This book presents numerical methods for solving a wide range of problems associated with the structure of atoms and simplest molecules, and their interaction with electromagnetic radiation, electrons, and other particles. It introduces the ATOM-M software package, presenting a unified software suite, written in Fortran, for carrying out precise atomic and molecular numeric calculations.
The book shows how to apply these numerical methods to obtain many different characteristics of atoms, molecules, and the various processes within which they interact. In an entirely self-sufficient approach, it teaches the reader how to use the codes provided to build atomic and molecular systems from the ground up and obtain the resulting one-electron wave functions. The computational programs presented and made available in this book allow calculations in the one-electron Hartree–Fock approximation and take into account many-electron correlations within the framework of the random-phase approximation with exchange or many-body perturbation theory.
Ideal for scholars interested in numerical computation of atomic and molecular processes, the material presented in this book is useful to both experts and novices, theorists, and experimentalists.
Author(s): Miron Y. Amusia, Larissa V. Chernysheva
Series: Springer Series on Atomic, Optical, and Plasma Physics 117
Edition: 1
Publisher: Springer Nature Switzerland AG
Year: 2021
Language: English
Pages: 456
City: Cham, Switzerland
Tags: Atoms,Hartree-Fock Wave Functions, Two-Atomic Molecules, Random Phase Approximation with Exchange, Auger Decay, Radiative Decay, Bremsstrahlung, Electron Scattering, Photoionization, Generalized Oscillator Strengths, Atomic Processes Software Package, Molecular Processes Software Package
Preface
Dedication
Contents
General References and Abbreviations
General References
Abbreviation for Basic Methods and Processes
1 Short Review
1.1 Some Qualitative Notes
1.2 Quantum–Mechanical Description of the Electronic Structure of Atomic–Molecular Systems
1.3 Hartree–Fock Approximation
1.4 Residual Interaction
1.5 Diagrammatical Technique
1.6 Accounting for Residual Interaction
1.7 Random Phase Approximation with Exchange
1.8 Rearrangement Method
1.9 Objects of Research and Considered Processes
1.10 Description of the ATOM-M System of Programs
References
2 Physical Content of the ATOM-M System Programs
2.1 Wave Functions of the Ground State of an Atom in the Hartree–Fock Approximation
2.2 Wave Functions of the Ground State of an Atom in the Hartree–Fock-Dirac Approximation
2.3 Wave Functions of the Excited State in the Hartree–Fock Approximation
2.4 Wave Functions of an Excited State of an Atom in the Hartree–Fock–Dirac Approximation
2.5 Wave Functions in the Hartree–Fock Approximation for Diatomic Molecules
2.6 Wave Functions in the Hartree–Fock Approximation for Endohedrals
2.7 Photoionization Cross Section and Oscillator Strength
2.8 Angular Distribution of Photoelectrons in the Dipole Approximation
2.9 Scattering Cross Section and Generalized Oscillator Strength for Fast Electrons
2.10 Scattering Cross Section for Fast Electrons in the Logarithmic Approximation
2.11 Angular Distribution of Photoelectrons Beyond the Dipole Approximation
2.12 Spin Polarization Parameters of Photoelectrons
2.13 Angular Distribution of Secondary Electrons in the Dipole Approximation
2.14 Angular Distribution of Secondary Electrons Beyond the Dipole Approximation
2.15 Compton Effect
2.16 Inelastic Scattering of Low and Intermediate Energies Electrons
2.17 Near-Threshold Ionization with Account for Post-collision Interaction
2.18 Self-energy Part of the One-Particle Green’s Function
2.19 Photoabsorption and One-Electron Ionization with Account for the Self-energy Part of an Electron
2.20 Scattering of Positrons
2.21 Non-radiative or Auger Vacancy Decay
2.22 Radiative Decay of Vacancies in HF and RPAE
2.23 Electron-Induced Triplet Excitations in the First and Second Orders of the Distorted Wave Method
2.24 Bremsstrahlung Spectrum
2.25 Capturing Negative Mesons
2.26 Photoionization of Diatomic Molecules
2.27 Photoionization of Endohedrals A@CN and A@CN1@CN2
2.28 Inelastic Scattering of Fast Electrons and GOS in Endohedrals A@CN and A@CN1@CN2
2.29 Decay of Vacancies in Endohedrals A@CN
2.30 Angular Distribution of Photoelectrons from Endohedrals A@CN Beyond the Dipole Approximation
References
3 Mathematical Description of the Properties of Atomic and Molecular Structure
References
4 Wave Functions of the Ground State of Atoms and Simple Molecules in the Hartree–Fock Approximation
4.1 Theoretical Model
4.1.1 Spherically Symmetric Potential
4.1.2 Axially Symmetric Potential
4.2 Numerical Model
4.2.1 General Consideration
4.2.2 Calculation of Yk and Xk
4.2.3 Numerical Procedure for a Differential Equation
4.2.4 Energy Eigenvalue Correction
4.2.5 Total Energy of an Atom in the Hartree–Fock Approximation
4.2.6 Spin-Polarized HF Approximation
4.2.7 Inclusion of the Endohedral’s Potential
4.2.8 Numerical Procedure for HF Equations with Axially Symmetric Potential
References
5 Wave Functions of the Ground State of an Atom in the Hartree–Fock–Dirac Approximation
5.1 Theoretical Model
5.2 Numerical Model
5.2.1 General Consideration
5.2.2 Change of Variables
5.2.3 Functions tildePi (ρ) and tildeQi (ρ)
5.2.4 Numerical Procedure for Differential Equation
5.2.5 Energy Eigenvalue Correction
References
6 Wave Functions of Excited States of Atoms and Simple Molecules in the Hartree–Fock Approximation
6.1 Theoretical Model
6.1.1 General Consideration
6.1.2 The Case of an Atom and an Endohedral
6.1.3 Diatomic Molecule
6.2 Numerical Model
6.2.1 General Consideration
6.2.2 Numerical Procedure for Continuous Spectrum States
6.2.3 Convergence Procedure for Calculating the Exchange Term for Atoms
6.2.4 Off-Diagonal Parameters
6.2.5 Normalization and Phase Shift of the Radial Wave Function in Continuous Spectrum
6.2.6 Radial Hartree Equation for a Meson and a Positron in the Field of a Frozen Core of an Atom and an Endohedral
6.2.7 Numerical Procedure for HF Equations with Axially Symmetric Potential
References
7 Wave Functions of an Excited State of an Atom in the Hartree–Fock–Dirac Approximation
7.1 Theoretical Model
7.2 Numerical Model
References
8 Choice of Wave Functions
8.1 Theoretical Model
8.1.1 Spherical Symmetry (Atoms)
8.1.2 Axial Symmetry (Diatomic Molecules)
8.2 Numerical Model
References
9 Photoionization Cross Section, Oscillator Strengths of Discrete Transitions, Polarizability
9.1 Theoretical Model
9.1.1 Spherical Symmetry (Atoms)
9.1.2 Axial Symmetry (Diatomic Molecules)
9.2 Numerical Model
9.2.1 Dipole Matrix Elements in the Hartree–Fock Approximation
9.2.2 Coulomb Matrix Elements
9.2.3 RPAE Equation for Dipole Matrix Elements
9.2.4 Reduction of RPAE Equation to a System of Algebraic Equations
9.2.5 Solution of RPAE Equation
9.2.6 Solution of RPAE Equation for Discrete States
9.2.7 Solution of RPAE Equation for a Continuous Spectrum
9.2.8 Photoionization Cross Section
9.2.9 Photoionization Quasi-Cross Sections
References
10 Scattering Cross Section of Fast Electrons, Generalized Oscillator Strengths, and the Compton Effect
10.1 Theoretical Model
10.2 Numerical Model
10.2.1 Matrix Elements of Bessel Functions in the Hartree–Fock Approximation
10.2.2 Coulomb Multipole Matrix Elements
10.2.3 RPAE Equation for Multipole Matrix Elements
10.2.4 Scattering Cross Section of Fast Electrons in the Logarithmic Approximation
10.2.5 Compton Effect
References
11 Angular Distribution of Photoelectrons and Secondary Electrons Outside the Dipole Approximation
11.1 Theoretical Model
11.1.1 Angular Distribution of Photoelectrons
11.1.2 Angular Distribution of Electrons Knocked Out in the Process of Scattering
11.2 Numerical Model
11.2.1 Non-dipole Angular Anisotropy Parameters for s-subshells in HF
11.2.2 Non-dipole Angular Anisotropy Parameters for s-subshells in the RPAE
11.2.3 Non-dipole Angular Anisotropy Parameters for p-subshells
11.2.4 Non-dipole Angular Anisotropy Parameters for d-subshells
11.2.5 Non-dipole Angular Anisotropy Parameters for Semi-Closed Shell Atoms
References
12 Spin Polarization Parameters of Photoelectrons
12.1 Theoretical Model
12.1.1 Spin Polarization Parameters in the Dipole Approximation
12.1.2 Spin Polarization Parameters with Allowance for Quadrupole Terms
12.2 Numerical Model
12.2.1 Spin Polarization Parameters in the Dipole Approximation
12.2.2 Spin Polarization Parameters with Allowance for Quadrupole Terms
References
13 Angular Distribution of Secondary Electrons Arising from the Scattering of Fast Particles by Atoms
13.1 Theoretical Model
13.2 Numerical Model
13.2.1 Angular Anisotropy Parameters for s-subshells
13.2.2 Angular Anisotropy Parameters for p-subshells
13.2.3 Angular Anisotropy Parameters for d-subshells
References
14 Scattering of Particles of Low and Medium Energies by Atoms
14.1 Theoretical Model
14.1.1 The Self-energy Part of the One-Particle Green’s Function
14.1.2 Scattering Phases and Wave Functions with Exact Account of the Self-Energy Part
14.1.3 Phases, Scattering Cross Sections, and Wave Functions in the Frame of the SRPAE
14.1.4 Scattering of Slow Positrons by Atoms
14.1.5 Scattering and Capture of µ−Mesons by Atoms
14.2 Numerical Model
14.2.1 Scattering Cross Section and Phases in the Framework of the SRPAE
14.2.2 Scattering Phases with Account for Polarization Corrections
14.2.3 Scattering of Slow Positrons by Atoms
14.2.4 Cross Sections of µ−Mesons Scattering and Capture
References
15 Non-radiative or Auger Vacancy Decay
15.1 Theoretical Model
15.1.1 One-Electron Auger Decay
15.1.2 Double Auger Decay
15.2 Numerical Model
15.2.1 Probability of One-Electron Auger Decay
15.2.2 The Probability of Double Auger Decay
References
16 One-Photon Decay of Single- and Double-Hole States
16.1 Theoretical Model
16.1.1 One-Photon Decay of States with a Single Vacancy
16.1.2 One-Photon Decay of Double-Vacancy States
16.2 Numerical Model
16.2.1 The Probability of One-Photon Decay of Single-Vacancy States
16.2.2 The Probability of One-Photon Decay of Double-Vacancy States
References
17 Bremsstrahlung Spectra in High and Intermediate Energy Collisions
17.1 Theoretical Model
17.1.1 High Energy Particles
17.1.2 Intermediate Energy Particles
17.2 Numerical Model
17.2.1 Bremsstrahlung Spectrum for High Energy Particles
17.2.2 Bremsstrahlung Spectrum for Intermediate Energy Particles
References
18 Photoabsorption Cross Section with Account for Inelastic Photoelectron Scattering
18.1 Theoretical Model
18.1.1 Numerical Model
References
19 Ionization and Excitation of an Atom by Electron Impact
19.1 Theoretical Model
19.1.1 Ionization of an Atom by Electron Impact
19.1.2 Ionization of an Atom at the Threshold of Triplet Autoionizing Level Excitation with Allowance for “Post-collision Interaction”
19.1.3 Excitation of a Triplet Level by Electrons
19.2 Numerical Model
19.2.1 Ionization of an Atom by Electron Impact
19.2.2 Ionization Cross Section of an Atom by Electrons at the Threshold of Triplet Autoionizing Level Excitation with Allowance for “Post-collision Interaction”
19.2.3 Excitation of a Triplet Level by Electrons
References
20 Photoionization of Endohedrals and Vacancies Decay in Them
20.1 Theoretical Model
20.1.1 General Remarks
20.1.2 An Atom Inside a Fullerene Shell
20.1.3 Numerical Model
References
21 Inelastic Scattering of Fast Electrons by Endohedrals
21.1 Theoretical Model
21.1.1 Endohedral with One Fullerene Shell
21.1.2 Angular Distribution of Secondary Electrons
21.2 Numerical Model
21.2.1 Generalized Oscillator Strength
21.2.2 Angular Anisotropy Parameters for s-subshells
21.2.3 Angular Anisotropy Parameters for p-subshells
21.2.4 Angular Anisotropy Parameters for d-subshells
21.2.5 Angular Anisotropy Parameters of Atoms with Semi-Closed Shells
References
22 Structure of the ATOM-M System
22.1 General Consideration
22.2 Description of Modules
22.3 List of Modules
22.4 Input and Output (I/O) Data
22.5 Data Assignment Examples
22.5.1 Ground and Excited States of an Atom in the HF Approximation
22.5.2 Ground and Excited States of an Atom in the Hartree–Fock–Dirac Approximation
22.5.3 Wave Functions of Diatomic Molecules in the Hartree–Fock Approximation in the Ground and Excited States
22.5.4 Photoionization Cross Section and Dipole Angular Anisotropy Parameter
22.5.5 Polarizability of an Atom
22.5.6 Fast Electrons Scattering Cross Section and Generalized Oscillator Strengths
22.5.7 Non-dipole Angular Anisotropy Parameters of Secondary Electrons at q = 0
22.5.8 Spin Polarization Parameters of Photoelectrons (A, ξ, α)
22.5.9 Angular Distribution of Secondary Electrons in Fast Particles Scattering
22.5.10 Scattering of Low and Medium-Energy Electrons by Atoms and Endohedrals
22.5.11 Differential Cross Section of Elastic Electron Scattering by Atoms and Endohedrals
22.5.12 Non-radiative (Auger) Vacancy Decay
22.5.13 Radiative Decay
22.5.14 Bremsstrahlung of Intermediate and High Energy Incident Particles
22.5.15 Photoabsorption Cross Section
22.5.16 Capture of µ-Mesons by Atoms
22.5.17 Photoionization of Endohedrals A@CN and A@CN1@CN2
22.6 The Limits of Applicability of ATOM-M Program System
22.7 Execution Levels of ATOM-M System
References
23 Examples of Calculation Results Using ATOM-M
23.1 General Remarks
23.2 Results of the First Group of Calculations
23.3 Results of the Second Group of Calculations
23.4 Main Physical Results
References
Appendix
Conclusions
Index
