Fermion pair correlation function exchange hole ( s = s' ) (Pauli - - PowerPoint PPT Presentation

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May 15, 2023 238 likes •287 views

Jellium model - Hartree-Fock approximation Jellium model with interactions charge neutrality kinetic electron-electron ion-ion electron-ion interaction interaction energy interaction Coulomb interaction field operator ''free electrons''

SLIDE 1

Jellium model - Hartree-Fock approximation

Jellium model with interactions

kinetic energy electron-electron interaction electron-ion interaction ion-ion interaction

charge neutrality

field operator ''free electrons'' Coulomb interaction

SLIDE 2

Jellium model - Hartree-Fock approximation

variational energy

groundstate free electron gas density: variational parameter

kinetic energy electron-ion ion-ion

uniform electron density

SLIDE 3

Jellium model - Hartree-Fock approximation

electron-electron interaction

Fermion pair correlation function

exchange hole (s = s' )

(Pauli exclusion principle) radius ~ kF

SLIDE 4

Fermion pair correlation function exchange hole ( s = s' ) (Pauli - - PowerPoint PPT Presentation

Jellium model - Hartree-Fock approximation

Jellium model with interactions

kinetic energy electron-electron interaction electron-ion interaction ion-ion interaction

charge neutrality

field operator ''free electrons'' Coulomb interaction

Jellium model - Hartree-Fock approximation

variational energy

groundstate free electron gas density: variational parameter

kinetic energy electron-ion ion-ion

uniform electron density

Jellium model - Hartree-Fock approximation

electron-electron interaction

Fermion pair correlation function

exchange hole (s = s' )

(Pauli exclusion principle) radius ~ kF

Jellium model - Hartree-Fock approximation

electro-static energy

uniform charge neutral system

variational ground state energy

stable density

lattice constant

comparison with alkali metals

element Li Na K

3.22 3.96 4.86

d ≈ 2.5˚ A a ≈ 4˚ A