Why is the bandwidth of sodium observed to be narrower in photoemission experiments?

The experimentally predicted narrowing in the bandwidth of sodium is interpreted in terms of the non-local self-energy effect on quasi-particle energies of the electron liquid. The calculated self-energy correction is a monotonically increasing function of the wavenumber variable. The usual analysis of photo-emission experiments assumes the final state energies on the nearly-free-electron-like model and hence it incorrectly ascribes the non-local self-energy correction to the final state energies to the occupied state energies, thus leading to a seeming narrowing in the bandwidth.Comment: 9 page

The on-top pair-correlation density in the homogeneous electron liquid

The ladder theory, in which the Bethe-Goldstone equation for the effective potential between two scattering particles plays a central role, is well known for its satisfactory description of the short-range correlations in the homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in the limit of large transfer momentum between two scattering particles, we obtain accurate results for the on-top pair-correlation density $g(0)$, in both three dimensions and two dimensions. Furthermore, we prove, in general, the ladder theory satisfies the cusp condition for the pair-correlation density $g(r)$ at zero distance $r=0$.Comment: 8 pages, 4 figure

Quasiparticle Effective Mass for the Two- and Three-Dimensional Electron Gas

We calculate the quasiparticle effective mass for the electron gas in two and three dimensions in the metallic region. We employ the single particle scattering potential coming from the Sj\"{o}lander-Stott theory and enforce the Friedel sum rule by adjusting the effective electron mass in a scattering calculation. In 3D our effective mass is a monotonically decreasing function of $r_s$ throughout the whole metallic domain, as implied by the most recent numerical results. In 2D we obtain reasonable agreement with the experimental data, as well as with other calculations based on the Fermi liquid theory. We also present results of a variety of different treatments for the effective mass in 2D and 3D.Comment: 12 pages, 2 figure

Self-consistent Overhauser model for the pair distribution function of an electron gas in dimensionalities D=3 and D=2

We present self-consistent calculations of the spin-averaged pair distribution function $g(r)$ for a homogeneous electron gas in the paramagnetic state in both three and two dimensions, based on an extension of a model that was originally proposed by A. W. Overhauser [Can. J. Phys. {\bf 73}, 683 (1995)] and further evaluated by P. Gori-Giorgi and J. P. Perdew [Phys. Rev. B {\bf 64}, 155102 (2001)]. The model involves the solution of a two-electron scattering problem via an effective Coulombic potential, that we determine within a self-consistent Hartree approximation. We find numerical results for $g(r)$ that are in excellent agreement with Quantum Monte Carlo data at low and intermediate coupling strength $r_s$, extending up to $r_s\approx 10$ in dimensionality D=3. However, the Hartree approximation does not properly account for the emergence of a first-neighbor peak at stronger coupling, such as at $r_s=5$ in D=2, and has limited accuracy in regard to the spin-resolved components $g_{\uparrow\uparrow}(r)$ and $g_{\uparrow\downarrow}(r)$. We also report calculations of the electron-electron s-wave scattering length, to test an analytical expression proposed by Overhauser in D=3 and to present new results in D=2 at moderate coupling strength. Finally, we indicate how this approach can be extended to evaluate the pair distribution functions in inhomogeneous electron systems and hence to obtain improved exchange-correlation energy functionals.Comment: 14 pages, 7 figuers, to apear in Physical Review

Global raster dataset on historical coastline positions and shelf sea extents since the Last Glacial Maximum

Motivation: Historical changes in sea level caused shifting coastlines that affected the distribution and evolution of marine and terrestrial biota. At the onset of the Last Glacial Maximum (LGM) 26 ka, sea levels were >130 m lower than at present, resulting in seaward-shifted coastlines and shallow shelf seas, with emerging land bridges leading to the isolation of marine biota and the connection of land-bridge islands to the continents. At the end of the last ice age, sea levels started to rise at unprecedented rates, leading to coastal retreat, drowning of land bridges and contraction of island areas. Although a growing number of studies take historical coastline dynamics into consideration, they are mostly based on past global sea-level stands and present-day water depths and neglect the influence of global geophysical changes on historical coastline positions. Here, we present a novel geophysically corrected global historical coastline position raster for the period from 26 ka to the present. This coastline raster allows, for the first time, calculation of global and regional coastline retreat rates and land loss rates. Additionally, we produced, per time step, 53 shelf sea rasters to present shelf sea positions and to calculate the shelf sea expansion rates. These metrics are essential to assess the role of isolation and connectivity in shaping marine and insular biodiversity patterns and evolutionary signatures within species and species assemblages. Main types of variables contained: The coastline age raster contains cells with ages in thousands of years before present (bp), representing the time since the coastline was positioned in the raster cells, for the period between 26 ka and the present. A total of 53 shelf sea rasters (sea levels <140 m) are presented, showing the extent of land (1), shelf sea (0) and deep sea (NULL) per time step of 0.5 kyr from 26 ka to the present. Spatial location and grain: The coastline age raster and shelf sea rasters have a global representation. The spatial resolution is scaled to 120 arcsec (0.333° × 0.333°), implying cells of c. 3,704 m around the equator, 3,207 m around the tropics (±30°) and 1,853 m in the temperate zone (±60°). Time period and temporal resolution: The coastline age raster shows the age of coastline positions since the onset of the LGM 26 ka, with time steps of 0.5 kyr. The 53 shelf sea rasters show, for each time step of 0.5 kyr, the position of the shelf seas (seas shallower than 140 m) and the extent of land. Level of measurement: Both the coastline age raster and the 53 shelf sea rasters are provided as TIFF files with spatial reference system WGS84 (SRID 4326). The values of the coastline age raster per grid cell correspond to the most recent coastline position (in steps of 0.5 kyr). Values range from 0 (0 ka, i.e., present day) to 260 (26 ka) in bins of 5 (0.5 kyr). A value of “no data” is ascribed to pixels that have remained below sea level since 26 ka. Software format: All data processing was done using the R programming language

Density functional theories and self-energy approaches

A purpose-designed microarray platform (Stressgenes, Phase 1) was utilised to investigate the changes in gene expression within the liver of rainbow trout during exposure to a prolonged period of confinement. Tissue and blood samples were collected from trout at intervals up to 648 h after transfer to a standardised confinement stressor, together with matched samples from undisturbed control fish. Plasma ACTH, cortisol, glucose and lactate were analysed to confirm that the neuroendocrine response to confinement was consistent with previous findings and to provide a phenotypic context to assist interpretation of gene expression data. Liver samples for suppression subtractive hybridisation (SSH) library construction were selected from within the experimental groups comprising “early” stress (2–48 h) and “late” stress (96–504 h). In order to reduce redundancy within the four SSH libraries and yield a higher number of unique clones an additional subtraction was carried out. After printing of the arrays a series of 55 hybridisations were executed to cover 6 time points. At 2 h, 6 h, 24 h, 168 h and 504 h 5 individual confined fish and 5 individual control fish were used with control fish only at 0 h. A preliminary list of 314 clones considered differentially regulated over the complete time course was generated by a combination of data analysis approaches and the most significant gene expression changes were found to occur during the 24 h to 168 h time period with a general approach to control levels by 504 h. Few changes in expression were apparent over the first 6 h. The list of genes whose expression was significantly altered comprised predominantly genes belonging to the biological process category (response to stimulus) and one cellular component category (extracellular region) and were dominated by so-called acute phase proteins. Analysis of the gene expression profile in liver tissue during confinement revealed a number of significant clusters. The major patterns comprised genes that were up-regulated at 24 h and beyond, the primary examples being haptoglobin, β-fibrinogen and EST10729. Two representative genes from each of the six k-means clusters were validated by qPCR. Correlations between microarray and qPCR expression patterns were significant for most of the genes tested. qPCR analysis revealed that haptoglobin expression was up-regulated approximately 8-fold at 24 h and over 13-fold by 168 h.This project was part funded by the European Commission (Q5RS-2001-02211), Enterprise Ireland and the Natural Environment Research Council of the United Kingdom

Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas

We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts (i) fulfills more known integral and differential properties of the exact pair-correlation function, (ii) is analytic both in real and in reciprocal space, and (iii) accurately interpolates the newest, extensive diffusion-Monte Carlo data of Ortiz, Harris and Ballone [Phys. Rev. Lett. 82, 5317 (1999)]. This can be of interest for the study of electron correlations of real materials and for the construction of new exchange and correlation energy density functionals.Comment: 14 pages, 5 figures, submitted to Phys. Rev.