Origin of the neutron skin thickness of 208Pb in nuclear mean-field models

We study whether the neutron skin thickness (NST) of 208Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to NST arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical relativistic models, predict a bulk contribution in NST of 208Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that NST of 208Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of NST of 208Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of NST. We also note that most models predict a mixed-type (between halo and skin) neutron distribution for 208Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the 208Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the 208Pb nucleon densities.Comment: 11 pages, 4 figures; minor stylistic changes in text, new Ref. [56] added (new measurement of the neutron skin thickness of 208Pb

EC budget support: thumbs up or down?

Budget support is a form of macro-economic financial assistance that is designed to prioritise the fight against poverty and the achievement of the Millennium Development Goals (MDGs). The European Commission (EC) is providing more and more budget support under the Cotonou Partnership Agreement (CPA), which structures the provision of assistance by the European Union (EU) to the African, Caribbean and Pacific (ACP) countries. The EC also provides macro-economic support through its cooperation agreements with a number of non-ACP countries, for which it is now also introducing budget support. During the course of its work in the ACP regions, the European Centre for Development Policy Management (ECDPM) was approached by parliamentarians, representatives of non-governmental organisations and partner government officials, all of whom had certain questions to ask about the background to and operation of budget support. These actors regard budget support as an increasingly important mechanism for development cooperation, and one that has potentially far-reaching implications for their work. At the same time, it is a relatively new mechanism, is poorly understood and is driven by a relatively small group of experts in aid agencies and partner country finance or planning ministries. We have prepared this Discussion Paper in response to these queries. Our aim is to give policy-makers and practitioners in-depth information on the nature and potential of, and the constraints associated with, budget support as a development cooperation modality. The paper explains the complex nature of budget support and its implications for the actors involved, as well as highlighting issues that have a bearing on its success. Budget support creates opportunities that are not always fully appreciated by its critics. At the same time, it creates risks which tend to be downplayed by its supporters. Against this background, this paper also aims to contribute to this intensely debated issue by providing a balanced view for those seeking to understand its complexities. As this is intended to be a relatively brief paper, it is limited to key policy issues and the challenges arising from recent experiences with budget support. For this reason, we have not devoted much space to discussing the issue of sector budget support. We advise the reader to consult the bibliography for more detailed information on the practice and technicalities of this rapidly evolving mechanism. Finally, it is important to recognise that the move towards budget support has aroused many questions among partner government officials, donor agencies, consultants and academic institutes, which tend to feed into the production of specialist documents assessing approaches and experiences. For this reason, this paper can do no more than to describe the current state of a rapidly evolving debate and practice. We hope to be able to follow up this initial study and produce further publications on specific issues, tailored to the needs of individual ACP audiences, as part of our future work

Analysis of bulk and surface contributions in the neutron skin of nuclei

The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy having multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult. The analysis of the experimental data may imply some assumptions about the bulk or surface nature of the formation of the neutron skin. Here, we study the bulk or surface character of neutron skins of nuclei following from calculations with Gogny, Skyrme, and covariant nuclear mean-field interactions. These interactions are successful in describing nuclear charge radii and binding energies but predict different values for neutron skins. We perform the study by fitting two-parameter Fermi distributions to the calculated self-consistent neutron and proton densities. We note that the equivalent sharp radius is a more suitable reference quantity than the half-density radius parameter of the Fermi distributions to discern between the bulk and surface contributions in neutron skins. We present calculations for nuclei in the stability valley and for the isotopic chains of Sn and Pb.Comment: 13 pages, 9 figure

Contact angle of sessile drops in Lennard-Jones systems

Molecular dynamics simulation is used for studying the contact angle of nanoscale sessile drops on a planar solid wall in a system interacting via the truncated and shifted Lennard-Jones potential. The entire range between total wetting and dewetting is investigated by varying the solid--fluid dispersive interaction energy. The temperature is varied between the triple point and the critical temperature. A correlation is obtained for the contact angle in dependence of the temperature and the dispersive interaction energy. Size effects are studied by varying the number of fluid particles at otherwise constant conditions, using up to 150 000 particles. For particle numbers below 10 000, a decrease of the contact angle is found. This is attributed to a dependence of the solid-liquid surface tension on the droplet size. A convergence to a constant contact angle is observed for larger system sizes. The influence of the wall model is studied by varying the density of the wall. The effective solid-fluid dispersive interaction energy at a contact angle of 90 degrees is found to be independent of temperature and to decrease linearly with the solid density. A correlation is developed which describes the contact angle as a function of the dispersive interaction, the temperature and the solid density. The density profile of the sessile drop and the surrounding vapor phase is described by a correlation combining a sigmoidal function and an oscillation term

Observation of Three-dimensional Long-range Order in Smaller Ion Coulomb Crystals in an rf Trap

Three-dimensional long-range ordered structures in smaller and near-spherically symmetric Coulomb crystals of ^{40}Ca^+ ions confined in a linear rf Paul trap have been observed when the number of ions exceeds ~1000 ions. This result is unexpected from ground state molecular dynamics (MD) simulations, but found to be in agreement with MD simulations of metastable ion configurations. Previously, three-dimensional long-range ordered structures have only been reported in Penning traps in systems of ~50,000 ions or more.Comment: 5 pages; 4 figures; to appear in Phys. Rev. Lett.; changed content

Quaternary quadratic lattices over number fields

We relate proper isometry classes of maximal lattices in a totally definite quaternary quadratic space (V,q) with trivial discriminant to certain equivalence classes of ideals in the quaternion algebra representing the Clifford invariant of (V,q). This yields a good algorithm to enumerate a system of representatives of proper isometry classes of lattices in genera of maximal lattices in (V,q)

From finite nuclei to the nuclear liquid drop: leptodermous expansion based on the self-consistent mean-field theory

The parameters of the nuclear liquid drop model, such as the volume, surface, symmetry, and curvature constants, as well as bulk radii, are extracted from the non-relativistic and relativistic energy density functionals used in microscopic calculations for finite nuclei. The microscopic liquid drop energy, obtained self-consistently for a large sample of finite, spherical nuclei, has been expanded in terms of powers of A^{-1/3} (or inverse nuclear radius) and the isospin excess (or neutron-to-proton asymmetry). In order to perform a reliable extrapolation in the inverse radius, the calculations have been carried out for nuclei with huge numbers of nucleons, of the order of 10^6. The Coulomb interaction has been ignored to be able to approach nuclei of arbitrary sizes and to avoid radial instabilities characteristic of systems with very large atomic numbers. The main contribution to the fluctuating part of the binding energy has been removed using the Green's function method to calculate the shell correction. The limitations of applying the leptodermous expansion to actual nuclei are discussed. While the leading terms in the macroscopic energy expansion can be extracted very precisely, the higher-order, isospin-dependent terms are prone to large uncertainties due to finite-size effects.Comment: 13 pages revtex4, 7 eps figures, submitted to Phys. Rev.

A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

Consider, in the domain of outer communication of a Kerr-Newman black hole, a point (observation event) and a timelike curve (worldline of light source). Assume that the worldline of the source (i) has no past end-point, (ii) does not intersect the caustic of the past light-cone of the observation event, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic of (Morse) index k from the observation event to the worldline of the source, hence an observer at the observation event sees infinitely many images of the source. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in the domain of outer communication are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman spacetime the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal.Comment: 14 pages, 2 figures; REVTEX; submitted to J. Math. Phy

Analysis of bulk and surface contributions in the neutron skin of nuclei

The neutron skin thickness of nuclei is a sensitive probe of the nuclear symmetry energy having multiple implications for nuclear and astrophysical studies. However, precision measurements of this observable are difficult. The analysis of the experimental data may imply some assumptions about the bulk or surface nature of the formation of the neutron skin. Here, we study the bulk or surface character of neutron skins of nuclei following from calculations with Gogny, Skyrme, and covariant nuclear mean-field interactions. These interactions are successful in describing nuclear charge radii and binding energies but predict different values for neutron skins. We perform the study by fitting two-parameter Fermi distributions to the calculated self-consistent neutron and proton densities. We note that the equivalent sharp radius is a more suitable reference quantity than the half-density radius parameter of the Fermi distributions to discern between the bulk and surface contributions in neutron skins. We present calculations for nuclei in the stability valley and for the isotopic chains of Sn and Pb.Comment: 13 pages, 9 figure