On the calculation and use of effective single-particle energies: the example of the neutron 1d3/2-1d5/2 splitting along N = 20 isotones.

The rich phenomenology of quantum many-body systems such as atomic nuclei is complex to interpret. Often, the behaviour (e.g. evolution with the number of constituents) of measurable/observable quantities such as binding or excitation energies can be best understood based on a simplified picture involving auxiliary quantities that are not observable, i.e. whose values vary with parameters that are internal to the theoretical construction (contrarily to measurable/observable quantities). While being useful, the simplified interpretation is thus theoretical-scheme dependent. This applies, in particular, to the so-called single-nucleon shell structure based on auxiliary effective single-particle energies (ESPEs). In this context, the present work aims at (i) recalling the way to compute ESPEs out of solutions of many-body Schrödinger's equation, (ii) illustrating the use of ESPEs within the frame of state-of-the-art ab initio calculations to interpret the outcome of a recent nuclear experiment, and (iii) demonstrating the impact of several alterations on the computation of ESPEs. While the chosen alterations constitute approximations within the ab initio scheme, they are built-in when employing other theoretical constructs at play in nuclear physics. The present considerations are thus meant to empirically illustrate variations that can be expected between ESPEs computed within different (equally valid) theoretical schemes. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Impact of correlations on nuclear binding energies: Ab initio calculations of singly and doubly open-shell nuclei.

A strong effort will be dedicated in the coming years to extend the reach of ab initio nuclear-structure calculations to heavy doubly open-shell nuclei. In order to do so, the most efficient strategies to incorporate dominant many-body correlations at play in such nuclei must be identified. With this motivation in mind, the present work analyses the step-by-step inclusion of many-body correlations and their impact on binding energies of Calcium and Chromium isotopes. Employing an empirically-optimal Hamiltonian built from chiral effective field theory, binding energies along both isotopic chains are studied via a hierarchy of approximations based on polynomially-scaling expansion many-body methods. More specifically, calculations are performed based on (i) the spherical Hartree-Fock-Bogoliubov mean-field approximation plus correlations from second-order Bogoliubov many-body perturbation theory or Bogoliubov coupled cluster with singles and doubles on top of it, along with (ii) the axially-deformed Hartree-Fock-Bogoliubov mean-field approximation plus correlations from second-order Bogoliubov many-body perturbation theory built on it. The corresponding results are compared to experimental data and to those obtained via valence-space in-medium similarity renormalization group calculations at the normal-ordered two-body level that act as a reference in the present study. The spherical mean-field approximation is shown to display specific shortcomings in Ca isotopes that can be understood analytically and that are efficiently corrected via the consistent addition of low-order dynamical correlations on top of it. While the same setting cannot appropriately reproduce binding energies in doubly open-shell Cr isotopes, allowing the unperturbed mean-field state to break rotational symmetry permits to efficiently capture the static correlations responsible for the phenomenological differences observed between the two isotopic chains. Eventually, the present work demonstrates that polynomially-scaling expansion methods based on unperturbed states that possibly break (and restore) symmetries constitute an optimal route to extend ab initio calculations to heavy closed- and open-shell nuclei.

Nuclear Charge Radii of the Nickel Isotopes

Collinear laser spectroscopy is performed on the nickel isotopes ^{58-68,70}Ni, using a time-resolved photon counting system. From the measured isotope shifts, nuclear charge radii R_{c} are extracted and compared to theoretical results. Three ab initio approaches all employ, among others, the chiral interaction NNLO_{sat}, which allows an assessment of their accuracy. We find agreement with experiment in differential radii δ⟨r_{c}^{2}⟩ for all employed ab initio methods and interactions, while the absolute radii are consistent with data only for NNLO_{sat}. Within nuclear density functional theory, the Skyrme functional SV-min matches experiment more closely than the Fayans functional Fy(Δr,HFB).

A poly-epoxy surface explored by Hartree-Fock ΔSCF simulations of C1s XPS spectra.

Whereas poly-epoxy polymers represent a class of materials with a wide range of applications, the structural disorder makes them difficult to model. In the present work, we use good experimental model samples in the sense that they are pure, fully polymerized, flat and smooth, defect-free, and suitable for ultrahigh vacuum x-ray photoelectron spectroscopy, XPS, experiments. In parallel, we perform Hartree-Fock, HF, calculations of the binding energies, BEs, of the C1s electrons in a model molecule composed of the two constituents of the poly-epoxy sample. These C1s BEs were determined using the HF ΔSCF method, which is known to yield accurate values, especially for the shifts of the BEs, ΔBEs. We demonstrate the benefits of combining rigorous theory with careful XPS measurements in order to obtain correct assignments of the C1s XPS spectra of the polymer sample. Both the relative binding energies-by the ΔSCF method-and relative intensities-in the sudden approximation, SA, are calculated. It results in an excellent match with the experimental spectra. We are able to identify 9 different chemical environments under the C1s peak, where an exclusively experimental work would have found only 3 contributions. In addition, we observe that some contributions are localized at discrete binding energies, whereas others allow a much wider range because of the variation of their second neighbor bound polarization. Therefore, HF-ΔSCF simulations significantly increase the spectral resolution of XPS and thus offer a new avenue for the exploration of the surface of polymers.

Self-assembly of metal nanostructures on binary alloy surfaces.

Deposition of metals on binary alloy surfaces offers new possibilities for guiding the formation of functional metal nanostructures. This idea is explored with scanning tunneling microscopy studies and atomistic-level analysis and modeling of nonequilibrium island formation. For Au/NiAl(110), complex monolayer structures are found and compared with the simple fcc(110) bilayer structure recently observed for Ag/NiAl(110). We also consider a more complex codeposition system, (Ni + Al)/NiAl(110), which offers the opportunity for fundamental studies of self-growth of alloys including deviations for equilibrium ordering. A general multisite lattice-gas model framework enables analysis of structure selection and morphological evolution in these systems.

Nanodomains due to phason defects at a quasicrystal surface.

Among the three coexisting types of terraces found on the twofold surface of the d-Al-Cu-Co quasicrystal, nanodomains are essentially observed on the transition-metal rich ones, with a coherent interface boundary. Both clean surface and Ag growth analyses, demonstrate that nanodomain surfaces are structurally identical to one of the two other terraces, which contains 85 at. % Al. We provide evidence that the nanodomains are a manifestation of phason defects that extend downward toward the bulk, and state that nanodomains develop because the energetic cost of creating the phason is outweighed by the change in surface energy. Consequently, the formation of nanodomains involves more than just the surface layer, but is driven by surface energetics.