Self-Consistent Fields in Atoms

Hartree and Thomas-Fermi Atoms

1st Edition - October 31, 2013
Author: N. H. March
Editor: D. Ter Haar
Language: English

Self-Consistent Fields in Atoms: Hartree and Thomas-Fermi Atoms covers the various aspects of atomic properties, including energy levels, binding energies, X-ray scattering… Read more

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Self-Consistent Fields in Atoms: Hartree and Thomas-Fermi Atoms covers the various aspects of atomic properties, including energy levels, binding energies, X-ray scattering activity, and magnetic properties. This book emphasizes the Hartree field concept. This book is organized into two parts encompassing 13 chapters. Part I examines first the concepts of central field wave functions and angular momentum operators. This part also deals with the concept of self-consistent field, Thomas-Fermi atom, energies of atoms and ions, and other atomic properties. The electron-electron correlation and the relativistic effects in heavy atoms are reviewed in this part. Part II presents the applications of the theory and methods used for determining the characteristic values and functions of Schrödinger’s wave equations for a non-Coulomb central field of force. This part also looks into the simplification of the Hartree-Fock method. This book will prove useful to physicists and researchers in the allied fields.

Outline

PART I

1. Central Field Wave Functions and Angular Momentum Operators

1.1. Introduction

1.2. Angular Momentum and Central Fields

1.3. Shapes of Atomic Wave Functions

Problems

2. Concept of Self-Consistent Field

2.1. Size of Atomic Wave Functions

2.2. Wave Equation for Helium Atom

2.3. Hartree's Self-Consistent Field

Problems

3. Thomas-Fermi Atom

3.1. Classical Energy Equation for Fastest Electron

3.2. Electron Density and Maximum Electronic Momentum

3.3. Electron Density for Coulomb Field

3.4. Approximate Self-Consistent Fields in Atoms and Ions

Problems

4. Energies of Atoms and Ions

4.1. Variational Derivation of Thomas-Fermi Equation

4.2. Evaluation of Total Electronic Energy for Heavy Ions

4.3. Relation between Different Energy Terms for Heavy Atoms

4.4. Foldy's Calculation of Atomic Binding Energies

Problems

5. Other Atomic Properties

5.1. Internal Diamagnetic Field in Atoms

5.2. Orbital Diamagnetic Susceptibility

5.3. Linear Momentum Distribution in Atoms

5.4 Orbital Angular Momentum

5.5. Eigenvalues for Potentials Related to Thomas-Fermi Self-Consistent Fields

Problems

6. X-Ray Scattering and Electron Densities in Atoms

6.1. Coherent Scattering

6.2. Incoherent Scattering

Problems

7. Electron Exchange and Slater Determinants

7.1. Spin-Orbitals and Total Wave Function for Ground State of Helium Atom

7.2. Slater Determinants and Antisymmetric Wave Functions

7.3. Inclusion of Exchange in Thomas-Fermi Theory

7.4. Variational Derivation of Exchange Corrections to Hartree Theory

Problems

8. Electron-Electron Correlation

8.1. Descriptions in Terms of Charge Density

8.2. Exchange and Correlation Holes in Atoms

8.3. Collective Effects

Problems

9. Relativistic Effects in Heavy Atoms

9.1. Dirac Wave Equation

9.2. Central Field Solutions of Dirac Equation

9.3. Relativistic Thomas-Fermi Theory

Problems

Appendices

1.1. Orthogonality of Solutions of Schrodinger Equation

2.1. Radial Wave Functions for Hydrogen Atom

2.2. Variation Method

2.3. Hartree Equations Derived from a Variational Principle

3.1. Solutions of the Dimensionless Thomas-Fermi Equation

5.1. Hamiltonian for Charged Particle in an Electromagnetic Field

5.2. Momentum Wave Functions in Atoms and Wave Equation in Momentum Space

6.1. Morse, Young and Haurwitz Wave Functions for Heavier Atoms

6.2. X-Ray Scattering from Gas of Non-Spherical Molecules

6.3. Self-Consistent Field for H2 Molecule

8.1. Relation between Charge Density and its Gradient at Nucleus

9.1. Solution of Dirac Equation for Hydrogen Atom

References