Table Of Content13
Springer Series on
Atf:)lUs+Plas.lDas
Editor: P. Lamhropoulos
Springer Series on
-tolDs+Plas.lDas
Editors: G. Ecker P. Lambropoulos 1.1. Sobel'man H. Walther
Managing Editor: H.K.V. Lotsch
Volume 1 Polarized Electrons 2nd Edition
By J. Kessler
Volume 2 Multiphoton Processes
Editors: P. Lambropoulos and S.J. Smith
Volume 3 Atomic Many-Body Theory 2nd Edition
By I. Lindgren and J. Morrison
Volume 4 Elementary Processes in Hydrogen-Helium Plasmas
Cross Sections and Reaction Rate Coefficients
By R.K. Janev, W.D. Langer, K. Evans, Jr. and D.E. Post, Jr.
Volume 5 Pulsed Electrical Discharge in Vacuum
By G.A. Mesyats and D.1. Proskurovsky
Volume 6 Atomic and Molecular Spectroscopy
Basic Aspects and Practical Applications
By S. Svanberg
Volume 7 Interference of Atomic States
By E.B. Alexandrov, M.P. Chaika and G.1. Khvostenko
Volume 8 Plasma Physics Basic Theory with Fusion Applications
By K. Nishikawa and M. Wakatani
Volume 9 Plasma Spectroscopy
The Influence of Microwave and Laser Fields
By E.A. Oks
Volume 10 Film Deposition by Plasma Techniques
By M. Konuma
Volume 11 Resonance Phenomena in Electron-Atom Collisions
By V.L. Lengyel, V.T. Navrotsky and E.P. Sabad
Volume 12 Atomic Spectra and Radiative Transitions 2nd Edition
By 1.1. Sobel'man
Volume 13 Multiphoton Processes in Atoms
By N.B. Delone and V.P. Krainov
N.B. Delone V.P. Krainov
Multiphoton Processes
in Atoms
With 139 Figures and 12 Tables
Springer-Verlag
Berlin Heidelberg New York London Paris
Tokyo Hong Kong Barcelona Budapest
Professor Nikolai B. Delone Professor Vladimir P. Krainov
General Physics Institute Department of Theoretical Physics
Russian Academy of Sciences, 38 Vavilov Street Moscow Institute of Physics and Technology
117942 Moscow, Russia 141700 Dolgopzudny
Moscow Region, Russia
Series Editors:
Professor Dr. Giinter Ecker
Ruhr-Universitat Bochum, Institut fUr Theoretische Physik, Lehrstuhl I, Universitatsstrasse 150,
D-44801 Bochum-Querenburg, Germany
Professor Peter Lambropoulos, Ph.D.
Max-Planck-Institut fUr Quantenoptik
D-85748 Garching, Germany, and
Foundation of Research and Technology - Hellas (FO.R.T.H.)
Institute of Electronic Structure and Laser (IESL) and
University of Crete, PO Box 1527, Heraklion, Crete 71110, Greece
Professor Igor 1. So bel'man
Lebedev Physical Institute, Russian Academy of Sciences,
Leninsky Prospekt 53, Moscow, Russia
Professor Dr. Herbert Walther
Sektion Physik der Universitat Miinchen, Am Coulombwall 1,
D-85748 Garching/Miinchen, Germany
Managing Editor: Dr. Helmut K.V. Lotsch
Springer-Verlag, Tiergartenstrasse 17, D-69121 Heidelberg, Germany
ISBN-13:978-3-642-97511-0 e-ISBN-13: 978-3-642-97509-7
001:10.1007/978-3-642-97509-7
Library of Congress Cataloging-in-Publication Data. Delone, N.B. Multiphoton processes in atoms/N.B.
Delone, V.P. Krainov. p. cm. - (Springer series on atoms + plasmas; 13) Includes bibliographical
references and index. ISBN-13: 978-3-642-97511-0 (New York: alk. paper). 1. Multiphoton processes.
2. Atoms. I. Krainov, V.P. (Vladimir Pavlovich), 1938-. II. Title. III.
Series. QC793.5.P42D45 1993 539.7'5--dc20 93-25345
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Preface
Multiphoton processes in atoms have been investigated both theoretically and
experimentally for more than a quarter of a century. Various stages have been
passed during this period: from fundamental investigations to practical applica
tions in spectroscopy, nonlinear optics, laser engineering, and in the physics of
interaction of laser radiation and matter.
Many papers, reviews, as well as several monographs, have focussed on
multiphoton processes in atoms. We decided to write this book for three
reasons.
The first is to put forth the latest interpretations of recent experimental data.
For example, the book by M.H. Mittleman Introduction to the Theory of
Laser-Atom Interactions (Plenum, New York 1982) contains some experimental
information about multiphoton processes in atoms, but results obtained in the
1980s, of course, are not included. N.B. Delone and V.P. Krainov's Atoms in
Strong Light Fields (Springer, Berlin, Heidelberg 1985) was an expansion of
previous Russian editions (1978 and 1984) where the primary focus is on
experimental methods and approaches for the theoretical description of multi
photon processes. Discussion of physical phenomena was not as detailed as it
should be. Finally, the book of F. Faisal Theory of Multiphoton Processes
(Wiley, New York 1986) contains only a theoretical description of multiphoton
processes; experimental data were discussed only briefly.
The second reason is that in the past few years, important discoveries have
been made in the physics of multiphoton processes in atoms, which have
significantly changed several fundamental theoretical premises. Two examples
are the above-threshold absorption of photons, and the conditions of applicabil
ity of time-dependent perturbation theory.
The final reason is the progress made in laser technology which now allows
superintense electromagnetic fields to be obtained. Of interest here are prob
lems of atomic stability, giant AC-Stark shifts, relativistic effects and so on. We
consider these problems in detail. Thus, we can say that, today, multiphoton
processes in atoms have been investigated sufficiently thoroughly that some new
conclusions can be made. Presenting them is the goal of our book.
Unlike our previous monograph "Atoms in Strong Light Fields" published
by Springer-Verlag, we direct our attention here to the physical phenomena
which occur in the interaction of laser radiation with an isolated atom. In each
chapter we first consider simple systems and then more complex atoms and
models, first dealing with weak electromagnetic fields, then moderate, and
VI Preface
finally superintense fields. Experimental methods and details of theoretical
interpretation are discussed if they are necessary for clarification.
Unfortunately, we cannot do justice to all multiphoton processes in atoms.
We restrict ourselves to mUltiphoton ionization processes. Multiphoton excita
tion and multiphoton scattering are not treated; several other topics are briefly
discussed in the concluding chapter.
In writing this monograph, we often used the Multiphoton Bibliography
(University of Colorado and University of Rochester, 1979-1990), edited by S.
Smith, J.H. Eberly and J. Gallagher, a volume that is very valuable for physicists
working in various areas of atomic and laser physics.
Many of the problems considered in this book were discussed at the Moscow
Seminar for Multiphoton Processes at the General Physics Institute of the
Russian Academy of Sciences. We express our deep gratitude to the participants
of this seminar for useful advice.
Moscow, October 1993 N.B. Delone
V.P. Krainov
Contents
1. Introduction. . . . . . . . . . . . 1
2. AC-Stark Shift of Atomic Levels .. 10
2.1 Single-Level Quantum System 11
2.2 The Linear Stark Shift for a Hydrogen Atom
in an Oscillating Field . . . . . . . . . . . . 13
2.3 Atomic Response to an External Oscillating Field. 14
2.4 The Perturbation of Non-Degenerate Atomic States
in a Weak Field .............. . 16
2.5 Perturbation of the Hydrogen Atom Spectrum
in a Strong Field ............. . 21
2.6 Perturbation of Rydberg States in a Weak Field 24
2.7 Stark Effect in a Super-Atomic Radiation Field 28
2.8 The Stark Atom . . . . . . . . 32
2.9 AC-Stark Shift in Negative Ions 34
2.10 Dynamical Stark Resonance .. 36
2.11 AC-Stark Shift and Ionization . 39
3. Ionization of a Particle with a Short-Range Potential Well 41
3.1 The Keldysh-Faisal-Reiss Approximation 42
3.1.1 The Keldysh Approach .. . 43
3.1.2 The Reiss Approach ....... . 44
3.1.3 Other S-Matrix Approaches 46
3.1.4 Above-Threshold Ionization in Keldysh-Type
Approaches ............... . 47
3.2 Model One-Particle Potentials of Negative Ions 48
3.2.1 Multiphoton Detachment of an Electron from H- 49
3.2.2 Multiphoton Detachment of Electrons
from Complex Negative Ions . . . . . . . . 52
3.3 Residual Interaction Between Electrons ..... 55
3.4 Removal of Internal Electrons from Negative Ions 57
3.5 Numerical Solutions for the Strong-Field Case 58
3.6 Experiments on Multiphoton Detachment
of Negative Ions . . . . . . . . . . . . 60
3.6.1 Integral Rates and Cross Sections 60
3.6.2 Angular Distributions of Electrons 63
3.6.3 AC-Stark Shift of Photodetachment Thresholds 64
VIII Contents
4. Tunneling Ionization of Atoms . . . . . . . . . . . . . 66
4.1 Landau-Dykhne Adiabatic Approximation . . . . 66
4.2 Rates of Tunneling Ionization for Atoms and Ions 68
4.3 Energy Spectrum of Electrons . . . 70
4.3.1 Linearly Polarized Radiation . . 70
4.3.2 Circularly Polarized Radiation . 70
4.3.3 Non-Monochromatic Radiation 71
4.3.4 Ponderomotive Acceleration of Electrons 71
4.3.5 Angular Distributions of Ejected Electrons 73
4.4 Above-Barrier Decay of Atoms 74
4.5 Experimental Data and Interpretation 76
4.6 Relativistic Effects . . . . . . . . . . 78
5. Direct (Nonresonant) Multiphoton Ionization of Atoms 81
5.1 Multiphoton Ionization of Hydrogen Atom 83
5.1.1 Method of Sturmian Green's Functions . . 84
5.1.2 Other Methods for Calculation of M ultiphoton
Cross Sections . . . . . . . . . . . . . . . . 87
5.1.3 WKB Approximation for Multiphoton Ionization 90
5.1.4 Experimental Multiphoton Cross Sections of Direct
Ionization of Hydrogen Atom ..... 94
5.1.5 Polarization Dependence of Multiphoton
Cross Sections . . . . . . . . . . . 94
5.1.6 Photoelectron Angular Distributions . . 97
5.2 Alkali Atoms ................ 98
5.2.1 Perturbation Theory Calculations of Multiphoton
Cross Sections . . . . . . . . . . . . . . . . 99
5.2.2 Experimental Multiphoton Cross Sections 100
5.2.3 Polarization Dependence of Multiphoton Cross
Sections . . . . . . . . . . . . . . . . . 102
5.2.4 Dependence of Multiphoton Cross Sections
on the Electron Ejection Angle . . 103
5.3 Atoms with Many Valence Electrons . . . . . . 106
5.3.1 Structure of Many-Electron Atoms . . . . 107
5.3.2 Experimental Multiphoton Ionization Cross
Sections for Alkaline-Earth Atoms .... 107
5.3.3 Experimental and Theoretical Multiphoton
Cross Sections for Atoms of Noble Gases . 109
5.3.4 Nonperturbational Numerical Calculations 112
5.3.5 Residual Interactions Between Valence Electrons 113
5.3.6 Polarization Dependence of Multiphoton
Cross Sections . . . . . . . . 115
5.3.7 Electron Angular Distributions . . . . . 116
Contents IX
6. Resonance-Enhanced Ionization .......... . 118
6.1 Resonance-Enhanced Ionization in a Weak Field 119
6.2 Field Effects in Resonance-Enhanced Ionization 120
6.2.1 Hydrogen Atom . . . 120
6.2.2 Alkali Atoms ............. . 122
6.2.3 Atoms of Noble Gases ......... . 123
6.2.4 Rabi Oscillations in Resonance Transitions 124
6.2.5 Non-Monochromatic Fields 127
6.3 Angular Distributions of Photoelectrons in Resonance
Enhanced Multiphoton Ionization of Atoms 128
6.4 Exotic Resonances . . . . . . 130
6.4.1 Quadrupole Resonances . . . . . . . 131
6.4.2 Forbidden Resonances ....... . 132
6.4.3 Non-Resonant Excitation of Intermediate
Resonances ......... . 134
6.5 Resonances with Autoionizing States . . . . . 135
6.5.1 Structure of Autoionizing States 136
6.5.2 Multiphoton Ionization via Autoionizing States 137
6.5.3 Excitation of an Autoionizing State by a Weak
Electromagnetic Field ........... . 137
6.5.4 Excitation of an Autoionizing State by a Strong
Electromagnetic Field 140
6.5.5 Experimental Studies 142
6.6 Further Experiments . . . . 145
7. Above-Threshold Ionization of Atoms 147
7.1 The Nature of Above-Threshold Multiphoton Ionization 147
7.2 Compound Matrix Elements for Processes of Kth
and (K + l)th Orders .......... . 148
7.3 WKB Estimates of Dipole Matrix Elements 150
7.4 A Critical Field . . . . . . . . . . . . .. 152
7.5 Two-Photon Above-Threshold Ionization of a Hydrogen
Atom by Radiation of Less than Critical Intensity 153
7.6 Multiphoton Above-Threshold Ionization of a Hydrogen
Atom by Radiation of Less than Critical Intensity 156
7.7 Experimental Aspects. Parameters that Influence the
Photoelectron Spectra . . . . . . . . . . . 157
7.7.1 Non-Uniform Space-Time Distribution
of the Laser Radiation . . . . . . . . 158
7.7.2 Laser Pulse Length ........ . 159
7.7.3 The Ponderomotive Force in a Long Laser Pulse 161
7.7.4 Charge Density 161
7.7.5 Laser Intensity . . . . . 161
7.8 Experimental Data for I < Ie 162
X Contents
7.8.1 Appearance Intensity .......... . 162
7.8.2 Nonlinear Power for Electron Production
in Various Above-Threshold Maxima . . . 162
7.8.3 Ratio of the Rates for (K + I)-Photon and
K-Photon Processes ......... . 162
7.8.4 Electron Angular Distributions in Above-
Threshold Maxima. Comparison
to Threshold Ionization Peaks Predictions 163
7.9 Theoretical Description of Above-Threshold Ionization
at I < Ie ..................... . 165
7.10 Experimental Data for I > Ie and Their Interpretation 168
7.10.1 Electron Energy Spectra ...... . 168
7.10.2 Electron Angular Distributions 170
7.10.3 Dependence of Electron Energy Spectra
on the Laser Polarization . . . . . . . 171
7.11 Theoretical Interpretation of Electron Energy Spectra
for I > Ie ................... . 172
7.11.1 Predictions of the Ke1dysh-Reiss Approach 173
7.11.2 Role of the Atomic Potential 174
7.11.3 Numerical Calculations . . . . . . . . . 175
7.11.4 Method of Essential States ...... . 176
7.11.5 Method of Multichannel Above-Threshold
Ionization ............... 178
7.11.6 Coulomb-Vo lkov Approximation . . . . 179
7.12 Above-Threshold Ionization by Ultra-Short Laser Pulses 179
7.13 Other Effects ................. 181
7.13.1 Saturation of Above-Threshold Ionization . 181
7.13.2 Tunneling Limiting Case ......... 182
7.13.3 Nonlinear Photodetachment of an Electron
from a Negative Ion ..... 182
7.13.4 Excitation of Higher Harmonics 184
8. Multiple Ionization of Atoms ....... 185
8.1 Mechanisms of Multiple Ionization. . 186
8.2 Stepwise Production of Multiply Charged Ions 192
8.2.1 Doubly Charged Ions of Alkaline-Earth Atoms 192
a) Method of Electron Spectroscopy. . . . . 192
b) Method of Resonances in the Frequency Dependence
of Yields of A + and A2+ Ions ........ 196
8.2.2 Multiply Charged Ions of Noble Gases . . . . . . 201
8.2.3 Theoretical Description of the Stepwise Production
of Multiply Charged Ions. . . . . . . . . . . . . 209
a) Rate Equations. . . . . . . . . . . . . . . . 210
b) Multiphoton Ionization Cross Sections of MUltiply
Charged Ions ............. 212
c) Production of an Ion in an Excited State . . . .. 213
