Electronic correlation mapping: from finite to extended systems
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Weinheim
Wiley-VCH
2006
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 173 - 185 |
| Physical Description: | XIII, 192 S. graph. Darst. |
| ISBN: | 3527403507 3527404120 9783527403509 |
Staff View
MARC
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| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2006 | |
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| adam_text | Contents
1 Qualitative and General Features
of Electron-Electron Scattering
1
1.1
Mapping Momentum-distribution Functions
.................. 1
1.2
Role of Momentum Transfer during Electron-Electron Scattering
....... 5
1.3
Approximate Formula for the Electron-Electron Ionization Cross Section
. . 8
1.3.1
Example: An Atomic Target
...................... 11
1.3.2
Electron-Electron Cross Section for Scattering from Condensed Matter
13
1.3.3
Electron Scattering Cross Section from Ordered Materials
...... 14
1.3.4
Initial-vs. Final-state Interactions
................... 15
1.4
Averaged Electron-Electron Scattering Probabilities
.............. 15
1.4.1
Integrated Cross Section for Strongly Localized States
........ 16
1.4.2
Low-energy Regime
.......................... 19
1.5
Electron-Electron Scattering in an Extended System
............. 19
2
Spin-effects on the Correlated Two-electron Continuum
23
2.1
Generalities on the Spin-resolved Two-electron Emission
........... 24
2.2
Formal Symmetry Analysis
........................... 27
2.3
Parametrization of the Spin-resolved Cross Sections
.............. 29
2.4
Exchange-induced Spin Asymmetry
...................... 30
2.5
Physical Interpretation of the Exchange-induced Spin Asymmetry
...... 32
2.6
Spin Asymmetry in Correlated Two-electron Emission from Surfaces
.... 33
2.7
General Properties of the Spin Asymmetry
................... 35
2.7.1
Spin Asymmetry in Pair Emission from Bulk Matter
......... 36
2.7.2
Spin-polarized Homogenous Electron Gas
............... 37
VIII Contents
2.7.3
Behavior of the Exchange-induced Spin Asymmetry in Scattering from
Atomic Systems
............................ 37
2.7.4
Threshold Behavior of the Spin Asymmetry
.............. 39
3
Mechanisms of Correlated Electron Emission
43
3.1
Exterior Complex Scaling
............................ 44
3.2
The Convergent Close Coupling Method
.................... 45
3.3
Analytical Models
................................ 46
3.3.1
Dynamical Screening
.......................... 47
3.3.2
Influence of the Density of Final States
................ 48
3.4
Analysis of the Measured Angular Distributions
................ 51
3.4.1
The Intermediate Energy Regime
................... 51
3.5
Characteristics of the Correlated Pair Emission at Low Energies
....... 53
3.5.1
Influence of the Exchange Interaction on the Angular Pair Correlation
55
3.6
Threshold Behavior of the Energy and the Angular Pair Correlation
..... 57
3.6.1
Generalities of Threshold Pair Emission
................ 57
3.6.2
Threshold Pair Emission from a Coulomb Potential
.......... 59
3.6.3
Regularities of the Measured Pair Correlation at Low Energies
.... 60
3.6.4
Role of Final-state Interactions in Low-energy Correlated Pair
Emission
................................ 62
3.6.5
Interpretation of Near-threshold Experiments
............. 63
3.7
Remarks on the Mechanisms of Electron-pair Emission from Atomic Systems
70
4
Electron-electron Interaction in Extended Systems
73
4.1
Exchange and Correlation Hole
......................... 74
4.2
Pair-correlation Function
............................ 76
4.2.1
Effect of Exchange on the Two-particle Probability Density
..... 78
4.3
Momentum-space Pair Density and Two-particle Spectroscopy
........ 79
4.3.1
The
S
Matrix Elements
......................... 79
4.3.2
Transition Probabilities and Cross Sections
.............. 81
4.3.3
Two-particle Emission and the Pair-correlation Function
....... 82
Contents
IX
5
The Electron-Electron Interaction in Large Molecules and Clusters
85
5.1
Retardation and Nonlocality of the Electron-Electron Interaction in Extended
Systems
..................................... 86
5.2
Electron Emission from
Fullerenes
and Clusters
................ 90
5.2.1
The Spherical Jellium Model
...................... 91
5.2.2
Angular Pair Correlation
........................ 92
5.2.3
Total Cross Sections
.......................... 95
5.2.4
Finite-size Effects
........................... 96
5.2.5
Influence of Exchange
......................... 97
6
Pair Emission from Solids at Surfaces
101
6.1
Qualitative Analysis
............................... 102
6.1.1
Model Crystal Potential
........................ 103
6.1.2
Scattering from the Surface Potential
................. 105
6.1.3
Qualitative Features of Interacting Two-particle Emission from
Surfaces
................................. 106
6.1.4
Explicit Results for Two-particle Scattering from Metal Surfaces
. . . 107
6.2
Mechanisms of Correlated Electron Emission
.................
Ill
6.2.1
Angular Pair Correlation
........................
Ill
6.2.2
Energy Pair Correlation
........................ 114
6.2.3
Influence of Exchange on the Energy Pair Correlation
......... 117
6.2.4
Pair Diffraction
............................. 120
6.3
Role of the Dynamical Collective Nature of the Two-particle Interaction
... 123
6.4
Quantitative Description of Pair Emission from Surfaces
........... 126
6.4.1
Treating Strong Two-particle Correlations
............... 127
6.4.2
Relativistic Layer KKR Method
.................... 130
6.4.3
Two-particle Energy Correlation in the Pair Emission from Tungsten
. 132
6.4.4
Angular Pair Correlation: Role of the Electron-Electron Interaction
. 133
7
Pair Emission from Alloys
135
7.1
Correlated Two-particle Scattering from Binary Substitutional Alloys
.... 136
7.1.1
Pair Emission from Alloys in Transmission Mode
........... 136
χ
Contents
ΊΑ.
2
Pair
Emission
in Reflection Mode
................... 137
7.1.3
Scattering
Potential
from Binary Alloys
................ 138
7.1.4
Electronic States and Disorder Averaged Spectral Functions
..... 139
7.2
Incorporation of Damping of the Electronic States
............... 140
7.3
Configurationally Averaged Cross Section
................... 142
7.3.1
Analytical Model for Configurationally Averaged Cross Section
. . . 144
7.4
Numerical Results and Illustrations
....................... 146
Color Figures
149
Appendices
A Electronic States in a Periodic Potential
155
В
Screening Within Linear Response Theory
159
B.I
Kubo
Formalism
................................ 159
B.2 Density-density Correlation Functions
..................... 160
С
Lindhard Function
163
C.I Thomas-Fermi Approximation
......................... 164
C.2 Friedel Oscillations
............................... 165
C.3 Plasmon Excitations
............................... 165
D
Dynamic Structure Factor and the Pair-distribution Function
167
D.I Excitation Processes and the Dynamical Structure Factor
........... 169
D.2 Properties of the Pair-distribution Function
................... 171
References
173
Index
187
|
| adam_txt |
Contents
1 Qualitative and General Features
of Electron-Electron Scattering
1
1.1
Mapping Momentum-distribution Functions
. 1
1.2
Role of Momentum Transfer during Electron-Electron Scattering
. 5
1.3
Approximate Formula for the Electron-Electron Ionization Cross Section
. . 8
1.3.1
Example: An Atomic Target
. 11
1.3.2
Electron-Electron Cross Section for Scattering from Condensed Matter
13
1.3.3
Electron Scattering Cross Section from Ordered Materials
. 14
1.3.4
Initial-vs. Final-state Interactions
. 15
1.4
Averaged Electron-Electron Scattering Probabilities
. 15
1.4.1
Integrated Cross Section for Strongly Localized States
. 16
1.4.2
Low-energy Regime
. 19
1.5
Electron-Electron Scattering in an Extended System
. 19
2
Spin-effects on the Correlated Two-electron Continuum
23
2.1
Generalities on the Spin-resolved Two-electron Emission
. 24
2.2
Formal Symmetry Analysis
. 27
2.3
Parametrization of the Spin-resolved Cross Sections
. 29
2.4
Exchange-induced Spin Asymmetry
. 30
2.5
Physical Interpretation of the Exchange-induced Spin Asymmetry
. 32
2.6
Spin Asymmetry in Correlated Two-electron Emission from Surfaces
. 33
2.7
General Properties of the Spin Asymmetry
. 35
2.7.1
Spin Asymmetry in Pair Emission from Bulk Matter
. 36
2.7.2
Spin-polarized Homogenous Electron Gas
. 37
VIII Contents
2.7.3
Behavior of the Exchange-induced Spin Asymmetry in Scattering from
Atomic Systems
. 37
2.7.4
Threshold Behavior of the Spin Asymmetry
. 39
3
Mechanisms of Correlated Electron Emission
43
3.1
Exterior Complex Scaling
. 44
3.2
The Convergent Close Coupling Method
. 45
3.3
Analytical Models
. 46
3.3.1
Dynamical Screening
. 47
3.3.2
Influence of the Density of Final States
. 48
3.4
Analysis of the Measured Angular Distributions
. 51
3.4.1
The Intermediate Energy Regime
. 51
3.5
Characteristics of the Correlated Pair Emission at Low Energies
. 53
3.5.1
Influence of the Exchange Interaction on the Angular Pair Correlation
55
3.6
Threshold Behavior of the Energy and the Angular Pair Correlation
. 57
3.6.1
Generalities of Threshold Pair Emission
. 57
3.6.2
Threshold Pair Emission from a Coulomb Potential
. 59
3.6.3
Regularities of the Measured Pair Correlation at Low Energies
. 60
3.6.4
Role of Final-state Interactions in Low-energy Correlated Pair
Emission
. 62
3.6.5
Interpretation of Near-threshold Experiments
. 63
3.7
Remarks on the Mechanisms of Electron-pair Emission from Atomic Systems
70
4
Electron-electron Interaction in Extended Systems
73
4.1
Exchange and Correlation Hole
. 74
4.2
Pair-correlation Function
. 76
4.2.1
Effect of Exchange on the Two-particle Probability Density
. 78
4.3
Momentum-space Pair Density and Two-particle Spectroscopy
. 79
4.3.1
The
S
Matrix Elements
. 79
4.3.2
Transition Probabilities and Cross Sections
. 81
4.3.3
Two-particle Emission and the Pair-correlation Function
. 82
Contents
IX
5
The Electron-Electron Interaction in Large Molecules and Clusters
85
5.1
Retardation and Nonlocality of the Electron-Electron Interaction in Extended
Systems
. 86
5.2
Electron Emission from
Fullerenes
and Clusters
. 90
5.2.1
The Spherical Jellium Model
. 91
5.2.2
Angular Pair Correlation
. 92
5.2.3
Total Cross Sections
. 95
5.2.4
Finite-size Effects
. 96
5.2.5
Influence of Exchange
. 97
6
Pair Emission from Solids at Surfaces
101
6.1
Qualitative Analysis
. 102
6.1.1
Model Crystal Potential
. 103
6.1.2
Scattering from the Surface Potential
. 105
6.1.3
Qualitative Features of Interacting Two-particle Emission from
Surfaces
. 106
6.1.4
Explicit Results for Two-particle Scattering from Metal Surfaces
. . . 107
6.2
Mechanisms of Correlated Electron Emission
.
Ill
6.2.1
Angular Pair Correlation
.
Ill
6.2.2
Energy Pair Correlation
. 114
6.2.3
Influence of Exchange on the Energy Pair Correlation
. 117
6.2.4
Pair Diffraction
. 120
6.3
Role of the Dynamical Collective Nature of the Two-particle Interaction
. 123
6.4
Quantitative Description of Pair Emission from Surfaces
. 126
6.4.1
Treating Strong Two-particle Correlations
. 127
6.4.2
Relativistic Layer KKR Method
. 130
6.4.3
Two-particle Energy Correlation in the Pair Emission from Tungsten
. 132
6.4.4
Angular Pair Correlation: Role of the Electron-Electron Interaction
. 133
7
Pair Emission from Alloys
135
7.1
Correlated Two-particle Scattering from Binary Substitutional Alloys
. 136
7.1.1
Pair Emission from Alloys in Transmission Mode
. 136
χ
Contents
ΊΑ.
2
Pair
Emission
in Reflection Mode
. 137
7.1.3
Scattering
Potential
from Binary Alloys
. 138
7.1.4
Electronic States and Disorder Averaged Spectral Functions
. 139
7.2
Incorporation of Damping of the Electronic States
. 140
7.3
Configurationally Averaged Cross Section
. 142
7.3.1
Analytical Model for Configurationally Averaged Cross Section
. . . 144
7.4
Numerical Results and Illustrations
. 146
Color Figures
149
Appendices
A Electronic States in a Periodic Potential
155
В
Screening Within Linear Response Theory
159
B.I
Kubo
Formalism
. 159
B.2 Density-density Correlation Functions
. 160
С
Lindhard Function
163
C.I Thomas-Fermi Approximation
. 164
C.2 Friedel Oscillations
. 165
C.3 Plasmon Excitations
. 165
D
Dynamic Structure Factor and the Pair-distribution Function
167
D.I Excitation Processes and the Dynamical Structure Factor
. 169
D.2 Properties of the Pair-distribution Function
. 171
References
173
Index
187 |
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| id | DE-604.BV021603051 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:48:23Z |
| indexdate | 2024-07-09T20:39:41Z |
| institution | BVB |
| isbn | 3527403507 3527404120 9783527403509 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014818362 |
| oclc_num | 64301621 |
| open_access_boolean | |
| owner | DE-703 DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-703 DE-355 DE-BY-UBR DE-11 |
| physical | XIII, 192 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Wiley-VCH |
| record_format | marc |
| spelling | Berakdar, Jamal 1964- Verfasser (DE-588)128384751 aut Electronic correlation mapping from finite to extended systems Jamal Berakdar Weinheim Wiley-VCH 2006 XIII, 192 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 173 - 185 Electron configuration Electronic excitation Electronic structure Festkörper (DE-588)4016918-2 gnd rswk-swf Elektronenkorrelation (DE-588)4210527-4 gnd rswk-swf Festkörper (DE-588)4016918-2 s Elektronenkorrelation (DE-588)4210527-4 s DE-604 Ergänzung Berakdar, Jamal Concepts of highly excited electronic systems Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014818362&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berakdar, Jamal 1964- Electronic correlation mapping from finite to extended systems Electron configuration Electronic excitation Electronic structure Festkörper (DE-588)4016918-2 gnd Elektronenkorrelation (DE-588)4210527-4 gnd |
| subject_GND | (DE-588)4016918-2 (DE-588)4210527-4 |
| title | Electronic correlation mapping from finite to extended systems |
| title_auth | Electronic correlation mapping from finite to extended systems |
| title_exact_search | Electronic correlation mapping from finite to extended systems |
| title_exact_search_txtP | Electronic correlation mapping from finite to extended systems |
| title_full | Electronic correlation mapping from finite to extended systems Jamal Berakdar |
| title_fullStr | Electronic correlation mapping from finite to extended systems Jamal Berakdar |
| title_full_unstemmed | Electronic correlation mapping from finite to extended systems Jamal Berakdar |
| title_short | Electronic correlation mapping |
| title_sort | electronic correlation mapping from finite to extended systems |
| title_sub | from finite to extended systems |
| topic | Electron configuration Electronic excitation Electronic structure Festkörper (DE-588)4016918-2 gnd Elektronenkorrelation (DE-588)4210527-4 gnd |
| topic_facet | Electron configuration Electronic excitation Electronic structure Festkörper Elektronenkorrelation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014818362&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT berakdarjamal electroniccorrelationmappingfromfinitetoextendedsystems |