Density-functional calculation of ionization energies of current-carrying atomic states

Current-density-functional theory is used to calculate ionization energies of current-carrying atomic states. A perturbative approximation to full current-density-functional theory is implemented for the first time, and found to be numerically feasible. Different parametrizations for the current-dependence of the density functional are critically compared. Orbital currents in open-shell atoms turn out to produce a small shift in the ionization energies. We find that modern density functionals have reached an accuracy at which small current-related terms appearing in open-shell configurations are not negligible anymore compared to the remaining difference to experiment.Comment: 7 pages, 2 tables, accepted by Phys. Rev.

Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Bounds on the exchange-correlation energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasi-one dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained, and give evidence of an interesting dimensional crossover between two and one dimensions

Spin currents and spin dynamics in time-dependent density-functional theory

We derive and analyse the equation of motion for the spin degrees of freedom within time-dependent spin-density-functional theory (TD-SDFT). Results are (i) a prescription for obtaining many-body corrections to the single-particle spin currents from the Kohn-Sham equation of TD-SDFT, (ii) the existence of an exchange-correlation (xc) torque within TD-SDFT, (iii) a prescription for calculating, from TD-SDFT, the torque exerted by spin currents on the spin magnetization, (iv) a novel exact constraint on approximate xc functionals, and (v) the discovery of serious deficiencies of popular approximations to TD-SDFT when applied to spin dynamics.Comment: now includes discussion of OEP and GGA; to appear in Phys. Rev. Let

The spin angular gradient approximation in the density functional theory

A spin angular gradient approximation for the exchange correlation magnetic field in the density functional formalism is proposed. The usage of such corrections leads to a consistent spin dynamical approach beyond the local approximation. The proposed technique does not contain any approximations for the form of potential and can be used in modern full potential band structure methods. The obtained results indicate that the direct 'potential' exchange in 3d magnets is rather small compared to the indirect 'kinetic' exchange, thus justifies the dynamical aspect of the local density approximation in 3d metals

Observability of Earth-skimming Ultra-high Energy Neutrinos

Neutrinos with energies above 10^8 GeV are expected from cosmic ray interactions with the microwave background and are predicted in many speculative models. Such energetic neutrinos are difficult to detect, as they are shadowed by the Earth, but rarely interact in the atmosphere. Here we propose a novel detection strategy: Earth-skimming neutrinos convert to charged leptons that escape the Earth, and these leptons are detected in ground level fluorescence detectors. With the existing HiRes detector, neutrinos from some proposed sources are marginally detectable, and improvements of two orders of magnitude are possible at the proposed Telescope Array.Comment: 4 pages, 3 figure

Some Remarks on Theories with Large Compact Dimensions and TeV-Scale Quantum Gravity

We comment on some implications of theories with large compactification radii and TeV-scale quantum gravity. These include the behavior of high-energy gravitational scattering cross sections and consequences for ultra-high-energy cosmic rays and neutrino scattering, the question of how to generate naturally light neutrino masses, the issue of quark-lepton unification, the equivalence principle, and the cosmological constant.Comment: 28 pages, Late

Determination of absolute neutrino masses from Z-bursts

Ultrahigh energy neutrinos (UHE\nu) scatter on relic neutrinos (R\nu) producing Z bosons, which can decay hadronically producing protons (Z-burst). We compare the predicted proton spectrum with the observed ultrahigh energy cosmic ray (UHECR) spectrum and determine the mass of the heaviest R\nu via a maximum likelihood analysis. Our prediction depends on the origin of the power-like part of the UHECR spectrum: m_\nu=2.75^{+1.28}_{-0.97} eV for Galactic halo and 0.26^{+0.20}_{-0.14} eV for extragalactic (EG) origin. The necessary UHE\nu flux should be detected in the near future.Comment: slight rewording, revised neutrino fluxes, conclusions unchanged, version to appear in Phys. Rev. Let

Dynamical parton distributions of the nucleon and very small-x physics

Utilizing recent DIS measurements (F_{2,L}) and data on dilepton and high-E_{T} jet production we determine the dynamical parton distributions of the nucleon generated radiatively from valence-like positive input distributions at optimally chosen low resolution scales. These are compared with `standard' distributions generated from positive input distributions at some fixed and higher resolution scale. It is shown that up to the next to leading order NLO(\bar{MS}, DIS) of perturbative QCD considered in this paper, the uncertainties of the dynamical distributions are, as expected, smaller than those of their standard counterparts. This holds true in particular in the presently unexplored extremely small-x region relevant for evaluating ultrahigh energy cross sections in astrophysical applications. It is noted that our new dynamical distributions are compatible, within the presently determined uncertainties, with previously determined dynamical parton distributions.Comment: 21 pages, 2 tables, 16 figures, v2: added Ref.[60], replaced Fig.

Cosmic Rays as Probes of Large Extra Dimensions and TeV Gravity

If there are large extra dimensions and the fundamental Planck scale is at the TeV scale, then the question arises of whether ultra-high energy cosmic rays might probe them. We study the neutrino-nucleon cross section in these models. The elastic forward scattering is analyzed in some detail, hoping to clarify earlier discussions. We also estimate the black hole production rate. We study energy loss from graviton mediated interactions and conclude that they can not explain the cosmic ray events above the GZK energy limit. However, these interactions could start horizontal air showers with characteristic profile and at a rate higher than in the Standard Model.Comment: 14 pages, 4 figures; minor changes, replaced with version to be published in Phys. Rev.

On the cosmic ray bound for models of extragalactic neutrino production

We obtain the maximum diffuse neutrino intensity predicted by hadronic photoproduction models of the type which have been applied to the jets of active galactic nuclei or gamma ray bursts. For this, we compare the proton and gamma ray fluxes associated with hadronic photoproduction in extragalactic neutrino sources with the present experimental upper limit on cosmic ray protons and the extragalactic gamma ray background, employing a transport calculation of energetic protons traversing cosmic photon backgrounds. We take into account the effects of the photon spectral shape in the sources on the photoproduction process, cosmological source evolution, the optical depth for cosmic ray ejection, and discuss the possible effects of magnetic fields in the vicinity of the sources. For photohadronic neutrino sources which are optically thin to the emission of neutrons we find that the cosmic ray flux imposes a stronger bound than the extragalactic gamma ray background in the energy range between 10^5 GeV and 10^11 GeV, as previously noted by Waxman & Bahcall (1999). We also determine the maximum contribution from the jets of active galactic nuclei, using constraints set to their neutron opacity by gamma-ray observations. This present upper limit is consistent with the jets of active galactic nuclei producing the extragalactic gamma ray background hadronically, but we point out future observations in the GeV-to-TeV regime could lower this limit. We also briefly discuss the contribution of gamma ray bursts to ultra-high energy cosmic rays as it can be inferred from possible observations or limits on their correlated neutrino fluxes.Comment: 16 pages, includes 7 figures, using REVtex3.1, accepted for publication in Phys.Rev.D after minor revision