Atomic Spectra and Radiative Transitions

ISBN-13: 9783540545187 / Angielski / Miękka / 1992 / 356 str.

I. I. Sobel'man;Sobelman; Igor I. Sobelman

Opis

This guide to atomic spectroscopy covers the systematics of atomic spectra and radiative transitions and discusses continuous spectrum radiation, excitation of atoms and spectral line broadening. The theory of atomic structure is based on Racah techniques in angular momentum.

Spis treści

I Elementary Information on Atomic Spectra.- 1 The Hydrogen Spectrum.- 1.1 Schrödinger’s Equation for the Hydrogen Atom.- 1.1.1 Energy Levels.- 1.1.2 Wave Functions.- 1.2 Series Regularities.- 1.2.1 Radiative Transition Selection Rules.- 1.2.2 Spectral Series of the Hydrogen Atom.- 1.2.3 Hydrogenlike Ions.- 1.3 Fine Structure.- 1.3.1 Velocity Dependence of Electron Mass.- 1.3.2 Spin-Orbit Interaction.- 1.3.3 Fine Structure. Selection Rules.- 1.3.4 Lamb Shift.- 2 Systematics of the Spectra of Multielectron Atoms.- 2.1 Central Field.- 2.1.1 Central Field Approximation.- 2.1.2 Parity of States.- 2.1.3 Systematics of Electron States in a Central Field.- 2.2 Electrostatic and Spin-Orbit Splitting in the LS Coupling Approximation.- 2.2.1 Spectral Terms. LS Quantum Numbers.- 2.2.2 Fine Structure of Terms.- 2.2.3 Finding the Terms of Multielectron Configurations.- 2.2.4 Radiative Transitions.- 2.3 jj Coupling Approximation.- 2.3.1 Various Coupling Schemes.- 2.3.2 Systematics of Electron States with jj Coupling.- 3 Spectra of Multielectron Atoms.- 3.1 Periodic System of Elements.- 3.2 Spectra of the Alkali Elements.- 3.2.1 Term Scheme.- 3.2.2 Series Regularities.- 3.2.3 Fine Structure.- 3.2.4 Copper, Silver, and Gold Spectra.- 3.3 Spectra of the Alkaline Earth Elements.- 3.3.1 He Spectrum.- 3.3.2 Spectra of the Alkaline Earth Elements.- 3.3.3 Zinc, Cadmium, and Mercury Spectra.- 3.4 Spectra of Elements with p Valence Electrons.- 3.4.1 One p Electron Outside Filled Shells.- 3.4.2 Configuration p2.- 3.4.3 Configuration p3.- 3.4.4 Configuration p4.- 3.4.5 Configuration p5.- 3.4.6 Configuration p6.- 3.5 Spectra of Elements with Unfilled d and f Shells.- 3.5.1 Elements with Unfilled d Shells.- 3.5.2 Elements with Unfilled f Shells.- II Theory of Atomic Spectra.- 4 Angular Momenta.- 4.1 Angular Momentum Operator. Addition of Angular Momenta.- 4.1.1 Angular Momentum Operator.- 4.1.2 Orbital Angular Momentum.- 4.1.3 Electron Spin.- 4.1.4 Addition of Two Angular Momenta.- 4.1.5 Addition of Three or More Angular Momenta.- 4.2 Angular Momentum Vector Addition Coefficients.- 4.2.1 Clebsch-Gordan and Associated Coefficients.- 4.2.2 Summary of Formulas for 3j Symbols.- 4.2.3 Racah W Coefficients and 6j Symbols.- 4.2.4 Summary of Formulas for 6j Symbols.- 4.2.5 9j Symbols.- 4.3 Irreducible Tensor Operators.- 4.3.1 Spherical Tensors.- 4.3.2 Matrix Elements.- 4.3.3 Some Examples of Calculation of Reduced Matrix Elements.- 4.3.4 Tensor Product of Operators.- 4.3.5 Matrix Elements with Coupled Angular Momenta.- 4.3.6 Direct Product of Operators.- 5 Systematics of the States of Multielectron Atoms.- 5.1 Wave Functions.- 5.1.1 Central Field Approximation.- 5.1.2 Two-Electron Wave Functions in LSMLMS Representation.- 5.1.3 Two-Electron Wave Functions in mm’SMs Representation.- 5.1.4 Multielectron Wave Functions in a Parentage Scheme Approximation.- 5.1.5 Fractional Parentage Coefficients.- 5.1.6 Classification of Identical Terms of ln Configuration According to Seniority (Seniority Number).- 5.2 Matrix Elements of Symmetric Operators.- 5.2.1 Statement of the Problem.- 5.2.2 F Matrix Elements. Parentage Scheme Approximation.- 5.2.3 F Matrix Elements. Equivalent Electrons.- 5.2.4 Q Matrix Elements. Parentage Scheme Approximation.- 5.2.5 Q Matrix Elements. Equivalent Electrons.- 5.2.6 Summary of Results.- 5.3 Electrostatic Interaction in LS Coupling. Two-Electron Configuration.- 5.3.1 Coulomb and Exchange Integrals.- 5.3.2 Configuration Mixing.- 5.4 Electrostatic Interaction in LS Coupling. Multielectron Configuration.- 5.4.1 Configurations ln and lnl’.- 5.4.2 More Than Half Filled Shells.- 5.4.3 Filled (Closed) Shells.- 5.4.4 Applicability of the Single-Configuration Approximation.- 5.5 Multiplet Splitting in LS Coupling.- 5.5.1 Preliminary Remarks.- 5.5.2 Landé Interval Rule.- 5.5.3 One Electron Outside Closed Shells.- 5.5.4 Configuration ln.- 5.5.5 Parentage Scheme Approximation.- 5.5.6 Fine-Structure Splitting of Levels of He.- 5.5.7 Spin-Spin and Spin-Other Orbit Interactions.- 5.6 jj Coupling.- 5.6.1 Wave Functions.- 5.6.2 Spin-Orbit and Electrostatic Interactions.- 5.7 Intermediate Coupling and Other Types of Coupling.- 5.7.1 Transformations Between LS and jj Coupling Schemes.- 5.7.2 Intermediate Coupling.- 5.7.3 jl Coupling.- 5.7.4 Experimental Date.- 5.7.5 Other Types of Coupling.- 6 Hyperfine Structure of Spectral Lines.- 6.1 Nuclear Magnetic Dipole and Electric Quadrupole Moments.- 6.1.1 Magnetic Moments.- 6.1.2 Quadrupole Moments.- 6.2 Hyperfine Splitting.- 6.2.1 General Character of the Splitting.- 6.2.2 Calculation of the Hyperfine Splitting Constant A.- 6.2.3 Calculation of the Hyperfine Splitting Constant B.- 6.2.4 Radiative Transitions Between Hyperfine-Structure Components.- 6.2.5 Isotope Shift of the Atomic Levels.- 7 The Atom in an External Electric Field.- 7.1 Quadratic Stark Effect.- 7.2 Hydrogenlike Levels. Linear Stark Effect.- 7.3 Inhomogeneous Field. Quadrupole Splitting.- 7.4 Time-Dependent Field.- 7.4.1 Amplitude Modulation.- 7.4.2 The Hydrogen Atom in a Rotating Electric Field.- 8 The Atom in an External Magnetic Field.- 8.1 Zeeman Effect.- 8.2 Paschen-Back Effect.- 8.2.1 Strong Field.- 8.2.2 Splitting of Hyperfine Structure Components in a Magnetic Field.- 9 Radiative Transitions.- 9.1 Electromagnetic Radiation.- 9.1.1 Quantization of the Radiation Field.- 9.1.2 Radiative Transition Probabilities.- 9.1.3 Correspondence Principle for Spontaneous Emission.- 9.1.4 Dipole Radiation.- 9.1.5 Stimulated Emission and Absorption.- 9.1.6 Effective Cross Sections of Absorption and Stimulated Emission.- 9.2 Electric Dipole Radiation.- 9.2.1 Selection Rules, Polarization and Angular Distribution.- 9.2.2 Oscillator Strengths and Line Strengths.- 9.2.3 LS Coupling Approximation. Relative Intensities of Multiplet Components.- 9.2.4 One Electron Outside Closed Shell.- 9.2.5 Multielectron Configurations. Different Coupling Schemes.- 9.2.6 Relative Intensities of Zeeman and Stark Components of Lines.- 9.3 Multipole Radiation.- 9.3.1 Fields of Electric and Magnetic Multipole Moments.- 9.3.2 Intensity of Multipole Radiation.- 9.3.3 Selection Rules.- 9.3.4 Electric Multipole Radiation.- 9.3.5 Magnetic Dipole Radiation.- 9.3.6 Transitions Between Hyperfine Structure Components. Radio Emission from Hydrogen.- 9.4 Calculation of Radiative Transition Probabilities.- 9.4.1 Approximate Methods.- 9.4.2 Three Ways of Writing Formulas for Transition Probabilities.- 9.4.3 Theorems for Sums of Oscillator Strengths.- 9.4.4 Semiempirical Methods of Calculating Oscillator Strengths.- 9.4.5 Electric Dipole Transition Probabilities in the Coulomb Approximation.- 9.4.6 Intercombination Transitions.- 9.5 Continuous Spectrum.- 9.5.1 Classification of Processes.- 9.5.2 Photorecombination and Photoionization: General Expressions for Effective Cross Sections.- 9.5.3 Bremsstrahlung: General Expressions for Effective Cross Sections.- 9.5.4 Radiation and Absorption Coefficients.- 9.5.5 Photorecombination and Photoionization: Hydrogenlike Atoms.- 9.5.6 Photorecombination and Photoionization: Nonhydrogenlike Atoms.- 9.5.7 Bremsstrahlung in a Coulomb Field.- 9.6 Formulas for Q Factors.- 9.6.1 Symmetry and Sum Rules.- 9.6.2 LS Coupling. Allowed Transitions.- 9.6.3.jl Coupling.- 9.7 Tables of Oscillator Strengths and Radiative Transition Probabilities.- 9.7.1 Transition Probabilities for the Hydrogen Atom.- 9.7.2 Radiative Transition Probabilities in the Bates-Damgaard Approximation.- 9.7.3 Oscillator Strengths and Probabilities of Some Selected Transitions.- 9.7.4 Effective Cross Sections and Rates of Photorecombination.- 10 Relativistic Corrections in the Spectroscopy of Multicharged Ions.- 10.1 Dirac Equation. Pauli Equation.- 10.1.1 Dirac Equation.- 10.1.2 Electron Spin.- 10.1.3 Non-Relativistic Approximation. Pauli Equation.- 10.2 Central Field.- 10.2.1 Non-Relativistic Approximation.- 10.2.2 Second Approximation with Respect to v/c. Fine Splitting.- 10.2.3 Dirac Equation for a Central Field.- 10.2.4 Coulomb Field. Energy Levels, Fine Splitting.- 10.2.5 Coulomb Field. Radial Functions.- 10.3 Relativistic Corrections.- 10.3.1 Calculation of Some Radial Integrals.- 10.3.2 Hyperfine Splitting Constant A.- 10.3.3 Hyperfine Splitting Constant B.- 10.3.4 Nucleus Finite-Size Correction.- 10.3.5 Radiative Corrections. Lamb Shift.- 11 Spectra of Multicharged Ions.- 11.1 Energy Levels.- 11.2 Forbidden Transitions.- 11.2.1 H-like Ions.- 11.2.2 He-like Ions.- 11.3 Satellite Structure.- References.- List of Symbols.

Blurb

Atomic Spectra and Radiative Transitions covers the systematics of atomic spectra, continuous spectrum radiation, and the excitation of atoms. This second edition has additional chapters on relativistic corrections in the spectra of highly charged ions, which rounds off the previous treatment. Extensive tables of oscillator strengths (both dipole and quadrupole), probabilities and cross sections of radiative transitions complete this textbook, making it invaluable also as a reference work.