Recent results obtained by applying the method of self-consistent Green's functions to nuclei and nuclear matter are reviewed. Particular attention is given to the description of experimental data obtained from the (e,e ′ p) and (e,e ′ 2N) reactions that determine one and two-nucleon removal probabilities in nuclei since the corresponding amplitudes are directly related to the imaginary parts of the single-particle and two-particle propagators. For this reason and the fact that these amplitudes can now be calculated with the inclusion of all the relevant physical processes, it is useful to explore the efficacy of the method of self-consistent Green's functions in describing these experimental data. Results for both finite nuclei and nuclear matter are discussed with particular emphasis on clarifying the role of short-range correlations in determining various experimental quantities. The important role of long-range correlations in determining the structure of lowenergy correlations is also documented. For a complete understanding of nuclear phenomena it is therefore essential to include both types of physical correlations. We demonstrate that recent experimental results for these reactions combined with the reported theoretical calculations yield a very clear understanding of the properties of all protons in the nucleus. We propose that this knowledge of the properties of constituent fermions in a correlated many-body system is a unique feature of nuclear physics.

Ab initio calculations have shown that chiral two-and three-nucleon interactions correctly reproduce binding energy systematics and neutron drip lines of oxygen and nearby isotopes. Exploiting the novel Gorkov-Green's function approach applicable to genuinely open-shell nuclei, we present the first ab initio investigation of Ar, K, Ca, Sc, and Ti isotopic chains. In doing so, stringent tests of internucleon interaction models are provided in the medium-mass region of the nuclear chart. Leading chiral three-nucleon interactions are shown to be mandatory to reproduce the trend of binding energies throughout these chains and to obtain a good description of two-neutron separation energies. At the same time, nuclei in this mass region are systematically overbound by about 40 MeV. While the fundamental N = 20 and 28 magic numbers do emerge from basic internucleon interactions, the former is shown to be significantly overestimated, which points to deficiencies of state-of-the-art chiral potentials. The present results demonstrate that ab initio many-body calculations can now access entire medium-mass isotopic chains including degenerate open-shell nuclei and provide a critical testing ground for modern theories of nuclear interactions.

We extend the formalism of self-consistent Green's function theory to include three-body interactions and apply it to isotopic chains around oxygen for the first time. The third-order algebraic diagrammatic construction equations for two-body Hamiltonians can be exploited upon defining system-dependent oneand two-body interactions coming from the three-body force, and, correspondingly, dropping interactionreducible diagrams. The Koltun sum rule for the total binding energy acquires a correction due to the added three-body interaction. This formalism is then applied to study chiral two-and three-nucleon forces evolved to low momentum cutoffs. The binding energies of nitrogen, oxygen, and fluorine isotopes are reproduced with good accuracy and demonstrate the predictive power of this approach. Leading order three-nucleon forces consistently bring results close to the experiment for all neutron rich isotopes considered and reproduce the correct driplines for oxygen and nitrogen. The formalism introduced also allows us to calculate form factors for nucleon transfer on doubly magic systems.

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.

An ab initio calculation scheme for finite nuclei based on self-consistent Green's functions in the Gorkov formalism is developed. It aims at describing properties of doubly magic and semimagic nuclei employing state-of-the-art microscopic nuclear interactions and explicitly treating pairing correlations through the breaking of U(1) symmetry associated with particle number conservation. The present paper introduces the formalism necessary to undertake applications at (self-consistent) second order using two-nucleon interactions in a detailed and self-contained fashion. First applications of such a scheme will be reported soon in a forthcoming publication. Future works will extend the present scheme to include three-nucleon interactions and implement more advanced truncation schemes.