Gradient expansion correction to the Dirac exchange term in statistical models for the Na atom with shell structure

Abstract. Compressible plasma turbulence is investigated in the fast solar wind at proton kinetic scales by the combined use of electron density and magnetic field measurements. Both the scale-dependent cross-correlation (CC) and the reduced magnetic helicity (σm) are used in tandem to determine the properties of the compressible fluctuations at proton kinetic scales. At inertial scales the turbulence is hypothesised to contain a mixture of Alfvénic and slow waves, characterised by weak magnetic helicity and anti-correlation between magnetic field strength B and electron density ne. At proton kinetic scales the observations suggest that the fluctuations have stronger positive magnetic helicities as well as strong anti-correlations within the frequency range studied. These results are interpreted as being characteristic of either counter-propagating kinetic Alfvén wave packets or a mixture of anti-sunward kinetic Alfvén waves along with a component of kinetic slow waves. Keywords. Interplanetary physics (MHD waves and turbulence)

Prediction of the binding energy of self interstitial atoms in alpha iron by a graph neural network

The Thomas–Fermi–Dirac (TFD) and multiple-scattering Xα (MS-Xα) methods are compared, for single atoms and for molecules and solids. Both methods are derived from Hamiltonians by variation of the charge density or spin orbitals, respectively, and the Hamiltonians for the two methods differ only in the kinetic energy term. It is pointed out that the main errors in the TFD method arise from the statistical version of the kinetic energy term. The Xα method, which uses the exact kinetic energy term, can be regarded as a modification of the TFD method which removes all the major errors in that method. The Coulomb energy and the exchange-correlation term are identical in both methods. By the example of the TFD method for the carbon atom we illustrate the various features of both methods, and it is pointed out that many features of the calculation of total energy by the Xα method, as described by the overlapping-sphere approach, can be understood better by studying the same problem from the TFD point of view.

To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into $d$-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e. Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.

A new method is proposed for constructing approximations to the electron–electron interaction. In this approach tools of density functional theory, such as the gradient expansion, are employed. Traditional gradient expansions depend on the electron density ρ. Here, however, we propose an alternative route to ρ functionals, we derive functionals that depend solely on the noninteracting kinetic energy density τ(r) defined by τ(r)=12∑iocc|∇φi(r)|2, where φi is a single-particle orbital. We demonstrate the potential of our approach by constructing an approximation to the exchange energy (EX) of electrons that rivals the accuracy of generalized gradient approximations of density functional theory. The strategy presented here is quite general and suitable to construct a variety of nonelectron-density functionals.

Considering the Na atom as an example, an approximation to the electron number density is constructed from H-like wavefunctions. Using this electron density the Thomas-Fermi-Dirac energy density functional, with the Weizsäcker and Hodges gradient expansion corrections to the kinetic energy term, is optimized with respect to the Z in the wavefunctions. The total energy obtained for the Na atom is −170.1 a.u., while the energy calculated by the Roothan-Hartree-Fock method is −161.8 a.u. The Weizsäcker and Hodges corrections are found significant, with values of +9.8 a.u. and +1.4 a.u., respectively.

On the recoil of a nuclear target hit by a nucleon

Self-consistent-field wavefunctions near the Hartree–Fock limit have been calculated by the Roothaan expansion method for OF(2π) at several internuclear separations; the total energy at the Hartree–Fock minimum (1.321 Å) was found to be − 174.19502 hartree. Based on the assumption that the correlation energy was approximately the same as for O2−, and also by interpolating the correlation energy of OF across the CF, NF, OF, and F2 sequence, the binding energy D(OF) was deduced to be 3.0+0.3−0.8 eV. A Dunham analysis of the potential-energy curve gave values for the various spectroscopic constants. In addition, the ionization potential and electron affinity for the vertical processes, and the dipole and quadrupole moments of OF+(3Σ), OF(2π), and OF−(1Σ) were also calculated.

The wealth of information accumulated recently by ab initio/DFT calculations of adsorption energetics and reactivity on metal surfaces makes it possible to systematically compare projections of the DFT and UBI-QEP approaches. We make such comparisons covering both qualitative regularities in and the quantitative accuracy of binding energies and activation barriers. We focus on the following areas: (1) DFT verification of the UBI-QEP assumptions and rigorous projections concerning atomic and molecular binding energies at low coverage; (2) coverage effects revealing in the M-A bond energy competition (metal sharing A-M-A) under atomic co-adsorption; (3) reactivity patterns including both qualitative (periodic dependence of the activation barriers, barrier vs. reaction enthalpy relationships, geometry of the transition state, etc.) and quantitative aspects. We demonstrate the broad agreement between the DFT and UBI-QEP projections and point out the areas where further testing by the ab initio/DFT techniques might be necessary and illuminating. In particular, while discussing the ab initio/DFT absolute values of the atomic binding energies Q A and their periodic trends, we revised our previous assumptions about monotonic changes of the Q A values with the changing atom A valence and along the VIII and IB group metals, where the periodic trends appear to be complicated. Accordingly, we make corrections to the original UBI-QEP parameters, summarizing the current recommended values of Q A.

On a cosmological aspect of the phase transition at the grand unification temperature

A collective model for inner shell ionization of very heavy targets

The exchange of a pair of low-mass neutrinos between electrons, protons, and neutrons produces a "long-range" 1/r^{5} potential, which can be sought for in phenomena originating on the atomic and subatomic length scales. We calculate the effects of neutrino-pair exchange on transition and binding energies in atoms and nuclei. In the case of atomic s-wave states, there is a large enhancement of the induced energy shifts due to the lack of a centrifugal barrier and the highly singular nature of the neutrino-mediated potential. We derive limits on neutrino-mediated forces from measurements of the deuteron binding energy and transition energies in positronium, muonium, hydrogen, and deuterium, as well as isotope-shift measurements in calcium ions. Our limits improve on existing constraints on neutrino-mediated forces from experiments that search for new macroscopic forces by 18 orders of magnitude. Future spectroscopy experiments have the potential to probe long-range forces mediated by the exchange of pairs of standard-model neutrinos and other weakly charged particles.

The binding energy of single atoms of the Period-6 transition elements on atomically perfect single-crystal planes of tungsten was measured by utilizing low-temperature-pulse field desorption, in a ultrahighvacuum field-ion microscope. For any given adatom, the dependence of the binding energy on surface crystallography was observed to be inconsistent with a pairwise interaction model. A new model incorporating a surface-charge redistribution into a pairwise potential is shown to be consistent with the data. The variation in binding energy with electronic configuration of the adatom is interpreted in terms of an electron-energy band model. The binding energy depends upon the electron occupancy of two subbands assumed to exist in the d levels of the atom, when it is adsorbed on the surface. Finally, the abnormal field-desorption properties of adatoms on the (110) plane are discussed in terms of its anomalous work function.

The localized-orbital locator, which describes the features of bonding in terms of the local kinetic energy, is approximately expressed as a function of electron density and its first and second derivatives. Calculations based on accurate electron densities derived from X-ray diffraction data are carried out for crystals with different types of chemical bonds. It is demonstrated that the localized-orbital locator reveals the features of atomic interactions in a solid state and allows the covalent, ionic and van der Waals bonds to be distinguished.

Higher-order gradient corrections for exchange-correlation functionals