Electron correlation energy in confined two-electron systems

Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted Hartree-Fock and radial limit energies over a range of confinement radii from 0.05 - 10 a0. At small R, the correlation energies approach limiting values that are independent of Z while at intermediate R, systems with Z > 1 exhibit a characteristic maximum in the correlation energy resulting from an increase in the angular correlation energy which is offset by a decrease in the radial correlation energy

Measurement of SUSY masses via cascade decays for SPS 1a

If R-parity conserving supersymmetry exists below the TeV-scale, new particles will be produced and decay in cascades at the LHC. The lightest supersymmetric particle will escape the detectors, thereby complicating the full reconstruction of the decay chains. In this paper we expand on existing methods for determining the masses of the particles in the cascade from endpoints of kinematical distributions. We perform scans in the mSUGRA parameter space to delimit the region where this method is applicable. From the examination of theoretical distributions for a wide selection of mass scenarios it is found that caution must be exerted when equating the theoretical endpoints with the experimentally obtainable ones. We provide analytic formulae for the masses in terms of the endpoints most readily available. Complications due to the composite nature of the endpoint expressions are discussed in relation to the detailed analysis of two points on the SPS 1a line. Finally we demonstrate how a Linear Collider measurement can improve dramatically on the precision of the masses obtained

Constraints on diffuse neutrino background from primordial black holes

We calculated the energy spectra and the fluxes of electron neutrino emitted in the process of evaporation of primordial black holes (PBHs) in the early universe. It was assumed that PBHs are formed by a blue power-law spectrum of primordial density fluctuations. We obtained the bounds on the spectral index of density fluctuations assuming validity of the standard picture of gravitational collapse and using the available data of several experiments with atmospheric and solar neutrinos. The comparison of our results with the previous constraints (which had been obtained using diffuse photon background data) shows that such bounds are quite sensitive to an assumed form of the initial PBH mass function.Comment: 18 pages,(with 7 figures

Potential-density pairs for axisymmetric galaxies: the influence of scalar fields

We present a formulation for potential-density pairs to describe axisymmetric galaxies in the Newtonian limit of scalar-tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential-density pairs of galactic disks for an exponential profile and their rotation curves.Comment: 8 pages, no figures, corrected version to the one that will appear in Gen. Relativ. Gravit., where a small typo in eq. (13) is presen

Stripes and holes in a two-dimensional model of spinless fermions and hardcore bosons

We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half-filling. The problem of a single stripe can be mapped to a spin-1/2 chain, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of two, three, and four stripes, finding that they repel, and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into particle-rich phase and hole-rich liquid, we evaluate the liquid's equation of state, finding the stripe-array is not stable for bosons but is possibly stable for fermions.Comment: 24 pages, 18 figure

Crucial Physical Dependencies of the Core-Collapse Supernova Mechanism

We explore with self-consistent 2D F{\sc{ornax}} simulations the dependence of the outcome of collapse on many-body corrections to neutrino-nucleon cross sections, the nucleon-nucleon bremsstrahlung rate, electron capture on heavy nuclei, pre-collapse seed perturbations, and inelastic neutrino-electron and neutrino-nucleon scattering. Importantly, proximity to criticality amplifies the role of even small changes in the neutrino-matter couplings, and such changes can together add to produce outsized effects. When close to the critical condition the cumulative result of a few small effects (including seeds) that individually have only modest consequence can convert an anemic into a robust explosion, or even a dud into a blast. Such sensitivity is not seen in one dimension and may explain the apparent heterogeneity in the outcomes of detailed simulations performed internationally. A natural conclusion is that the different groups collectively are closer to a realistic understanding of the mechanism of core-collapse supernovae than might have seemed apparent.Comment: 25 pages; 10 figure

A comparison of Finite Elements for Nonlinear Beams: The absolute nodal coordinate and geometrically exact formulations

Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other

Light propagation in statistically homogeneous and isotropic universes with general matter content

We derive the relationship of the redshift and the angular diameter distance to the average expansion rate for universes which are statistically homogeneous and isotropic and where the distribution evolves slowly, but which have otherwise arbitrary geometry and matter content. The relevant average expansion rate is selected by the observable redshift and the assumed symmetry properties of the spacetime. We show why light deflection and shear remain small. We write down the evolution equations for the average expansion rate and discuss the validity of the dust approximation.Comment: 42 pages, no figures. v2: Corrected one detail about the angular diameter distance and two typos. No change in result

A High Statistics Search for Ultra-High Energy Gamma-Ray Emission from Cygnus X-3 and Hercules X-1

We have carried out a high statistics (2 Billion events) search for ultra-high energy gamma-ray emission from the X-ray binary sources Cygnus X-3 and Hercules X-1. Using data taken with the CASA-MIA detector over a five year period (1990-1995), we find no evidence for steady emission from either source at energies above 115 TeV. The derived upper limits on such emission are more than two orders of magnitude lower than earlier claimed detections. We also find no evidence for neutral particle or gamma-ray emission from either source on time scales of one day and 0.5 hr. For Cygnus X-3, there is no evidence for emission correlated with the 4.8 hr X-ray periodicity or with the occurrence of large radio flares. Unless one postulates that these sources were very active earlier and are now dormant, the limits presented here put into question the earlier results, and highlight the difficulties that possible future experiments will have in detecting gamma-ray signals at ultra-high energies.Comment: 26 LaTeX pages, 16 PostScript figures, uses psfig.sty to be published in Physical Review

Dynamic Evolution Model of Isothermal Voids and Shocks

We explore self-similar hydrodynamic evolution of central voids embedded in an isothermal gas of spherical symmetry under the self-gravity. More specifically, we study voids expanding at constant radial speeds in an isothermal gas and construct all types of possible void solutions without or with shocks in surrounding envelopes. We examine properties of void boundaries and outer envelopes. Voids without shocks are all bounded by overdense shells and either inflows or outflows in the outer envelope may occur. These solutions, referred to as type $\mathcal{X}$ void solutions, are further divided into subtypes $\mathcal{X}_{\rm I}$ and $\mathcal{X}_{\rm II}$ according to their characteristic behaviours across the sonic critical line (SCL). Void solutions with shocks in envelopes are referred to as type $\mathcal{Z}$ voids and can have both dense and quasi-smooth edges. Asymptotically, outflows, breezes, inflows, accretions and static outer envelopes may all surround such type $\mathcal{Z}$ voids. Both cases of constant and varying temperatures across isothermal shock fronts are analyzed; they are referred to as types $\mathcal{Z}_{\rm I}$ and $\mathcal{Z}_{\rm II}$ void shock solutions. We apply the `phase net matching procedure' to construct various self-similar void solutions. We also present analysis on void generation mechanisms and describe several astrophysical applications. By including self-gravity, gas pressure and shocks, our isothermal self-similar void (ISSV) model is adaptable to various astrophysical systems such as planetary nebulae, hot bubbles and superbubbles in the interstellar medium as well as supernova remnants.Comment: 24 pages, 13 figuers, accepted by ApS