Ionization energies of beryllium in strong magnetic fields: a frozen core approximation

An effective frozen core approximation has been developed and applied to the calculation of energy levels and ionization energies of the beryllium atom in magnetic field strengths up to 2.35 x 10(5) T. Systematic improvement over the existing results for the beryllium ground and low-lying states has been accomplished by taking into account most of the correlation effects in the four-electron system. To our knowledge, this is the first calculation of the electronic properties of the beryllium atom in a strong magnetic field carried out using a configuration interaction approximation and thus allowing a treatment beyond that of Hartree-Fock. Differing roles played by strong magnetic fields in intrashell correlation within different states are observed. In addition, possible ways to gain further improvement in the energies of the states of interest are proposed and discussed briefly.

Multi-state CDW approximation to electron capture during slow p-H collisions

The first complete multi-state CDW close coupling calculations which use a fully normalized basis set are performed. The results obtained at impact energies in the region of 10 keV for total and n = 2 capture cross sections are in reasonably good accord with experiment despite the fact that only the ground states of both species and the n = 2 states of the projectile are incorporated into the model. The theory has significant advantages over other atomic and molecular expansions which may require extensive bases to obtain similar accuracy.

Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

Thin Ta films: growth, stability, and diffusion studied by molecular-dynamics simulations

We report results of classical molecular-dynamics simulations of bcc and beta-Ta thin films. Thermal PVD film growth, surface roughness, argon ion bombardment, phase stability and transformation, vacancy and adatom diffusion, and thermal relaxation kinetics are discussed. Distinct differences between the two structures are observed, including a complex vacancy diffusion mechanism in beta-Ta. Embedded atom method potentials, which were fitted to bcc properties, have been used to model the Ta-Ta interactions. In order to verify the application of these potentials to the more complex beta-Ta structure, we have also performed density functional theory calculations. Results and implications of these calculations are discussed.

Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

Extraction of electrode kinetic parameters from microdisc voltammetric data measured under transport conditions intermediate between steady-state convergent and transient linear diffusion as typically applies to room temperature ionic liquids

The extraction of electrode kinetic parameters for electrochemical couples in room-temperature ionic liquids (RTILs) is currently an area of considerable interest. Electrochemists typically measure electrode kinetics in the limits of either transient planar or steady-state convergent diffusion for which the voltammetic response is well understood. In this paper we develop a general method allowing the extraction of this kinetic data in the region where the diffusion is intermediate between the planar and convergent limits, such as is often encountered in RTILs using microelectrode voltammetry. A general working surface is derived, allowing the inference of Butler-Volmer standard electrochemical rate constants for the peak-to-peak potential separation in a cyclic voltammogram as a function of voltage scan rate. The method is applied to the case of the ferrocene/ferrocenium couple in [C(2)mim][N(Tf)(2)] and [C(4)mim][N(Tf)(2)].

A comparative electrochemical study of diffusion in room temperature ionic liquid solvents versus acetonitrile

Measurements on the diffusion coefficient of the neutral molecule N,N,N',N'-tetramethyl-para-phenylenediamine and the radical cation and dication generated by its one- and two-electron oxidation, respectively, are reported over the range 298-348 K in both acetonitrile and four room temperature ionic liquids (RTILs). Data were collected using single and double potential step chronamperometry at a gold disk electrode of micrometer dimension, and analysed via fitting to the appropriate analytical expression or, where necessary, to simulation. The variation of diffusion coefficient with temperature was found to occur in an Arrhenius-type manner for all combinations of solute and solvent. For a given ionic liquid, the diffusional activation energies of each species were not only closely equivalent to each other, but also to the RTIL's activation energy of viscous flow. In acetonitrile supported with 0.1 M tetrabutylammonium perchlorate, the ratio in diffusion coefficients of the radial cation and dication tot he neutral molecule were calculated as 0.89 +/- 0.05 and 0.51 +/- 0.03, respectively. In contrast, amongst the ionic liquids the same ratios were determined to be on average 0.53 +/- 0.04 and 0.33 +/- 0.03. The consequences of this dissimilarity are considered in terms of the modelling of voltammetric data gathered within ionic liquid solvents.