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Electronic Correlation Mapping: From Finite to Extended Systems

Electronic Correlation Mapping: From Finite to Extended Systems

Jamal Berakdar

ISBN: 978-3-527-61852-1

Dec 2007

205 pages

Select type: O-Book


An up-to-date selection of applications of correlation spectroscopy, in particular as far as the mapping of properties of correlated many-body systems is concerned.
The book starts with a qualitative analysis of the outcome of the two-particle correlation spectroscopy of localized and delocalized electronic systems as they occur in atoms and solids. The second chapter addresses how spin-dependent interactions can be imaged by means of correlation spectroscopy, both in spin-polarized and extended systems. A further chapter discusses possible pathways for the production of interacting two-particle continuum states.
After presenting some established ways of quantifying electronic correlations and pointing out the relationship to correlation spectroscopy, the author addresses in a separate chapter the electron-electron interaction in extended systems, and illustrates the ideas by some applications to fullerenes and metal clusters. The last two chapters are devoted to the investigation of the potential of two-particle spectroscopy in studying ordered surfaces and disordered samples.

Throughout the book the material is analyzed using rather qualitative arguments, and the results of more sophisticated theories serve the purpose of endorsing the suggested physical scenarios. The foundations of some of these theories have been presented in a corresponding volume entitled "Concepts of Highly Excited Electronic Systems" (3-527-40335-3).
1 Qualitative and General Features of Electron–Electron Scattering.

1.1 Mapping Momentum-distribution Functions.

1.2 Role of Momentum Transfer during Electron–Electron Scattering.

1.3 Approximate Formula for the Electron–Electron Ionization Cross Section.

1.3.1 Example: An Atomic Target.

1.3.2 Electron–Electron Cross Section for Scattering from Condensed Matter.

1.3.3 Electron Scattering Cross Section from Ordered Materials.

1.3.4 Initial- vs. Final-state Interactions.

1.4 Averaged Electron–Electron Scattering Probabilities.

1.4.1 Integrated Cross Section for Strongly Localized States.

1.4.2 Low-energy Regime.

1.5 Electron–Electron Scattering in an Extended System.

2 Spin-effects on the Correlated Two-electron Continuum.

2.1 Generalities on the Spin-resolved Two-electron Emission.

2.2 Formal Symmetry Analysis.

2.3 Parametrization of the Spin-resolved Cross Sections.

2.4 Exchange-induced Spin Asymmetry.

2.5 Physical Interpretation of the Exchange-induced Spin Asymmetry.

2.6 Spin Asymmetry in Correlated Two-electron Emission from Surfaces.

2.7 General Properties of the Spin Asymmetry.

2.7.1 Spin Asymmetry in Pair Emission from Bulk Matter.

2.7.2 Spin-polarized Homogenous Electron Gas.

2.7.3 Behavior of the Exchange-induced Spin Asymmetry in Scattering from AtomicSystems.

2.7.4 Threshold Behavior of  the Spin Asymmetry.

3 Mechanisms of Correlated Electron Emission.

3.1 Exterior Complex Scaling.

3.2 The Convergent Close Coupling Method.

3.3 Analytical Models.

3.3.1 Dynamical Screening.

3.3.2 Influence of the Density of Final States.

3.4 Analysis of the Measured Angular Distributions.

3.4.1 The Intermediate Energy Regime.

3.5 Characteristics of the Correlated Pair Emissionat Low Energies.

3.5.1 Influence of the Exchange Interaction on the Angular Pair Correlation.

3.6 Threshold Behavior of the Energy and the Angular Pair Correlation.

3.6.1 Generalities of Threshold Pair Emission.

3.6.2 Threshold Pair Emission from a Coulomb Potential.

3.6.3 Regularities of the Measured Pair Correlation at Low Energies.

3.6.4 Role of Final-state Interactions in Low-energy Correlated Pair Emission.

3.6.5 Interpretation of Near-threshold Experiments.

3.7 Remarks on the Mechanisms of Electron-pair Emission from Atomic Systems.

4 Electron–electron Interaction in Extended Systems.

4.1 Exchange and Correlation Hole.

4.2 Pair-correlation Function.

4.2.1 Effect of Exchange on the Two-particle Probability Density.

4.3 Momentum-space Pair Density and Two-particle Spectroscopy.

4.3.1 The S Matrix Elements.

4.3.2 Transition Probabilities and Cross Sections.

4.3.3 Two-particle Emission and the Pair-correlation Function.

5 The Electron–Electron Interaction in Large Molecules and Clusters.

5.1 Retardation and Nonlocality of the Electron–Electron Interaction in Extended Systems.

5.2 Electron Emission from Fullerenes and Clusters.

5.2.1 The Spherical Jellium Model.

5.2.2 Angular Pair Correlation.

5.2.3 Total Cross Sections.

5.2.4 Finite-size Effects.

5.2.5 Influence of Exchange.

6 Pair Emission from Solids at Surfaces.

6.1 Qualitative Analysis.

6.1.1 Model Crystal Potential.

6.1.2 Scattering from the Surface Potential.

6.1.3 Qualitative Features of Interacting Two-particle Emission from Surfaces.

6.1.4 Explicit Results for Two-particle Scattering from Metal Surfaces.

6.2 Mechanisms of Correlated Electron Emission.

6.2.1 Angular Pair Correlation.

6.2.2 Energy Pair Correlation.

6.2.3 Influence of Exchange on the Energy Pair Correlation.

6.2.4 Pair Diffraction.

6.3 Role of the Dynamical Collective Nature of the Two-particle Interaction.

6.4 Quantitative Description of Pair Emission from Surfaces.

6.4.1 Treating Strong Two-particle Correlations.

6.4.2 Relativistic Layer KKR Method.

6.4.3 Two-particle Energy Correlation in the Pair Emission from Tungsten.

6.4.4 Angular Pair Correlation: Role of the Electron–Electron Interaction.

7 Pair Emission from Alloys.

7.1 Correlated Two-particle Scattering from Binary Substitutional Alloys.

7.1.1 Pair Emission from Alloys in Transmission Mode.

7.1.2 Pair Emission in Reflection Mode.

7.1.3 Scattering Potential from Binary Alloys.

7.1.4 Electronic States and Disorder Averaged Spectral Functions.

7.2 Incorporation of Damping of the Electronic States.

7.3 Configurationally Averaged Cross Section.

7.3.1 Analytical Model for Configurationally Averaged Cross Section.

7.4 Numerical Results and Illustrations.

Color Figures.


A Electronic States in a Periodic Potential.

B ScreeningWithin Linear Response Theory.

B.1 KuboFormalism.

B.2 Density–density Correlation Functions.

C Lindhard Function.

C.1 Thomas–Fermi Approximation.

C.2 Friedel Oscillations.

C.3 Plasmon Excitations.

D Dynamic Structure Factor and the Pair-distribution Function.

D.1 Excitation Processes and the Dynamical Structure Factor.

D.2 Properties of the Pair-distribution Function .