Nonlocal Model Potential Research Articles

Shear viscosities of liquid sodium and potassium using Green-Kubo and “first principles” pseudopotential formalisms

This article presents an original work on velocity and stress autocorrelation functions, memory functions, spectral densities and atomic transport properties of two liquid alkali metals (sodium and potassium). For this, we carried out molecular dynamics (MD) simulations using Green-Kubo relation under the condition of very long-time duration to obtain reliable and accurate results.An originality of the present work is that the interatomic forces are described by pair potentials built within the “first principles” pseudopotential formalism using the non-local and energy dependent model potential of Shaw. It is completely free of adjustable parameters since the energy dependent parameters are determined self-consistently at the Fermi energy on an absolute energy scale. The Green-Kubo relationship is the main theoretical tool that allows us determining the atomic transport coefficients from appropriate time-autocorrelation functions. An important new result concerns the memory function. We demonstrate, for the first time to our knowledge, that it can be depicted as a sum of wavelets. The wavelets with their amazing features emphasize the nature of dynamic processes at the microscopic level. We also compared, for the first time to our knowledge, the spectral density associated to the velocity autocorrelation function (VACF), to experimental values obtained by incoherent inelastic neutron scattering. Finally, the temperature dependence of the self-diffusion coefficient (our previous study) and that of shear viscosity (present work) are both in excellent agreement with experiment.

Systematic nonlocal optical model potential for nucleons

Based on the Perey–Buck nonlocal optical model potential, F. Perey and B. Buck, Nucl. Phys. 32 (1962) 353, we obtain a new set of nonlocal optical model potential (NLOMP) parameters for proton and neutron scattering off nuclei. The experimental angular distributions of nucleon scattering off nuclei ranging from 27 Al to 208 Pb with incident energies around 10 MeV to 30 MeV are adopted in the fitting procedures. This NLOMP is energy independent. The chi-squares χ2 obtained in the fittings are comparable to those from the KD03 phenomenological local optical model potentials (OMP) A. Koning and J. Delaroche, Nucl. Phys. A 713 (2003) 231. Good agreement is found in comparisons between optical model calculations using this NLOMP and KD03 in their reproduction to the experimental angular distributions of elastic scattering cross-sections and analyzing powers.

The linear dependence of the term energy on quantum defects in ions with completely filled electron shells and its application for calculating parameters of the smooth nonlocal model potential

The energy levels of the valence electrons of free ions with completely filled electron shells are analyzed. A linear correlation between term energies E nl and quantum defects dn nl is assumed to exist at constant values of orbital quantum numbers and ion charges for the Li, Na, Cu, Ag, and Au rows. The empirical dependence of quantum defects dn nl on the principle quantum number n is found. It can be used to estimate unknown term energies. It is also demonstrated that the linear dependences of the smooth nonlocal model pseudopotential parameter A nl of free ions on the term energy E nl is the result of their linear dependences on quantum defects dn nl .

Phonon spectra of magnesium in the method of nonlocal smooth model potential

An expression for the characteristic function of a nonlocal smooth model potential of an elementary metal is obtained in terms of the full nonlocal theory. The magnesium phonon spectra calculated using the expressions for a characteristic function agree satisfactorily with the experimental data.

Calculation of the contribution of conduction electrons to the atomic factors of simple metals

An expression for the Fourier transform of the screening electron density of simple metals has been derived using smooth nonlocal model potentials of simple metals. The expression describes the contribution of conduction electrons to the atomic factors of X-ray scattering in simple metals. Aluminum was used as an example for numerical checking. Comparison with the results of similar calculations for the form factor of the Krasko-Gurskii model potential shows the importance of taking the nonlocality of the model potential into account.

A nonlocal smooth model potential of elementary metals: Computation of the form factor

In terms of the full nonlocal theory, an expression for the form factor of a smooth nonlocal model potential in an elementary metal is computed.

Temperature variation of electric field gradient in α-gallium metal

Electronic contributions to electric field gradient (EFG) in α-Ga metal as a function of temperature are calculated for the first time by using a temperature-dependent non-local model potential. The ionic contributions, evaluated in point-ion approximation, are taken from the work of Valic and Williams. The sign of the net calculated EFG as well as the decreasing trend in its magnitude with increase of temperature are in agreement with experiment. There are, however, quantitative differences between theory and experiment with regard to EFG parameters. Possible reasons for these discrepancies are discussed.

Room temperature Compton profiles of conduction electrons in α-Ga metal

Room temperature Compton profiles of momentum distribution of conduction electrons in α -Ga metal are calculated in band model. For this purpose, the conduction electron wave functions are determined in a temperature-dependent non-local model potential. The profiles calculated along the crystallographic directions, (100), (010), and (001) are found to be nearly isotropic. This conclusion is in reasonable agreement with experimental observations

Positronium scattering by atoms and molecules at low energies

The recent theoretical and experimental activities in positronium (Ps) scattering by atoms and molecules are reviewed with special emphasis at low energies. We critically compare the results of different groups – theoretical and experimental. The theoretical approaches considered include the R-matrix and close-coupling methods applied to Ps–H, Ps–He and Ps–Li scattering, and a coupled-channel approach with a nonlocal model potential for Ps scattering by H, He, H 2, Ne, Ar, Li, Na, K, Rb, Cs and Ps and for pickoff quenching in Ps–He scattering. Results for scattering lengths, partial, total and differential cross-sections as well as resonance and binding energies in different systems are discussed.

Thermodynamics and Structure of Liquid Metals from a New Consistent Optimized Random Phase Approximation

Abstract We study thermodynamics and structural properties of several liquid metals to assess the validity of the generalized non-local model potential (GNMP) of Li et al. [J. Phys. F16, 309 (1986)]. By using a new thermodynamically consistent version of the optimized random phase approx­ imation (ORPA), especially adapted to continuous reference potentials, we improve our previous results obtained within the variational approach based on the Gibbs -Bogoliubov inequality. Hinging on the unified and very accurate evaluation of structure factors and thermodynamic quantities provided by the ORPA, we find that the GNMP yields satisfactory results for the alkali metals. Those for the polyvalent metals, however, point to a substantial inadequacy of the GNMP for high valence systems.

Positronium atom scattering by H2 in a coupled-channel framework

The scattering of ortho-positronium (Ps) by H2 has been investigated using a three-Ps-state (Ps(1s, 2s, 2p)H2(X 1g+)) coupled-channel model and using the Born approximation for higher excitations and ionization of Ps and B 1u+ and b 3u+ excitations of H2. We employ a recently proposed time-reversal-symmetric non-local electron-exchange model potential. We present a calculational scheme for solving the body-frame fixed-nuclei coupled-channel scattering equations for Ps-H2, which simplifies the numerical solution technique considerably. Ps ionization is found to have the leading contribution to target-elastic and all target-inelastic processes. The total cross sections at low and medium energies are in good agreement with experiment.

Scattering of positronium by H, He, Ne, and Ar

The low-energy scattering of the ortho-positronium (Ps) by H, He, Ne, and Ar atoms has been investigated in the coupled-channel framework by using a recently proposed time-reversal symmetric non-local electron-exchange model potential with a single parameter C. For H and He, we use a three-Ps-state coupled-channel model and, for Ar and Ne, we use a static-exchange model. The sensitivity of the results is studied with respect to the parameter C. Present low-energy cross-sections for He, Ne and Ar are in good agreement with experiment.

Thermodynamics and pair structures of liquid alkali and alkaline-earth metals from the perturbative hypernetted-chain equation

We have theoretically studied liquid alkali and alkaline-earth metals by combining the second-order pseudopotential (PP) theory of ion-electron interaction and a statistical mechanical method for calculating ionic thermal motion. The latter is done by utilizing the perturbative hypernetted-chain equation recently proposed by the author. The PP is modelled through an ab initio method presented by Shaw, i.e., through the use of the optimized nonlocal model potential (OMP). Calculations are carried out with two different methods for extracting parameters in the OMP. They are due to Animalu and Heine (AH), and Ballentine and Gupta (BG). Results show that both of thermodynamic properties and pair structures are in good agreements with experimental data for alkali metals with the AH set of parameters. For alkaline-earth metals other than Ba, calculations with the BG set give the radial distributions and structure factors in good agreement with experimental data.

Electron exchange model potential: Application to positronium-helium scattering

The formulation of a suitable nonlocal model potential for electron exchange is presented, checked with electron-hydrogen and electron-helium scattering, and applied to the study of elastic and inelastic scattering and ionization of ortho positronium (Ps) by helium. The elastic scattering and the $n = 2$ excitations of Ps are investigated using a three-Ps-state close-coupling approximation. The higher ($n\ge 3$) excitations and ionization of Ps atom are treated in the framework of Born approximation with present exchange. Calculations are reported of phase shifts, and elastic, Ps-excitation, and total cross sections. The present target elastic total cross section agrees well with experimental results at thermal to medium energies.

Nonlocal pseudopotential calculation for the electron-ion correlation in liquid metals

A full nonlocal model potential is employed to calculate the screened electron charge density n(q) and to construct the interatomic pair potential, which is then used in the modified hypernetted-chain integral equation to determine the ion-ion static structure factor Sii(q). These two basic quantities are subsequently used as input data for the calculation of the electron-ion correlation. For the simple liquid metals Na, Mg, and Al, our calculated electron-ion structure factors Sei(q) agree very well with the positions of extrema of the experimental or computer-simulated Sei(q). Quantitative analysis of the two main contributions, n (q) and Sii(q), shows that Sei(q) obtained in a full nonlocal pseudopotential theory is in general different from that in the local pseudopotential theory. Such disparities in the two theoretical frameworks arise from the nonlocality of electron-ion pseudopotential, which, for a quantitative study, should be incorporated in the theory especially when one is treating the correlations of electrons and ions on an equal footing. At the level of achievement attained in this work, there is now a greater hope of understanding the electron-ion correlations if experimental errors for Sei(q) are considerably reduced. @S1063-651X~98!09208-3#

Effect of electron exchange in positronium-hydrogen scattering

The elastic and inelastic scattering of ortho-positronium (Ps) by the hydrogen atom have been investigated using a three-Ps-state close-coupling approximation. The higher excitations and ionization of the Ps atom are treated within the framework of the Born approximation. In both cases the effect of electron exchange has been included by a parameter-free nonlocal model potential derived from an antisymmetrization of the wavefunction followed by the removal of nonorthogonality. Calculations are reported of scattering lengths, phase shifts, and of elastic, Ps excitation, and total cross sections. The trend of present target elastic total cross section agrees qualitatively with available experimental results on Ps-impact scattering.

Structure of the liquid–vapor interface of a metal from a simple model potential: Corresponding states of the alkali metals

We present the results of self-consistent quantum Monte Carlo simulations of the structures of the liquid-vapor interfaces of alkali metals (Na, K, Rb, Cs) using a modified semiempirical empty-core model potential. The purpose of this investigation is to simplify the analysis of inhomogeneous metals sufficiently to permit qualitative inferences to be drawn about the properties of families of metals. Both electronic and ion density profiles along the normal to the surface show oscillations in the liquid–vapor transition zone. These oscillations closely resemble those found in previous simulation studies of the liquid–vapor interfaces of alkalis, based on sophisticated nonlocal model potentials. Because of its semianalytical representation, the model potential used in this paper allows considerable simplification in the computational scheme relative to the effort involved in the previously published simulations. We find liquid Na, K, Rb, and Cs to exhibit similar surface layering. Moreover, our results suggest the existence of a corresponding states representation of the properties of this class of metals. We expect this new analysis will be useful in predicting the qualitative properties of the surface structures of a broad range of pure liquid metals.

Taking into account of spin-orbit coupling during calculation of formfactors of nonlocal model potential

Taking into account of spin-orbit coupling during calculation of formfactors of nonlocal model potential

Description of proton elastic scattering on 6,7,9,11Li with microscopic effective interaction.

Proton elastic scattering on Li isotopes $^{6,7,9,11}\mathrm{Li}$ at ${\mathit{E}}_{\mathit{p}}$\ensuremath{\sim}60 MeV is described by a nonlocal optical model potential which is constructed by folding a microscopic density-dependent effective interaction with Hartree-Fock single-particle wave functions of the target nuclei. Experimental data are well-described systematically from $^{6}\mathrm{Li}$ to $^{11}\mathrm{Li}$ by our model calculation, implying that the underlying microscopic theory is applicable even at the extreme circumstance of the neutron drip line limit.

Electric field gradient in transition metal — scandium

Electric field gradient inhcp transition metal scandium has been calculated as the sum of contributions from lattice ions and conduction electrons. For the lattice contributionqlatt, a point-charge model has been assumed. The contribution from conduction electronsqel, on the other hand, has been evaluated by carrying out an energy-band calculation using non-local transition-metal model potential. The results obtained are:qel=−106.11×1013 esu/cm3 andqlatt=122.17×1013 esu/cm3. The net field gradient (qel+qlatt) of 16.06×1013 esu/cm3 agrees quite well with the experimental result, |qexpt|=13×1013 esu/cm3. Directions of further improvement in the theory are discussed.