Gorkov algebraic diagrammatic construction formalism at third order

Background. The Gorkov approach to self-consistent Green's function theory has been formulated in [V. Som\`a, T. Duguet, C. Barbieri, Phys. Rev. C 84, 064317 (2011)]. Over the past decade, it has become a method of reference for first-principle computations of semi-magic nuclear isotopes. The currently available implementation is limited to a second-order self-energy and neglects particle-number non-conserving terms arising from contracting three-particle forces with anomalous propagators. For nuclear physics applications, this is sufficient to address first-order energy differences, ground-state radii and moments on an accurate enough basis. However, addressing absolute binding energies, fine spectroscopic details of $N\pm1$ particle systems or delicate quantities such as second-order energy differences associated to pairing gaps, requires to go to higher truncation orders. Purpose. The formalism is extended to third order in the algebraic diagrammatic construction (ADC) expansion with two-body Hamiltonians. Methods. The expansion of Gorkov propagators in Feynman diagrams is combined with the algebraic diagrammatic construction up to the third order as an organization scheme to generate the Gorkov self-energy. Results. Algebraic expressions for the static and dynamic contributions to the self-energy, along with equations for the matrix elements of the Gorkov eigenvalue problem, are derived. It is first done for a general basis before specifying the set of equations to the case of spherical systems displaying rotational symmetry. Workable approximations to the full self-consistency problem are also elaborated on. The formalism at third order it thus complete for a general two-body Hamiltonian. Conclusion. Working equations for the full Gorkov-ADC(3) are now available for numerical implementation.Comment: 30 pages, 8 figures; published versio

Self-consistent Green's functions calculation of the nucleon mean-free path

The extension of Green's functions techniques to the complex energy plane provides access to fully dressed quasi-particle properties from a microscopic perspective. Using self-consistent ladder self-energies, we find both spectra and lifetimes of such quasi-particles in nuclear matter. With a consistent choice of the group velocity, the nucleon mean-free path can be computed. Our results indicate that, for energies above 50 MeV at densities close to saturation, a nucleon has a mean-free path of 4 to 5 femtometers.Comment: 5 pages, 4 figures. Minor changes, bibliography corrected. Accepted version in Phys. Rev. Let

Microscopic optical potentials for medium-mass isotopes derived at the first order of the Watson multiple scattering theory

We perform a first-principle calculation of optical potentials for nucleon elastic scattering off medium-mass isotopes. Fully based on a saturating chiral Hamiltonian, the optical potentials are derived by folding nuclear density distributions computed with ab initio self-consistent Green's function theory with a nucleon-nucleon $t$ matrix computed with a consistent chiral interaction. The dependence on the folding interaction as well as the convergence of the target densities are investigated. Numerical results are presented and discussed for differential cross sections and analyzing powers, with focus on elastic proton scattering off Calcium and Nickel isotopes. Our optical potentials generally show a remarkable agreement with the available experimental data for laboratory energies in the range 65-200 MeV. We study the evolution of the scattering observables with increasing proton-neutron asymmetry by computing theoretical predictions of the cross section and analyzing power over the Calcium and Nickel isotopic chains

Bogoliubov many-body perturbation theory for open-shell nuclei

A Rayleigh–Schrödinger many-body perturbation theory (MBPT) approach is introduced by making use of a particle-number-breaking Bogoliubov reference state to tackle (near-)degenerate open-shell fermionic systems. By choosing a reference state that solves the Hartree–Fock–Bogoliubov variational problem, the approach reduces to the well-tested Møller–Plesset, i.e., Hartree–Fock based, MBPT when applied to closed-shell systems. Due to its algorithmic simplicity, the newly developed framework provides a computationally simple yet accurate alternative to state-of-the-art non-perturbative manybody approaches. At the price of working in the quasi-particle basis associated with a single-particle basis of sufficient size, the computational scaling of the method is independent of the particle number. This paper presents the first realistic applications of the method ranging from the oxygen to the nickel isotopic chains on the basis of a modern nuclear Hamiltonian derived from chiral effective field theory

Imaging the initial condition of heavy-ion collisions and nuclear structure across the nuclide chart

A major goal of the hot QCD program, the extraction of the properties of the quark gluon plasma (QGP), is currently limited by our poor knowledge of the initial condition of the QGP, in particular how it is shaped from the colliding nuclei. To attack this limitation, we propose to exploit collisions of selected species to precisely assess how the initial condition changes under variations of the structure of the colliding ions. This knowledge, combined with event-by-event measures of particle correlations in the final state of heavy-ion collisions, will provide in turn a new way to probe the collective structure of nuclei, and to confront and exploit the predictions of state-of-the-art ab initio nuclear structure theories. The US nuclear community should capitalize on this interdisciplinary connection by pursuing collisions of well-motivated species at high-energy colliders.Comment: 23 pages, 6 figure

From the liquid drop model to lattice QCD: A brief history of nuclear interactions

International audienceThe present article aims to give a concise account of the main developments in nuclear structure theory, from its origin in the 1930s to date, taking the modelling of inter-nucleon interactions as guideline

Self-consistent Green's function theory for atomic nuclei

International audienceNuclear structure theory has recently gone through a major renewal with the development of ab initio techniques that can be applied to a large number of atomic nuclei, well beyond the light sector that had been traditionally targeted in the past. Self-consistent Green's function theory is one among these techniques. The present work aims to give an overview of the self-consistent Green's function approach for atomic nuclei, including examples of recent applications and a discussion on the perspectives for extending the method to nuclear reactions, doubly open-shell systems and heavy nuclei

Radii and Binding Energies in Helium and Oxygen Isotopes: A Puzzle for Nuclear Forces

International audienceWe discuss the importance of the root mean square matter radius as a key observable for testing the validity of the nuclear forces employed in nuclear structure calculations. The link between proton-nucleus scattering and radii is underlined, with the test case carried out for ^8He. When a systematic study of both nuclear radii and binding energies is feasible, as done in (even) oxygen isotopes from the valley of stability to the neutron drip line, we show that the combined comparison of measured radii and binding energies with ab initio calculations offers unique insight on input nuclear forces. The need to use newly developed interactions to improve the description of the radii is discussed