Radii and binding energies in oxygen isotopes: a puzzle for nuclear forces

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 {\it 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, {\it 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.Comment: 6 pages, 5 figures, Submitted to Nature Physics, April 12th 2016; first version (v1 Arxiv) Internal Report Preprint Irfu-18 December 2015. 6 p., 5 fig., Submitted to Physical Review Letters, April 29, May 3rd 2016; 2nd version. Int. Rep. Irfu-24 May 2016. Published in PRL, 27 July 2016 with the modified title (Radii and binding energies in oxygen isotopes: a challenge for nuclear forces

Thermodynamic properties of nuclear matter with three-body forces

We calculate thermodynamic quantities in symmetric nuclear matter within the self-consistent Green's functions method including three-body forces. The thermodynamic potential is computed directly from a diagrammatic expansion, implemented with the CD-Bonn and Nijmegen nucleon-nucleon potentials and the Urbana three-body forces. We present results for entropy and pressure up to temperatures of 20 MeV and densities of 0.32 fm^-3. While the pressure is sensitive to the inclusion of three-body forces, the entropy is not. The unstable spinodal region is identified and the critical temperature associated to the liquid-gas phase transition is determined. When three-body forces are added we find a strong reduction of the critical temperature, obtaining T_c ~ 12 MeV.Comment: 5 pages, 6 figure

Diagrammatic calculation of thermodynamical quantities in nuclear matter

In medium T-matrix calculations for symmetric nuclear matter at zero and finite temperatures are presented. The internal energy is calculated from the Galitskii-Koltun's sum rule and from the summation of the diagrams for the interaction energy. The pressure at finite temperature is obtained from the generating functional form of the thermodynamic potential. The entropy at high temperature is estimated and compared to expressions corresponding to a quasiparticle gas.Comment: 9 pages, 5 figure

In medium T-matrix for nuclear matter with three-body forces - binding energy and single particle properties

We present spectral calculations of nuclear matter properties including three-body forces. Within the in-medium T-matrix approach, implemented with the CD-Bonn and Nijmegen potentials plus the three-nucleon Urbana interaction, we compute the energy per particle in symmetric and neutron matter. The three-body forces are included via an effective density dependent two-body force in the in-medium T-matrix equations. After fine tuning the parameters of the three-body force to reproduce the phenomenological saturation point in symmetric nuclear matter, we calculate the incompressibility and the energy per particle in neutron matter. We find a soft equation of state in symmetric nuclear matter but a relatively large value of the symmetry energy. We study the the influence of the three-body forces on the single-particle properties. For symmetric matter the spectral function is broadened at all momenta and all densities, while an opposite effect is found for the case of neutrons only. Noticeable modification of the spectral functions are realized only for densities above the saturation density. The modifications of the self-energy and the effective mass are not very large and appear to be strongly suppressed above the Fermi momentum.Comment: 20 pages, 11 figure

Non-observable nature of the nuclear shell structure. Meaning, illustrations and consequences

The concept of single-nucleon shells constitutes a basic pillar of our understanding of nuclear structure. Effective single-particle energies (ESPEs) introduced by French and Baranger represent the most appropriate tool to relate many-body observables to a single-nucleon shell structure. As briefly discussed in [T. Duguet, G. Hagen, Phys. Rev. C {\bf 85}, 034330 (2012)], the dependence of ESPEs on one-nucleon transfer probability matrices makes them purely theoretical quantities that "run" with the non-observable resolution scale $\lambda$ employed in the calculation. Given that ESPEs provide a way to interpret the many-body problem in terms of simpler theoretical ingredients, the goal is to specify the terms, i.e. the exact sense and conditions, in which this interpretation can be conducted meaningfully. State-of-the-art multi-reference in-medium similarity renormalization group and self-consistent Gorkov Green's function many-body calculations are employed to corroborate the formal analysis. This is done by comparing the behavior of several observables and of non-observable ESPEs (and spectroscopic factors) under (quasi) unitary similarity renormalization group transformations of the Hamiltonian parameterized by the resolution scale $\lambda$. The non-observable nature of the nuclear shell structure, i.e. the fact that it constitutes an intrinsically theoretical object with no counterpart in the empirical world, must be recognized and assimilated. Eventually, practitioners can refer to nuclear shells and spectroscopic factors in their analyses of nuclear phenomena if, and only if, they use consistent structure and reaction theoretical schemes based on a fixed resolution scale they have agreed on prior to performing their analysis and comparisons.Comment: 14 pages, 9 figures, accepted for publication in Physical Review

Self-consistent Green's function approaches

We present the fundamental techniques and working equations of many-body Green's function theory for calculating ground state properties and the spectral strength. Green's function methods closely relate to other polynomial scaling approaches discussed in chapters 8 and 10. However, here we aim directly at a global view of the many-fermion structure. We derive the working equations for calculating many-body propagators, using both the Algebraic Diagrammatic Construction technique and the self-consistent formalism at finite temperature. Their implementation is discussed, as well as the inclusion of three-nucleon interactions. The self-consistency feature is essential to guarantee thermodynamic consistency. The pairing and neutron matter models introduced in previous chapters are solved and compared with the other methods in this book.Comment: 58 pages, 14 figures, Submitted to Lect. Notes Phys., "An advanced course in computational nuclear physics: Bridging the scales from quarks to neutron stars", M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Editor

Rooting the EDF method into the ab initio framework. PGCM-PT formalism based on MR-IMSRG pre-processed Hamiltonians

Recently, ab initio techniques have been successfully connected to the traditional valence-space shell model. In doing so, they can either explicitly provide ab initio shell-model effective Hamiltonians or constrain the construction of empirical ones. In the present work, the possibility to follow a similar path for the nuclear energy density functional (EDF) method is analyzed. For this connection to be actualized, two theoretical techniques are instrumental: the recently proposed ab initio PGCM-PT many-body formalism and the MR-IMSRG pre-processing of the nuclear Hamiltonian. Based on both formal arguments and numerical results, possible new lines of research are briefly discussed, namely to compute ab initio EDF effective Hamiltonians at low computational cost, to constrain empirical ones or to produce them directly via an effective field theory that remains to be invented.Comment: 20 pages, 7 figure

Probing the N = 32 shell closure below the magic proton number Z = 20: Mass measurements of the exotic isotopes 52,53K

The recently confirmed neutron-shell closure at N = 32 has been investigated for the first time below the magic proton number Z = 20 with mass measurements of the exotic isotopes 52,53K, the latter being the shortest-lived nuclide investigated at the online mass spectrometer ISOLTRAP. The resulting two-neutron separation energies reveal a 3 MeV shell gap at N = 32, slightly lower than for 52Ca, highlighting the doubly-magic nature of this nuclide. Skyrme-Hartree-Fock-Boguliubov and ab initio Gorkov-Green function calculations are challenged by the new measurements but reproduce qualitatively the observed shell effect.Comment: 5 pages, 5 figure

Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction

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 semi-magic 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.Comment: 38 page