Many-body atomic potentials in Thomas-Fermi theory

Many-body atomic potentials, ?, are functions of the nuclear coordinates, and are defined by differences of ground state energies, E, e.g., ?(1, 2) ≡ E(1, 2) ? E(1) ? E(2). We prove that in Thomas-Fermi theory the n-body potential always has the sign (?1)ⁿ for all coordinates. We also prove that the remainder in the expansion of the total energy E in terms of the ?'s, when truncated at the n-body terms, has the sign (?1)ⁿ⁺¹.     

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative ?² correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of ?⁴ order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g., ²⁰⁸Pb turns out to be only ∼−6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.     

Thomas-Fermi potentials for quasimolecular collision processes

Effective electronic single particle potentials obtained by solving the Thomas-Fermi equation with two centre boundary conditions via the relaxation procedure are compared to the phenomenological variable screening potentials of Wille and Eichler. The scope of further investigations is outlined.     

Extended Thomas-Fermi theory at finite temperature

We present a generalization of the extended Thomas-Fermi (ETF) theory to finite temperatures T. Starting from the Wigner-Kirkwood expansion of the Bloch density in powers of , we derive the gradient expansion of the free energy and entropy density functionals $\text{F}$[ρ] and σ[ρ] up to fourth order with their correct temperature-dependent coefficients. (Effective mass and spin-orbit contributions are taken into account up to second order.) For a harmonic-oscillator potential we show that both the h-expansion of the free energy and the entropy and the gradient expansion of the functionals [ρ] and σ[ρ] converge very fast and yield the exact quantum-mechanical results for kT ? 3 MeV, where the shell effects are washed out. Finally we discuss the Euler variational equation obtained with the new functionals and use its numerical solutions for semi-infinite symmetric nuclear matter to test the quality of parametrized trial densities. As an application, we present liquid-drop model parameters, calculated with a realistic Skyrme interaction, as functions of the temperature.     

Some corrections to the Thomas-Fermi theory

In the presented model the wave function describing the electron is a superposition of contributions from individual components of the system, in the case of metals - lattice ions and in this sense refers not to a single electron, but rather to the system as a whole. An unconventional approach to the Schro¨dinger equation can provide a simple analytical relationship between the total energy of the electron and the wave number. This expression can directly determine the basic parameters such as Fermi radius, the screening radius or work function and also produce a graphical interpretation of the Fermi surface.     

Dynamical Thomas-Fermi theory for giant monopole resonances

Transition densities for giant monopole resonances of spherical nuclei are obtained from a linearized fluid dynamical approach. The same semiclassical energy functional is used to calculate self-consistently static and time dependent properties.     

Asymptotic exactness of finite temperature Thomas-Fermi theory

By using entropy inequalities with coherent states we prove that for atoms and molecules the partition function of Thomas-Fermi theory becomes exact in the limit Z → ∞, in the appropriate scaling. Furthermore the Gibbs state over a suitable algebra converges to a pure state over classical densities in phase space.     

Some remarks on the time-dependent Thomas-Fermi theory

We investigate the Thomas Fermi limit (?=0) of the density operator in phase space for a system of noninteracting fermions evolving from the ground state in a time dependent potential. The semiclassical calculations for model situations in one spatial dimension are compared with the solution of the time dependent Schrödinger equation. The role of time dependent invariants and the relation to the hydrodynamical formulation of quantum mechanics is pointed out.     

Hypervirial perturbation theory for eigenenergies for two types of atomic potentials

Eigenenergies are calculated for the potentialsV ₁(r)=−(a/r)[1+(1+br)e^−2br ] andV ₂(r)=−(v/r)[1 −λr(1−Z ⁻¹)(1+λr)⁻¹], using renormalized series technique. Accurate results produced here for various eigenstates agree with those available in the literature.     

Long range effect in ion-implanted GaAs

Abstract

New experimental data are presented which indicate the change of defect centers concentration in GaAs at macroscopic (up to millimeters) distances from the implanted regions edge. These data were obtained by locally exited cathodoluminescence, by observation of photoconductivity detected locally by contactless MW technique, by conductivity, DLTS and Raman spectroscopy measurement. Interpretation of the mechanism of long range effect is presented.     

Long range diffusion in ultrametric spaces

A model for diffusion in spaces with ultrametric topology is introduced. The parameters of the model are two sets of numbers: the branching numberm _l+1 /m _l describing the hierarchical structure of the metric and the transition ratesr _l between different levels of the hierarchy. This model is expected to be relevant to the spin glas problem. The exact solution of the dynamical problem can be given in the general case. In the special casem _l =m ^l andr _l R ^l anomalous long time behaviour of the autocorrelation function is found which decays with a power law multiplied by a periodically varying amplitude.Dedicated to B. Mühlschlegel on the occasion of his 60th birthdayThis work has been supported by the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Long range height variations in surface growth

This paper presents novel results obtained from numerical investigation of surfacesgenerated by the two-dimensional isotropic Kuramoto-Sivashinsky equation with anadditional nonlinear term and a single independent parameter. Surface roughness exhibits acertain dependence on the system size that indicates power-law shape of the surfacespectrum for small wave numbers. This leads to a conclusion that although cellular surfacepatterns of definite scale dominate in the range of short distances, there are alsoscale-free long-range height variations present in large systems. The dependence of thespectral exponent on the equation parameter gives new insight into the influence of theadditional term in the equation on the scaling behavior for large systems.     

Long range density correlations in disordered solids

Although the structure of a glass closely resembles that of a dense liquid over short length scales, its solidity implies that the two-particle distribution function is long range. In this paper the explicit form of this long range behaviour is derived in terms of the elastic constants of the glass and the relationship is shown between density fluctuations and the microscopic form of the displacement vector u(r). With minor modifications these results are valid also for a crystal. Several ramifications of these results are explored.     

Long range correlation in earthquake precursory signals

Research on earthquake prediction has drawn serious attention of the geophysicist, geologist and investigators in different fields of science across the globe for many decades. Researchers around the world are actively working on recording pre-earthquake changes in non-seismic parameters through a variety of methods that include anomalous changes in geochemical parameters of the Earth’s crust, geophysical properties of the lithosphere as well as ionosphere etc. Several works also have been done in India to detect earthquake precursor signals using geochemical and geophysical methods. However, very few works have been done so far in India in this field through the application of nonlinear techniques to the recorded geophysical and geochemical precursory signals for earthquakes. The present paper deals with a short review of the early works on geochemical precursors that have been carried out in India as yet. With a view to detect earthquake precursory signals by means of gas-geochemical method we developed a network of seismo-geochemical monitoring observatories in India in hot springs and mud volcano crater. In the last few years we detected several geochemical anomalies and those were observed prior to some major earthquakes that occurred within a radius of 1500?km from the test sites. In the present paper we have applied nonlinear techniques to the long term, real-time and natural data sets of radon-222 and associated gamma originated out of the terrestrial degassing process of the earth. The results reveal a clear signature of the long range correlation present in the geochemical time series. This approach appears to be a potential tool to explore intrinsic information hidden within the earthquake precursory signals.