Particle-Number Restoration within the Energy Density Functional Formalism

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process which might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, M. Bender, arXiv:0809.2041] is shown to remove completely the anomalies encountered in particle-number restored calculations. In particular, it restores sum-rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy, but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.Comment: 37 pages, 14 figures, accepted for publication in PR

Configuration Mixing within the Energy Density Functional Formalism: Removing Spurious Contributions from Non-Diagonal Energy Kernels

Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics. These calculations rely on the extension of a single-reference energy functional, of the Gogny or the Skyrme types, to non-diagonal energy kernels. There is no rigorous constructive framework for this extension so far. The commonly accepted way proceeds by formal analogy with the expressions obtained when applying the generalized Wick theorem to the non-diagonal matrix element of a Hamilton operator between two product states. It is pointed out that this procedure is ill-defined when extended to EDF calculations as the generalized Wick theorem is taken outside of its range of applicability. In particular, such a procedure is responsible for the appearance of spurious divergences and steps in multi-reference EDF energies, as was recently observed in calculations restoring particle number or angular momentum. In the present work, we give a formal analysis of the origin of this problem for calculations with and without pairing, i.e. constructing the density matrices from either Slater determinants or quasi-particle vacua. We propose a correction to energy kernels that removes the divergences and steps, and which is applicable to calculations based on any symmetry restoration or generator coordinate. The method is formally illustrated for particle number restoration and is specified to configuration mixing calculations based on Slater determinants.Comment: 27 pages, 1 figure, accepted for publication in PR

The Recent Stellar Archeology of M31 - The Nearest Red Disk Galaxy

We examine the star-forming history (SFH) of the M31 disk during the past few hundred Myr. The luminosity functions (LFs) of main sequence stars at distances R_GC > 21 kpc (i.e. > 4 disk scale lengths) are matched by models that assume a constant star formation rate (SFR). However, at smaller R_GC the LFs suggest that during the past ~10 Myr the SFR was 2 - 3 times higher than during the preceding ~100 Myr. The rings of cool gas that harbor a significant fraction of the current star-forming activity are traced by stars with ages ~100 Myr, indicating that (1) these structures have ages of at least 100 Myr, and (2) stars in these structures do not follow the same relation between age and random velocity as their counterparts throughout the disks of other spiral galaxies, probably due to the inherently narrow orbital angular momentum distribution of the giant molecular clouds in these structures. The distribution of evolved red stars is not azimuthally symmetric, in the sense that their projected density along the north east segment of the major axis is roughly twice that on the opposite side of the galaxy. The north east arm of the major axis thus appears to be a fossil star-forming area that dates to intermediate epochs. Such a structure may be the consequence of interactions with a companion galaxy.Comment: To appear in The Astrophysical Journa

Combined neutron and x-ray tomography—a versatile and non-destructive tool in planetary geosciences

With several upcoming sample return missions, such as the Mars Sample Return Campaign, non-destructive methods will be key to maximizing their scientific output. In this study, we demonstrate that the combination of neutron and X-ray tomography provides an important tool for the characterization of such valuable samples. These methods allow quantitative analyses of internal sample features and also provide a guide for further destructive analyses with little to no sample treatment, which maintains sample integrity, including minimizing the risk of potential contamination. Here, we present and review the results from four case studies of terrestrial impactites and meteorites along with their analytical setup. Using combined X-ray and neutron tomography, a Ni-Fe silicide spherule, that is, projectile material, was located within a Libyan Desert Glass sample and the distribution of hydrous phases was pinpointed in selected impactite samples from the Chicxulub IODP-ICDP Expedition 364 drill core and the Luizi impact structure, as well as in the Miller Range 03346 Martian meteorite

Quantifying MRI frequency shifts due to structures with anisotropic magnetic susceptibility using pyrolytic graphite sheet

Magnetic susceptibility is an important source of contrast in magnetic resonance imaging (MRI), with spatial variations in the susceptibility of tissue affecting both the magnitude and phase of the measured signals. This contrast has generally been interpreted by assuming that tissues have isotropic magnetic susceptibility, but recent work has shown that the anisotropic magnetic susceptibility of ordered biological tissues, such as myelinated nerves and cardiac muscle fibers, gives rise to unexpected image contrast. This behavior occurs because the pattern of field variation generated by microstructural elements formed from material of anisotropic susceptibility can be very different from that predicted by modelling the effects in terms of isotropic susceptibility. In MR images of tissue, such elements are manifested at a sub-voxel length-scale, so the patterns of field variation that they generate cannot be directly visualized. Here, we used pyrolytic graphite sheet which has a large magnetic susceptibility anisotropy to form structures of known geometry with sizes large enough that the pattern of field variation could be mapped directly using MRI. This allowed direct validation of theoretical expressions describing the pattern of field variation from anisotropic structures with biologically relevant shapes (slabs, spherical shells and cylindrical shells)

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev.

Local-Group tests of dark-matter Concordance Cosmology: Towards a new paradigm for structure formation

(abridged) Predictions of the Concordance Cosmological Model (CCM) of the structures in the environment of large spiral galaxies are compared with observed properties of Local Group galaxies. Five new most probably irreconcilable problems are uncovered. However, the Local Group properties provide hints that may lead to a solution of the above problems The DoS and bulge--satellite correlation suggest that dissipational events forming bulges are related to the processes forming phase-space correlated satellite populations. Such events are well known to occur since in galaxy encounters energy and angular momentum are expelled in the form of tidal tails, which can fragment to form populations of tidal-dwarf galaxies (TDGs) and associated star clusters. If Local Group satellite galaxies are to be interpreted as TDGs then the sub-structure predictions of CCM are internally in conflict. All findings thus suggest that the CCM does not account for the Local Group observations and that therefore existing as well as new viable alternatives have to be further explored. These are discussed and natural solutions for the above problems emerge.Comment: A and A, in press, 25 pages, 9 figures; new version contains minor text adjustments for conformity with the published version and additional minor changes resulting from reader's feedback. The speculation on a dark force has been added. Also, the Fritz Zwicky Paradox is now included to agree with the published versio