Solitons and the delta function fermion gas in Hartree–Fock theory

1978 ◽  
Vol 19 (4) ◽  
pp. 860-868 ◽  
Author(s):  
Elliott H. Lieb ◽  
Manuel de Llano
Keyword(s):  
Delta Function ◽  
Hartree Fock ◽  
Fermion Gas

Hartree–Fock Alpha Cluster Density Distributions in Light A = 4n Nuclei Using Density Dependent Effective Interactions

1973 ◽  
Vol 51 (24) ◽  
pp. 2522-2549 ◽  
Author(s):  
K. R. Lassey ◽  
M. R. P. Manning ◽  
A. B. Volkov
Keyword(s):  
Delta Function ◽  
Skyrme Interaction ◽  
Effective Interactions ◽  
Density Dependent ◽  
Hartree Fock ◽  
Density Distributions ◽  
Cluster Density ◽  
The One ◽  
Alpha Cluster ◽  
Selection Of

Hartree–Fock calculations have been performed for the A = 4n nuclei 12C to 40Ca, employing a selection of density dependent effective interactions. This selection consists of two density and momentum dependent delta function interactions, similar to the Skyrme interaction, and two density and momentum dependent finite range interactions whose radial forms are given as a sum of two Gaussian functions. A basis of single-particle axially deformed harmonic oscillator functions is used. Special emphasis is given to the study of the occurrence of alpha-particle type clustering in the density distributions of light A = 4n nuclei and the influence of the strength of the one-body spin–orbit field.

A Lagrangian theory for nonlinear wave packets in a collisionless plasma

1972 ◽  
Vol 7 (2) ◽  
pp. 267-284 ◽  
Author(s):  
R. L. Dewar
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Collisionless Plasma ◽  
Delta Function ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Frequency ◽  
Nonlinear Schrödinger ◽  
Hartree Fock ◽  
Electrostatic Plasma Wave

A Lagrangian, for the slowly varying complex amplitude of an almost monochromatic electrostatic plasma wave in an unmagnetized plasma, is derived. The method is a variant of the averaged Lagrangian technique of Whitham, adapted for use in plasma physics by employing Low's Lagrangian, together with certain elimination procedures to simplify the Lagrangian to usable form. The expansion in powers of the wave amplitude is carried out to quartic terms, and non-adiabatic terms are also retained. Variations with respect to the amplitude lead to a nonlinear Schrödinger equation for the amplitude, while variations of the particle trajectories lead to a modified Vlasov equation, which includes the nonlinear reaction of the wave on the average trajectories. It is assumed that there are no resonant particles. These equations are coupled through the nonlinear frequency shift. It is found that the particle aspect of the plasma has a profound effect on the stability of the system, due to resonance of the wave envelope with particles moving at the group velocity. This effect, nonlinear Landau damping, is always destabilizing, leading to growth of modulations. In terms of the nonlinear Schrodinger equation, the effect changes the equation from a Hartree-Fock equation with a delta-function interaction to one with a non-momentum-conserving, non-local interaction. In the limit of fairly small wavelength, of the modulations, it is shown that the growth rate approaches that expected from plasma kinetic theory.

Low-density Hartree-Fock solutions for a one-dimensional gas with attractive delta-function interactions

1981 ◽  
Vol 23 (3) ◽  
pp. 1558-1560
Author(s):  
G. Gutiérrez ◽  
A. Plastino ◽  
G. Zannoli
Keyword(s):  
Delta Function ◽  
Low Density ◽  
One Dimensional ◽  
Hartree Fock

Study of charge transfer in FeTi

1983 ◽  
Vol 41 ◽  
pp. 296-297
Author(s):  
J. Taft∅
Keyword(s):  
Charge Transfer ◽  
Charge Distribution ◽  
Electron Scattering ◽  
Periodic System ◽  
Electron Distribution ◽  
Scattering Amplitude ◽  
Transition Elements ◽  
Hartree Fock ◽  
Cscl Structure ◽  
The Right

It is well known that for reflections corresponding to large interplanar spacings (i.e., sin θ/λ small), the electron scattering amplitude, f, is sensitive to the ionicity and to the charge distribution around the atoms. We have used this in order to obtain information about the charge distribution in FeTi, which is a candidate for storage of hydrogen. Our goal is to study the changes in electron distribution in the presence of hydrogen, and also the ionicity of hydrogen in metals, but so far our study has been limited to pure FeTi. FeTi has the CsCl structure and thus Fe and Ti scatter with a phase difference of π into the 100-ref lections. Because Fe (Z = 26) is higher in the periodic system than Ti (Z = 22), an immediate “guess” would be that Fe has a larger scattering amplitude than Ti. However, relativistic Hartree-Fock calculations show that the opposite is the case for the 100-reflection. An explanation for this may be sought in the stronger localization of the d-electrons of the first row transition elements when moving to the right in the periodic table. The tabulated difference between fTi (100) and ffe (100) is small, however, and based on the values of the scattering amplitude for isolated atoms, the kinematical intensity of the 100-reflection is only 5.10-4 of the intensity of the 200-reflection.

Single Atom Image Contrast in Fixed Beam Dark Field Electron Microscopy

1974 ◽  
Vol 32 ◽  
pp. 366-367
Author(s):  
Wah Chi
Keyword(s):  
Scattering Amplitude ◽  
Present Report ◽  
Dark Field ◽  
Image Contrast ◽  
Single Atom ◽  
Optical Theorem ◽  
Hartree Fock ◽  
Heavy Atoms ◽  
Beam Stop ◽  
Fixed Beam

Resolution and contrast are the important factors to determine the feasibility of imaging single heavy atoms on a thin substrate in an electron microscope. The present report compares the atom image characteristics in different modes of fixed beam dark field microscopy including the ideal beam stop (IBS), a wire beam stop (WBS), tilted illumination (Tl) and a displaced aperture (DA). Image contrast between one Hg and a column of linearly aligned carbon atoms (representing the substrate), are also discussed. The assumptions in the present calculations are perfectly coherent illumination, atom object is represented by spherically symmetric potential derived from Relativistic Hartree Fock Slater wave functions, phase grating approximation is used to evaluate the complex scattering amplitude, inelastic scattering is ignored, phase distortion is solely due to defocus and spherical abberation, and total elastic scattering cross section is evaluated by the Optical Theorem. The atom image intensities are presented in a Z-modulation display, and the details of calculation are described elsewhere.

Spatially Resolved Photoelectron Spectroscopy: Recent Progress and Future Plans

1990 ◽  
Vol 48 (2) ◽  
pp. 388-389
Author(s):  
A. M. Bradshaw
Keyword(s):  
Photoelectron Spectroscopy ◽  
Chemical Reactivity ◽  
Target Material ◽  
Orbital Energy ◽  
Light Sources ◽  
Analytical Technique ◽  
Hartree Fock ◽  
Spatially Resolved ◽  
Koopmans Theorem ◽  
Surface Analytical Technique

X-ray photoelectron spectroscopy (XPS or ESCA) was not developed by Siegbahn and co-workers as a surface analytical technique, but rather as a general probe of electronic structure and chemical reactivity. The method is based on the phenomenon of photoionisation: The absorption of monochromatic radiation in the target material (free atoms, molecules, solids or liquids) causes electrons to be injected into the vacuum continuum. Pseudo-monochromatic laboratory light sources (e.g. AlKα) have mostly been used hitherto for this excitation; in recent years synchrotron radiation has become increasingly important. A kinetic energy analysis of the so-called photoelectrons gives rise to a spectrum which consists of a series of lines corresponding to each discrete core and valence level of the system. The measured binding energy, EB, given by EB = hv−EK, where EK is the kineticenergy relative to the vacuum level, may be equated with the orbital energy derived from a Hartree-Fock SCF calculation of the system under consideration (Koopmans theorem).

EELS white line intensities calculated for the 3d and 4d metals

1989 ◽  
Vol 47 ◽  
pp. 388-389
Author(s):  
C. C. Ahn ◽  
D. H. Pearson ◽  
P. Rez ◽  
B. Fultz
Keyword(s):  
Experimental Data ◽  
Line Intensity ◽  
Transition Probabilities ◽  
Initial Increase ◽  
White Line ◽  
Hartree Fock ◽  
Line Intensities ◽  
Integrated Intensity ◽  
X Ray Absorption ◽  
The Continuum

Previous experimental measurements of the total white line intensities from L2,3 energy loss spectra of 3d transition metals reported a linear dependence of the white line intensity on 3d occupancy. These results are inconsistent, however, with behavior inferred from relativistic one electron Dirac-Fock calculations, which show an initial increase followed by a decrease of total white line intensity across the 3d series. This inconsistency with experimental data is especially puzzling in light of work by Thole, et al., which successfully calculates x-ray absorption spectra of the lanthanide M4,5 white lines by employing a less rigorous Hartree-Fock calculation with relativistic corrections based on the work of Cowan. When restricted to transitions allowed by dipole selection rules, the calculated spectra of the lanthanide M4,5 white lines show a decreasing intensity as a function of Z that was consistent with the available experimental data.Here we report the results of Dirac-Fock calculations of the L2,3 white lines of the 3d and 4d elements, and compare the results to the experimental work of Pearson et al. In a previous study, similar calculations helped to account for the non-statistical behavior of L3/L2 ratios of the 3d metals. We assumed that all metals had a single 4s electron. Because these calculations provide absolute transition probabilities, to compare the calculated white line intensities to the experimental data, we normalized the calculated intensities to the intensity of the continuum above the L3 edges. The continuum intensity was obtained by Hartree-Slater calculations, and the normalization factor for the white line intensities was the integrated intensity in an energy window of fixed width and position above the L3 edge of each element.

A first-principles Hartree-Fock description of MnO at high pressures

1998 ◽  
Vol 77 (4) ◽  
pp. 1063-1075
Author(s):  
W. C. Mackrodt, E.-A. Williamson, D. W
Keyword(s):  
First Principles ◽  
High Pressures ◽  
Hartree Fock
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