A minimal size for granular superconductors

We investigate the minimal size of small superconducting grains by means of a Ginzburg–Landau model confined to a sphere of radius R. This model is supposed to describe a material in the form of a ball, whose transition temperature when presented in bulk form, T₀, is known. We obtain an equation for the critical temperature as a function of R and of T₀, allowing us to obtain a minimal radius of the sphere below which no superconducting transition exists. An estimate of values of minimal radii for different materials is done.     

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 0.05-10a₀. 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.     

Quasi-wetting on a sphere

Wetting phenomena on a sphere of radius R are studied in the context of the Sullivan model. Neither a first nor a continuous transition is found for finite R. Only in the strict limit of R→∞ a second-order transition appears. For temperatures T higher than the wetting temperature in a flat geometry, T^∞_w, the thickness l of the enhanced density layer, which forms on the surface of the sphere, is for large R proportional to In R.     

On the vacancy in a metal

The self-consistent calculations of spatial distributions of electrons and potentials in an isolated spherical cavity (with atomic radius R _WS) of the Wigner-Seitz cell, the energy of the vacancy formation, and the vacancy contribution to the electrical resistance have been performed in terms of the modified Kohn-Sham method and the stabilized jellium model. The energy shift of the ground state of electrons in the Wigner-Seitz cell with radius R _v ? R _WS (where R _v is the average distance between vacancies), the contribution of vacancies to the electron work function, and the effective mass of electrons have been found using the calculated phase shifts of the scattering wave functions and the representation of a system of vacancies as a “superlattice” in a metal.     

The metamorphosis in the emission angular profile from an inverted two-level atoms system

A rich variety of angular distributions in the cooperative emission from a sphere of inverted N two-level atoms are shown to result from the eigenstructure of the complex kernel of scalar photon theory exp(ik₀R)/(ik₀R). This angular distribution is sensitive both to the size of the sphere and to the instant of observation of the emission.     

On the Ground State Energy of the¶Fractional Quantum Hall Effect

Let I(N,R) be the ground state energy of N electrons confined to a disc of radius R with a constant magnetic field B in the perpendicular direction. We show that, in the limit and , where ν is the Landau level filling factor, we have with . The factor is obtained through the solution of an extreme-value problem in measure theory. Received: 10 November 1998 / Accepted: 27 January 1999     

Description of small-angle neutron scattering data for nickel–chromium–aluminum alloy within quantum mechanics and classic polydisperse sphere model

The modified Yukawa potential is used to fit the nucleus model parameters to the data on small-angle neutron scattering on nickel—chromium—aluminum alloy for the product of the transferred momentum Q and the effective nucleus radius R, satisfying the condition QR ≤ ?. The analytical polydisperse sphere model is used to calculate the neutron scattering intensity and to determine the most probable macroscopic sphere radius R ₀ at QR ₀ ≥ 3?.     

<Superscript>1</Superscript>H NMR studies of cyclohexane confined in mesoporous solids: Melting point depression and pore size distribution

The pore size distributions of four controlled pore glasses and two silica gels with nominal diameters ranging from 6–24 nm were determined by measuring the¹H nuclear magnetic resonance (NMR) signal from the nonfrozen fraction of confined cyclohexane as a function of temperature, in steps of ca. 0.1–1 K. The intensity curves of the liquid component are well represented by a sum of two error functions. The mean melting point depression of cyclohexane confined in pores with radiusR follows the simplified Gibbs-Thompson equation δT=k _p/R with ak _p value of 72.4 Knm. To our knowledge, this is the first time that thek _p value of cyclohexane has been directly and accurately calibrated by NMR. As expected, thek _p value mainly determines the position of the pore size distribution curve, i.e., the mean pore radius. The overall pore size distributions determined by NMR are in reasonable agreement with the results specified by the manufacturer, or measured by us by the N₂ sorption technique. Although the melting point depression of confined cyclohexane is found to be less than previously assumed, this compound is still one of the most suitable candidates for NMR-based pore size determinations. However, pore sizes larger than approximately 50 nm in diameter will be difficult to determine accurately by NMR unless adsorbates undergoing larger melting point depressions than cyclohexane can be found.     

Characteristics of degenerated four wave mixing in ZnS/CdSe/ZnS quantum dot quantum well with multi-shell structure

The wave functions and eigenenergies of electrons in ZnS/CdSe/ZnS cylindrical quantum dot quantum well (QDQW) have been calculated by solving a three-dimensional nonlinear Schrödinger equation, in the framework of the effective-mass envelope-function theory. The third-order susceptibilities of the degenerated four waves mixing (DFWM) have been calculated theoretically by means of compact density matrix. The third-order susceptibilities as the function of the shell radius R₂, R₃ have been analyzed. The results show that the magnitude of nonlinear susceptibility is increased with the increasing of well radius. The resonance frequency of the photon have a shift when R₂ or R₃ is increasing and the relation between nonlinear susceptibility and relaxation time has also been studied.     

Toward the theory of electron and positron states in dielectric clusters

Analytical expressions for the binding energy of electrons and positrons in dielectric clusters, analyzed in this work, neglect the elastic effects. Therefore, we present the density-functional theory for neutral liquid clusters that experience the spontaneous deformation. Using the 1/R-expansion, R being the cluster radius, the exact analytical expressions for the size corrections to the chemical potential, surface tension, and atomic density are derived from the condition of mechanical equilibrium. The problem of calculating these corrections is reduced to calculating the quantities for a liquid with a flat surface. The size compression and tension of density occur in the 1/R and 1/R ² orders respectively. The sizes of charged rigid and elastic critical clusters, for which the electron or positron binding energy is close to zero, are calculated for Xe _N ^? , Kr _N ^? , Ar _N ^? , Ne _N ⁺ , He _N ⁺ . The calculations show significant contribution of self-compression to the binding energy of the excess electron in contrast to the positron.     

On size corrections to the diamagnetic susceptibility of a free electron gas

The magnetic behavior of spinless electrons confined in a cylinder of radiusR by a harmonic oscillator potential is calculated over the entire range of sizesR/r _H, wherer _H is the radius of the classical electron orbit due to a constant magnetic fieldH. The magnetic moment is shown to be large and positive in the small size limitR/r _H?1 in agreement with recent experimental work, while in the usual large size limitR/r _H?1 the Landau susceptibility is obtained. The model is compared with a similar calculation in which a periodic boundary condition is applied in order to show explicitly how qualitative differences arise in the small size limit, and the relevance of the results to calculations for rectangular and spherical geometries with hard wall boundary conditions is examined.     

Few-electron semiconductor quantum dots with Gaussian confinement

We have performed Hartree-Fock calculations of the electronic structure of N ≤ 10 electrons in a quantum dot modeled with a confining Gaussian potential well. We discuss the conditions for the stability of N bound electrons in the system. We show that the most relevant parameter determining the number of bound electrons is V ₀ R ². Such a feature arises from widely valid scaling properties of the confining potential. Gaussian Quantum dots having N = 2, 5, and 8 electrons are particularly stable in agreement with the Hund rule. The shell structure becomes less and less noticeable as the well radius increases.      

Binding energy of an off-center hydrogenic donor in a spherical Gaussian quantum dot

The energy levels of an off-center hydrogenic donor confined by a spherical Gaussian potential have been calculated as a function of the potential radius for different donor position by exact diagonalization method. The results have clearly demonstrated the so-called quantum size effect. The binding energy is dependent on the dot radius R, the impurity ion distance D, and the confining potential depth V₀.     

A holographic model of deconfinement and chiral symmetry restoration

We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L × U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4 + 1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1/2πR. For quark separations obeying L > L_c ? 0.97 ∗ R the chiral symmetry is restored at this temperature, but for L < L_c ? 0.97 ∗ R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T_χSB ? 0.154/L. All of these phase transitions are of first order.     

Non-empirical versus empirical choices for overlapping-sphere radii ratios in SCF-Xα-SW calculations on ClO4 - and SO2

Two non-empirical schemes for establishing ratios of atomic sphere radii for Xα-SW calculations are proposed and compared with known methods of partitioning molecules into atomic fragments along paths of maximum change in electrostatic potential or charge density. In the initial Xα-SW molecular charge distribution, the radius of a sphere around each atom containing the atomic number of electrons is shown to be constant within a few per cent no matter what atomic charges are assumed in constructing the charge distribution. This contrasts with the radius of a sphere containing the number of electrons put in for the atom in calculating its atomic charge density, which shows a significant inverse variation with the assumed charge. Ionization energies for ClO₄ ^- and SO₂ are calculated using ratios of sphere radii established both from the atomic number sphere sizes and from Slater's empirical atomic radii. The results are compared with experiment and with HF-LCAO calculations. The Xα-SW calculations using atomic number radii ratios are in the best overall agreement with experiment.     

Light scattering in a layer of correlatively arranged optically soft particles

The light scattering by an ensemble of monodisperse spatially correlated optically soft spherical particles is studied in the interference approximation. A model of the interaction of particles is proposed in which the spatial correlation between particles is determined by a radius R _c exceeding the particle radius R _p. The radial distribution function is calculated in the Percus-Yevick approximation for hard spheres of the radius R _c. To simulate the radiation scattering from an individual particle of the radius R _p, the Mie equations are used. It is shown that, in a medium of correlated small nonabsorbing particles of the radius R _c > R _p, an abnormal wavelength dependence of the refractive index is possible at a low volume concentration of particles. The results obtained explain some experimentally observed features of the scattering in sodium borosilicate glasses with a small concentration of scattering centers.     

Nuclear core dynamics and rearrangement energy for hypernuclei

The effect of the nuclear core dynamics on the binding energies of Λ hypernuclei is studied in the framework of variational correlated wave functions. In addition to the core energy and to a Λ single-particle contribution ϵ_ν, we exhibit a rearrangement energy E_R which in particular depends on the ΛN correlations F and on the difference δφ_N between the core wave function and its exact ground-state value. E_R is nonzero only if there are both ΛN correlations (F ≠ 1) and if δφ_N ≠ 0. The latter can result from core polarization by the Λ or from errors in the ground-state variational wave function of the core. E_R varies linearly with δφ_N for small δφ_N. Detailed numerical results for central ΛN and NN potentials with repulsive cores confirm these general features. For a give core wave function ΛN correlations reduce the radius of the core nucleons relative to their c.m.; however E_R leads to an expansion of the core rather than to a contraction with only ϵ_ν. The core polarization eneegy is quite small ⋍ 0.4 MeV. We study the effects of errors in the variational core wave function by detuning this as a function of one of the variational parameters.     

The anion and cation effects in the magnetic anisotropy of rare-earth compounds: Charge screening by conduction electrons

The formation of magnetic anisotropy (MA) in rare-earth compounds with transition metals has been analyzed. The screening of the charges creating the crystal field by conduction electrons has been shown to play an important role. The calculations took into account the Friedel charge-density oscillations. The model used for RCo₅ is the point-charge crystal field including nonuniform screening by conduction electrons with an anisotropic Fermi surface. The mechanisms of strong MA due to light-element impurities (hydrogen and nitrogen) are considered. The effective charge of an impurity can heavily depend on its ionic radius and the characteristics of the Fermi surface (in particular, on the Fermi momentum k _F ) of the screening electrons. The screening of the cation and anion charge in hydrides and nitrides based on the R₂Fe₁₇ and RFe₁₁Ti intermetallic compounds is discussed.     

Surface charge model of a carbon nanotube: self-consistent field from Thomas-Fermi theory

A model of a C nanotube is set up and solved self-consistently by numerical methods using the Thomas-Fermi statistical approach to treat the C 2s and 2p valence electrons. In the model presented here the C⁴⁺ ions are ‘smeared out’ uniformly over the surface of an infinitely long cylinder of radius R_t. Analytic forms of the self-consistent field are also presented far from the axis of the infinite tube, and well into its interior.     

Oscillator strength of electron-type color centers in KCl single crystals irradiated with electrons and protons

The absorption spectra of KCl single crystals irradiated with electrons and protons at energies of 15 and 100 keV and a particle flux ranging from 5×10¹² to 10¹⁵ cm^?2 are investigated. The absorption bands attributed to simple (F, F _a, K) and complex (M, R ₂, R ₄, N) color centers are identified in the spectra. The correlation dependences of the absorption coefficients for M, R ₂, and R ₄ centers on the absorption coefficient of F centers and the correlation dependences of the absorption coefficients for R ₂ and R ₄ centers on the absorption coefficient of M centers are established. The oscillator strengths are calculated for M, R ₂, and R ₄ color centers.