A microscopic calculation of the effective mass of one ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ impurity in homogeneous liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at zero temperature is performed for an extended Jastrow-Slater wave function, including two- and three-body dynamical correlations and also backflow correlations between the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atom and the particles in the medium. The effective mass at equilibrium density, m〈main${\mathrm{〉}}_4^{\mathrm{*}}$/${\mathit{m}}_4$=1.21, is in very good agreement with the recent experimental determination by Edwards et al. The three-particle correlations appear to give a small contribution to the effective mass and different approximations for the three-particle distribution function give almost identical results for ${\mathit{m}}_4^{\mathrm{*}}$/${\mathit{m}}_4$.

We perform a systematic analysis of the density dependence of 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 with 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 $L=66.5$ MeV, compatible with recent experimental constraints from isospin diffusion, $L=88\pm 25$ MeV. The correlation between the neutron skin thickness of neutron-rich isotopes and the slope $L$ and curvature $K_{\mathrm{sym}}$ parameters of the symmetry energy is studied. Our BHF results are in very good agreement with the correlations already predicted by other authors using nonrelativistic and relativistic effective models. The correlations of these two parameters and the neutron skin thickness with the transition density from nonuniform to $\beta$-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.

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 present results from Brueckner-Hartree-Fock calculations for $\beta$-stable neutron star matter with nucleonic and hyperonic degrees of freedom, employing the most recent parametrizations of the baryon-baryon interaction of the Nijmegen group. It is found that the only strange baryons emerging in $\beta$-stable matter up to total baryonic densities of 1.2 ${\mathrm{fm}}^{-3}$ are ${\Sigma }^{-}$ and $\Lambda .$ The corresponding equations of state are then used to compute properties of neutron stars such as masses and radii.