattering [2]. Astrophysical observations of compact objects are also a window into both the bulk and the microscopic properties of nuclear matter at extreme isospin asymmetries [3]. The symmetry energy determines to a large extent the composition of β-stable matter and therefore the structure and mass of a neutron star [4].The empirical knowledge gathered from all these sources should be helpful in identifying the major issues arising when the isospin content of nuclear systems is altered. Reliable theoretical investigations of neutron-rich (and possibly proton-rich) systems are...

The short-range and tensor components of the bare nucleon-nucleon interaction induce a sizeable depletion of low momenta in the ground state of a nuclear many-body system. The self-consistent Green's function method within the ladder approximation provides an \textit{ab-initio} description of correlated nuclear systems that accounts properly for these effects. The momentum distribution predicted by this approach is analyzed in detail, with emphasis on the depletion of the lowest momentum state. The temperature, density, and nucleon asymmetry (isospin) dependence of the depletion of the Fermi sea is clarified. A connection is established between the momentum distribution and the time-ordered components of the self-energy, which allows for an improved interpretation of the results. The dependence on the underlying nucleon-nucleon interaction provides quantitative estimates of the importance of short-range and tensor correlations in nuclear systems