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.
We present results from a new ab initio method that uses the self-consistent Gorkov-Green's function theory to address truly open-shell systems. The formalism has been recently worked out up to second order and is implemented here in nuclei on the basis of realistic nuclear forces. Benchmark calculations indicate that the method is in agreement with other ab initio approaches in doubly closed shell 40 Ca and 48 Ca. We find good convergence of the results with respect to the basis size in 44 Ca and 74 Ni and discuss quantities of experimental interest including ground-state energies, pairing gaps, and particle addition and removal spectroscopy. These results demonstrate that the Gorkov method is a valid alternative to multireference approaches for tackling degenerate or near-degenerate quantum systems. In particular, it increases the number of mid-mass nuclei accessible in an ab initio fashion from a few tens to a few hundred.
We present a systematic study of both nuclear radii and binding energies in (even) oxygen isotopes from the valley of stability to the neutron drip line. Both charge and matter radii are compared to state-of-the-art ab initio calculations along with binding energy systematics. Experimental matter radii are obtained through a complete evaluation of the available elastic proton scattering data of oxygen isotopes. We show that, in spite of a good reproduction of binding energies, ab initio calculations with conventional nuclear interactions derived within chiral effective field theory fail to provide a realistic description of charge and matter radii. A novel version of two- and three-nucleon forces leads to considerable improvement of the simultaneous description of the three observables for stable isotopes but shows deficiencies for the most neutron-rich systems. Thus, crucial challenges related to the development of nuclear interactions remain.
Background: Recent advances in nuclear structure theory have led to the availability of several complementary ab initio many-body techniques applicable to light and medium-mass nuclei as well as nuclear matter. After successful benchmarks between different approaches, the focus is moving to the development of improved models of nuclear Hamiltonians, currently representing the largest source of uncertainty in ab initio calculations of nuclear systems. In particular, none of the existing two-plus three-body interactions is capable of satisfactorily reproducing all the observables of interest in medium-mass nuclei.Purpose: A novel parameterisation of a Hamiltonian based on chiral effective field theory is introduced. Specifically, three-nucleon operators at next-to-next-to-leading order are combined with an existing (and successful) two-body interaction containing terms up to next-to-next-to-next-to-leading order. The resulting potential is labelled NN+3N (lnl). The objective of the present work is to investigate the performance of this new Hamiltonian across light and medium-mass nuclei.Methods: Binding energies, nuclear radii and excitation spectra are computed using state-of-the-art no-core shell model and self-consistent Green's function approaches. Calculations with NN+3N (lnl) are compared to two other representative Hamiltonians currently in use, namely NNLOsat and the older NN+3N (400).Results: Overall, the performance of the novel NN+3N (lnl) interaction is very encouraging. In light nuclei, total energies are generally in good agreement with experimental data. Known spectra are also well reproduced with a few notable exceptions. The good description of ground-state energies carries on to heavier nuclei, all the way from oxygen to nickel isotopes. Except for those involving excitation processes across the N = 20 gap, which is overestimated by the new interaction, spectra are of very good quality, in general superior to those obtained with NNLOsat. Although largely improving on NN+3N (400) results, charge radii calculated with NN+3N (lnl) still underestimate experimental values, as opposed to the ones computed with NNLOsat that successfully reproduce available data on nickel. Conclusions:The new two-plus three-nucleon Hamiltonian introduced in the present work represents a promising alternative to existing nuclear interactions. In particular, it has the favourable features of (i) being adjusted solely on A = 2, 3, 4 systems, thus complying with the ab initio strategy, (ii) yielding an excellent reproduction of experimental energies all the way from light to medium-heavy nuclei and (iii) well behaving under similarity renormalisation group transformations, with negligible four-nucleon forces being induced, thus allowing large-scale calculations up to medium-heavy systems. The problem of the underestimation of nuclear radii persists and will necessitate novel developments.
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