Excitation of Atoms and Broadening of Spectral Lines

ISBN-13: 9783642965586 / Angielski / Miękka / 2012 / 318 str.

I.I. Sobelman;L.A. Vainshtein;E.A. Yukov

Opis

New applications of atomic spectroscopy in laser physics, laser spectrosco py, laser frequency and wavelength measurements, plasma physics, astrophysics, and some other related problems have been developed very intensively in the last years. As a result, the approximate methods of calculation of the transition probabilities and cross sections necessary for all these applications have become of vastly increased importance. At the same time, some new problems have arisen in the theory of spectral line broadening such as the shape of nonlinear resonances in the spectra of gas lasers, interference effects, and some other problems connected with various spectroscopic methods of plasma diagnostics. This book is devoted to the systematic treatment of the theory of the elementary processes responsible for the excitation of atomic spectra and the theory of spectral line broadening. The choice of problems is significantly different from that traditional for books on the theory of atomic collisions. The main goal of the book is to present the most efficient and useful of comparatively simple approximate methods for the calcula tion and estimation of cross sections. Numerous tables containing the results of approximate cross section calculations for the most important elementary processes are included in the book. Comprehensive presenta tion of the theory of atomic collisions is out of the scope of this book and can be found elsewhere. However, the fundamentals of the general theory of collisions which are necessary for formulation of approximate methods are given in Chapter 2."

Spis treści

1. Elementary Processes Giving Rise to Spectra.- 1.1 Cross Sections.- 1.2 Populations of Atomic Levels in a Plasma; Rates of Direct and Reverse Processes.- 1.2.1 Thermodynamic Equilibrium.- 1.2.2 Rates of Direct and Reverse Processes.- 1.2.3 The Simplest Model.- 1.2.4 Coronal Limit.- 2. Theory of Atomic Collisions.- 2.1 Fundamentals of Scattering Theory.- 2.1.1 Elastic Scattering in a Central Field.- 2.1.2 Wave Functions ?k+, ?k?.- 2.1.3 Quasi-Classical Approximation.- 2.1.4 Inelastic Scattering.- 2.2 Theory of Electron-Atom Collisions.- 2.2.1 Introduction.- 2.2.2 General Formulas for Cross Sections.- 2.2.3 S-matrix and Collision Strength.- 2.2.4 Radial Equations.- 2.2.5 Integral Radial Equations.- 2.2.6 Polarization Potential.- 2.3 First-Order Approximation.- 2.3.1 General Formulas.- 2.3.2 List of Formulas for ? and Q-Factors.- 3. Approximate Methods for Calculating Cross Sections.- 3.1 Born Approximation.- 3.1.1 Collisions of Fast Electrons with Atoms; Multipole Expansion.- 3.1.2 Bethe Formula.- 3.1.3 Brief Description of Born Cross Sections.- 3.1.4 Ionization and Three-Body Recombination.- 3.2 Some Refinements of the Born Approximation.- 3.2.1 Introduction.- 3.2.2 Distortion of Incident and Scattered Waves; Excitation of Ions.- 3.2.3 Allowance for Exchange.- 3.2.4 Normalization.- 3.2.5 Concluding Remarks: Generalized Born Approximation.- 3.3 More Accurate Methods of Calculation of Excitation Cross Sections.- 3.3.1 Transitions Via Virtual States.- 3.3.2 Use of the K matrix.- 3.3.3 Polarization Potential.- 3.3.4 Close-Coupling Method.- 3.4 Excitation of Highly Charged Atoms.- 3.4.1 Introduction.- 3.4.2 Coulomb Green’s Function.- 3.4.3 Potential and Resonance Scattering.- 3.4.4 Discussion and Examples.- 3.5 Transitions Between Highly Excited Levels.- 3.5.1 Born Approximation.- 3.5.2 Transitions Between Highly Excited Levels in the Quasi-Classical Approximation.- 3.5.3 Transitions Between Adjacent Levels ?n = 1.- 4. Collisions Between Heavy Particles.- 4.1 Impact-Parameter Method.- 4.1.1 General Formulas.- 4.1.2 Two-State Approximation.- 4.2 Transitions Caused by a Multipole Interaction.- 4.2.1 Two-State Approximation.- 4.2.2 Two-Levels and Rotating-Axis Approximations.- 4.2.3 Treatment of the Repulsion of Nuclei.- 4.3 Charge Exchange.- 4.3.1 Special Features of Charge-Exchange Processes.- 4.3.2 Resonance Charge-Exchange.- 4.3.3 Two-State Approximation.- 4.3.4 Contribution of Inner Shells.- 4.3.5 Charge-Exchange in the Case of Multicharged Ions.- 5. Some Problems of Excitation Kinetics.- 5.1 Rate Coefficients for Elementary Proccesses in a Plasma. Approximation of Cross Sections and Rate Coefficients by Analytic Formulas.- 5.1.1 Excitation of Atoms and Ions.- 5.1.2 Transitions Between Closely Spaced Levels.- 5.1.3 Ionization.- 5.1.4 Recombination.- 5.1.5 Semiempirical Formulas for the Rates of Excitation, Ionization and Dielectronic Recombination.- 5.2 Dielectronic Recombination.- 5.2.1 Electron Capture and Underthreshold Resonances (Simplified Model).- 5.2.2 General Case.- 5.2.3 Formulas for Autoionization Probability.- 5.2.4 Possible Inaccuracies of the Simplified Model.- 5.2.5 Numerical Calculations and Analytical Approximation Formulas.- 5.3 Satellites of Resonance Lines in Spectra of Highly Charged Atoms.- 5.3.1 Excitation by Means of DR.- 5.3.2 Direct Inner-Shell Excitation.- 5.4 Populations of Excited Levels in a Plasma.- 5.4.1 Introduction.- 5.4.2 Populations of the Hydrogen Levels at Low Plasma Density.- 5.4.3 Intermediate Density. Collisional-Radiative Model of a Plasma.- 5.4.4 Quasi-Stationary Approach for Hydrogen.- 5.4.5 Hydrogenlike Ions.- 5.4.6 Population Densities of Highly Excited Levels at High Density; Steady-Flow Regime.- 6. Tables and Formulas for the Estimation of Effective Cross Sections.- 6.1 Tables of Numerical Results.- 6.1.1 Methods of Calculations and Survey of the Tables...- 6.1.2 Born Excitation Cross Sections for Neutral Hydrogen.- 6.1.3 Born Cross Sections Calculated in the Bates-Damgaard Approximation for Atomic Wave Functions.- 6.1.4 Normalized Cross Sections for Specific Atoms and Ions.- 6.1.5 Transitions Between Closely Spaced Levels.- 6.1.6 Ionization Cross Sections.- 6.1.7 Dielectronic Recombination Rate Coefficients.- 6.2 Formulas Defining the Angular Factors.- 6.2.1 Rules for the Addition of Cross Sections.- 6.2.2 LS Coupling; Qx Factors for Transitions Without Change of Spin.- 6.2.3 Intercombination Transitions (?S = 1).- 6.2.4 jl Coupling.- 6.2.5 3nj Symbols and Fractional Parentage Coefficients.- 7. Broadening of Spectral Lines.- 7.1 Model of a Classical Oscillator.- 7.1.1 Formulation of the Problem.- 7.1.2 Impact Broadening.- 7.1.3 Quasi-Static Broadening.- 7.1.4 Relationship and Limits of Applicability of the Impact and Quasi-Static Approximations.- 7.1.5 Doppler Effect.- 7.1.6 Convolution of the Doppler and Lorentzian Distributions.- 7.2 General Theory of Impact Broadening.- 7.2.1 Density Matrix Method in the Quasi-Classical Approximation.- 7.2.2 Degeneracy of Levels.- 7.2.3 Quantum Theory.- 7.2.4 Quantum Kinetic Equation Method.- 7.2.5 Absorbtion Spectrum.- 7.2.6 Interference Effects: Narrowing of Spectral Lines.- 7.3 Broadening of Lines of the Hydrogen Spectrum in a Plasma.- 7.3.1 Preliminary Estimates.- 7.3.2 Ion Broadening: Holtsmark Theory.- 7.3.3 Correction for Thermal Motion.- 7.3.4 Electron Broadening.- 7.3.5 Combined Effect of Electrons and Ions.- 7.3.6 Highly Excited States.- 7.4 Line Broadening of Nonhydrogenlike Spectra in a Plasma.- 7.4.1 Preliminary Estimates.- 7.4.2 Electron Broadening.- 7.5 Broadening by Uncharged Particles.- 7.5.1 Perturbation by Foreign Gas Atmos (Van der Waals Interaction).- 7.5.2 Self-Broadening.- 7.6 Spectroscopic Methods of Investigating Elastic Scattering of Slow Electrons.- 7.6.1 Perturbation of Highly Excited States.- 7.6.2 Fermi Formula.- References.- List of Symbols.