N. H. March

Wave functions and low-order density matrices for a class of two-electron 'artificial atoms' embracing Hookean and Moshinsky models

Abstract A class of model two-electron ‘artificial atoms’ is proposed which embraces both Hookean and Moshinsky models. Particle densities and spinless first-order density matrices are obtained for this class of models. These quantities and the interacting system kinetic energy can be calculated using the ground-state solution of an explicit single-particle radial Schrodinger equation.

Tcfor non-s-wave pairing superconductors correlated with coherence length and effective mass

For unconventional heavy Fermion superconductors, typified by UBe_13, the superconducting transition temperatures Tc are shown to correlate with a characteristic energy hbar^2 /(m* xi^2), m* being the effective mass and xi the coherence length. For four of the six materials for which Tc, m* and xi are available, kB Tc ~ 20 hbar^2 / (m* xi^2). One heavy Fermion material, UPd_2Al_3, reveals a tendency for the above linear behaviour to saturate at substantially larger hbar^2 / (m* xi^2) than for UBe_13. The sixth material considered, URu_2Si_2, falls between UBe_13 and UPd_2Al_3. To embrace d-wave pairing in cuprates, a log-log plot reveals that kB Tc ~ hbar^2 / (m* xi^2), but more materials for which m* and xi are measured will be required to substantiate the correlation in these high-Tc substances.

Limit of Fermi Liquid Regime and Binding Energy of Charged (2e) Boson in High T c Cuprates

Abstract Two-dimensional Fermi liquid theory applied to the normal state of high Tc cuprate materials predicts that the product of electrical resistivity and nuclear spin-lattice relaxation time should be proportional to temperature. This is vindicated for underdoped YBa2Cu4O8 above a certain crossover temperature. This latter temperature is then used to estimate the binding energy of the composite charged (2e) Bosons already present above the critical temperature Tc .

Freezing of ionic melts into normal and superionic phases

Abstract The freezing mechanisms of molten alkali halides typified by RbCl and NaCl on the one hand, and molten fluorite-type materials BaCl2 and SrCl2 on the other, are compared and contrasted. Experimentally, the volume change across the solid-liquid transition is large for the alkali halides (∼20%) and almost an order of magnitude smaller for the fluorites, where the freezing transition is to a superionic phase. For RbCl and NaCl therefore, the free energy gain associated with the large volume change is one major feature in freezing, the other being the strong charge ordering. This is made quantitative and structural predictions for molten RbCl are in excellent agreement with neutron data. The agreement for NaCl is of poorer quality, but still semiquantitative. In the case of freezing into the superionic phase, it turns out instead that the major features are the strong ordering of the divalent cation component and the difference in the partial molar volumes of anion and cation. The pronounced cation o...

Review article:electronic transport in short mean-free path liquid metals

Abstract Recent work on the theory of electronic transport is reviewed. Attention is focused on liquid metals but contact is made with theories of localization due to disorder.

The March model applied to boron cages

Abstract The so-called March model of fullerene, in which a self-consistent spherical distribution of π electrons is combined with the proper nuclear–nuclear potential energy for the correct structure, is here extended to boron cages. The Thomas–Fermi approximation of the initial studies is here replaced by Hartree–Fock calculations. Explicit results for B 2 k and B 2 k +1 + , with k ranging from 15 to 27, are discussed and compared with calculations on similar clusters found in the literature.

EXCHANGE AND CORRELATION IN DENSITY FUNCTIONAL THEORY OF ATOMS AND MOLECULES

The exchange and correlation energies and potentials, occurring in various density functional theory approaches and schemes are reviewed and their definitions compared. The ways of their determination and their long-range properties are discussed. General expressions for the exchange and correlation energy and the long-range asymptotic form of the exchange potential are obtained for mixed-state systems. Line-integral expressions for the exchange and correlation potentials, valid both for pure-state and mixed-state systems are derived. Approximation to the electrostatic-plus-exchange energy and corresponding potential for arbitrary mixed-state systems and approximation to the correlation energy and potential for a specific class of mixed-state systems are proposed. They are expressible in terms of any approximate functional of the density for the exchange energy and correlation energy, respectively, known for pure-state systems.

Differential equation for the ground-state density of artificial two-electron atoms with harmonic confinement

A long-term aim of density functional theory is to obtain a differential equation for the ground-state electron density ρ(r) in a closed-shell atom, the simplest example being He. Since He remains intractable analytically, artificial atoms with harmonic repulsive potential energy u(r12) have therefore been studied. Here we exploit recent work on ρ(r) for such a two-electron system, with u(r12) = λ/r212, to construct a second-order linear differential equation for ρ(r). This is compared and contrasted with available results for different choices of u(r12).

Theoretical Approaches to Thermal Conductivity in Liquids

Abstract We first review analytical and computer modelling approaches to heat conduction in insulating liquids. Thermal conductivity Δ can be calculated by approximate analytic theory, and also by molecular simulation which solves the many-body problem for molecules interacting through specific interactions. Equilibrium and non-equilibrium molecular dynamics, NEMD, techniques are now available that enable Δ to be computed for single-component monatomic and molecular liquids, as well as their mixtures. For mixtures, Δ can be determined from the distinct Onsager coefficients, individually computed using equilibrium molecular dynamics. Electronic contributions to the thermal conductivity of liquid metals are then considered, by invoking the Wiedemann-Franz Law relating thermal and electrical transport.

Superconducting transition temperatures and coherence length in non- s -wave pairing materials correlated with spin-fluctuation mediated interaction

Following earlier work on electron or hole liquids flowing through assemblies with magnetic fluctuations, we have recently exposed a marked correlation of the superconducting temperature