Multiphoton ionization of atoms in intense laser-light fields is gaining ground as a spectroscopic diagnostic tool. In this volume, Delone and Krainov present their and others' theoretical description of the process occurring in atoms under conditions of multi-photon impacts, in particular, the shift, broadening, and mixing of electronic states which complicate the interpretation of spectra. The topics of individual chapters include tunneling ionization, above-threshold ionization, ionization of multiply charged ions, resonance-enhenced ionization, super-intense radiation fields, and properties of Rydberg states in strong fields.

1. Introduction.- 2. AC-Stark Shift of Atomic Levels.- 2.1 Single-Level Quantum System.- 2.2 The Linear Stark Shift for a Hydrogen Atom in an Oscillating Field.- 2.3 Atomic Response to an External Oscillating Field.- 2.4 The Perturbation of Non-Degenerate Atomic States in a Weak Field.- 2.5 Perturbation of the Hydrogen Atom Spectrum in a Strong Field.- 2.6 Perturbation of Rydberg States in a Weak Field.- 2.7 Stark Effect in a Super-Atomic Radiation Field.- 2.8 The Stark Atom.- 2.9 AC-Stark Shift in Negative Ions.- 2.10 Dynamical Stark Resonance.- 2.11 AC-Stark Shift and Ionization.- 3. Ionization of a Particle with a Short-Range Potential Well.- 3.1 The Keldysh-Faisal-Reiss Approximation.- 3.1.1 The Keldysh Approach.- 3.1.2 The Reiss Approach.- 3.1.3 Other S-Matrix Approaches.- 3.1.4 Above-Threshold Ionization in Keldysh-Type Approaches.- 3.2 Model One-Particle Potentials of Negative Ions.- 3.2.1 Multiphoton Detachment of an Electron from H-.- 3.2.2 Multiphoton Detachment of Electrons from Complex Negative Ions.- 3.3 Residual Interaction Between Electrons.- 3.4 Removal of Internal Electrons from Negative Ions.- 3.5 Numerical Solutions for the Strong-Field Case.- 3.6 Experiments on Multiphoton Detachment of Negative Ions.- 3.6.1 Integral Rates and Cross Sections.- 3.6.2 Angular Distributions of Electrons.- 3.6.3 AC-Stark Shift of Photodetachment Thresholds.- 4. Tunneling Ionization of Atoms.- 4.1 Landau-Dykhne Adiabatic Approximation.- 4.2 Rates of Tunneling Ionization for Atoms and Ions.- 4.3 Energy Spectrum of Electrons.- 4.3.1 Linearly Polarized Radiation.- 4.3.2 Circularly Polarized Radiation.- 4.3.3 Non-Monochromatic Radiation.- 4.3.4 Ponderomotive Acceleration of Electrons.- 4.3.5 Angular Distributions of Ejected Electrons.- 4.4 Above-Barrier Decay of Atoms.- 4.5 Experimental Data and Interpretation.- 4.6 Relativistic Effects.- 5. Direct (Nonresonant) Multiphoton Ionization of Atoms.- 5.1 Multiphoton Ionization of Hydrogen Atom.- 5.1.1 Method of Sturmian Green's Functions.- 5.1.2 Other Methods for Calculation of Multiphoton Cross Sections.- 5.1.3 WKB Approximation for Multiphoton Ionization.- 5.1.4 Experimental Multiphoton Cross Sections of Direct Ionization of Hydrogen Atom.- 5.1.5 Polarization Dependence of Multiphoton Cross Sections.- 5.1.6 Photoelectron Angular Distributions.- 5.2 Alkali Atoms.- 5.2.1 Perturbation Theory Calculations of Multiphoton Cross Sections.- 5.2.2 Experimental Multiphoton Cross Sections.- 5.2.3 Polarization Dependence of Multiphoton Cross Sections.- 5.2.4 Dependence of Multiphoton Cross Sections on the Electron Ejection Angle.- 5.3 Atoms with Many Valence Electrons.- 5.3.1 Structure of Many-Electron Atoms.- 5.3.2 Experimental Multiphoton Ionization Cross Sections for Alkaline-Earth Atoms.- 5.3.3 Experimental and Theoretical Multiphoton Cross Sections for Atoms of Noble Gases.- 5.3.4 Nonperturbational Numerical Calculations.- 5.3.5 Residual Interactions Between Valence Electrons.- 5.3.6 Polarization Dependence of Multiphoton Cross Sections.- 5.3.7 Electron Angular Distributions.- 6. Resonance-Enhanced Ionization.- 6.1 Resonance-Enhanced Ionization in a Weak Field.- 6.2 Field Effects in Resonance-Enhanced Ionization.- 6.2.1 Hydrogen Atom.- 6.2.2 Alkali Atoms.- 6.2.3 Atoms of Noble Gases.- 6.2.4 Rabi Oscillations in Resonance Transitions.- 6.2.5 Non-Monochromatic Fields.- 6.3 Angular Distributions of Photoelectrons in Resonance- Enhanced Multiphoton Ionization of Atoms.- 6.4 Exotic Resonances.- 6.4.1 Quadrupole Resonances.- 6.4.2 Forbidden Resonances.- 6.4.3 Non-Resonant Excitation of Intermediate Resonances.- 6.5 Resonances with Autoionizing States.- 6.5.1 Structure of Autoionizing States.- 6.5.2 Multiphoton Ionization via Autoionizing States.- 6.5.3 Excitation of an Autoionizing State by a Weak Electromagnetic Field.- 6.5.4 Excitation of an Autoionizing State by a Strong Electromagnetic Field.- 6.5.5 Experimental Studies.- 6.6 Further Experiments.- 7. Above-Threshold Ionization of Atoms.- 7.1 The Nature of Above-Threshold Multiphoton Ionization.- 7.2 Compound Matrix Elements for Processes of Kth and (K+ 1)th Orders.- 7.3 WKB Estimates of Dipole Matrix Elements.- 7.4 A Critical Field.- 7.5 Two-Photon Above-Threshold Ionization of a Hydrogen Atom by Radiation of Less than Critical Intensity.- 7.6 Multiphoton Above-Threshold Ionization of a Hydrogen Atom by Radiation of Less than Critical Intensity.- 7.7 Experimental Aspects. Parameters that Influence the Photoelectron Spectra.- 7.7.1 Non-Uniform Space-Time Distribution of the Laser Radiation.- 7.7.2 Laser Pulse Length.- 7.7.3 The Ponderomotive Force in a Long Laser Pulse.- 7.7.4 Charge Density.- 7.7.5 Laser Intensity.- 7.8 Experimental Data for I < Ic.- 7.8.1 Appearance Intensity.- 7.8.2 Nonlinear Power for Electron Production in Various Above-Threshold Maxima.- 7.8.3 Ratio of the Rates for (K + 1)-Photon and K-Photon Processes.- 7.8.4 Electron Angular Distributions in Above- Threshold Maxima. Comparison to Threshold Ionization Peaks Predictions.- 7.9 Theoretical Description of Above-Threshold Ionization at I < Ic.- 7.10 Experimental Data for I > Ic and Their Interpretation.- 7.10.1 Electron Energy Spectra.- 7.10.2 Electron Angular Distributions.- 7.10.3 Dependence of Electron Energy Spectra on the Laser Polarization.- 7.11 Theoretical Interpretation of Electron Energy Spectra for I > Ic.- 7.11.1 Predictions of the Keldysh-Reiss Approach.- 7.11.2 Role of the Atomic Potential.- 7.11.3 Numerical Calculations.- 7.11.4 Method of Essential States.- 7.11.5 Method of Multichannel Above-Threshold Ionization.- 7.11.6 Coulomb-Volkov Approximation.- 7.12 Above-Threshold Ionization by Ultra-Short Laser Pulses.- 7.13 Other Effects.- 7.13.1 Saturation of Above-Threshold Ionization.- 7.13.2 Tunneling Limiting Case.- 7.13.3 Nonlinear Photodetachment of an Electron from a Negative Ion.- 7.13.4 Excitation of Higher Harmonics.- 8. Multiple Ionization of Atoms.- 8.1 Mechanisms of Multiple Ionization.- 8.2 Stepwise Production of Multiply Charged Ions.- 8.2.1 Doubly Charged Ions of Alkaline-Earth Atoms.- a) Method of Electron Spectroscopy.- b) Method of Resonances in the Frequency Dependence of Yields of A+ and A2+ Ions.- 8.2.2 Multiply Charged Ions of Noble Gases.- 8.2.3 Theoretical Description of the Stepwise Production of Multiply Charged Ions.- a) Rate Equations.- b) Multiphoton Ionization Cross Sections of Multiply Charged Ions.- c) Production of an Ion in an Excited State.- 8.2.4 Principal Conclusions on Stepwise Ionization.- 8.3 Simultaneous Detachment of Several Electrons.- 8.3.1 Experimental Data.- 8.3.2 Theoretical Description of Simultaneous Detachment of Several Electrons.- 8.3.3 General Conclusions on Simultaneous Detachment of Electrons.- 8.4 Detachment of Electrons from Inner Shells of Atoms and Ions.- 8.5 Multiple Ionization of Atoms in the Tunneling Limit.- 8.6 Production of Multiply Charged Ions in Laser Fields of Subatomic and Superatomic Intensity.- 8.6.1 Above-Barrier Ionization.- 8.6.2 Models of Multiple Ionization by Subatomic and Superatomic Fields.- a) Thomas-Fermi Model.- b) The Black Body Model.- c) The Model of Independent Electrons.- d) Vaporization Model of Multiple Ionization.- 8.7 Summary.- 9. Ionization by Fields of Subatomic Strength.- 9.1 Definition of an Atomic Field.- 9.2 Ionization of Atom…