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3 Atomic Many-Body Theory 2nd Edition By I. Lindgren and J. Morrison

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.

5 Pulsed Electrical Discharge in Vacuum By G. A. Mesyats and D. I. Proskurovsky

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12 Atomic Spectra and Radiative Transitions 2nd Edition By I. I. Sobel'man

13 Multiphoton Processes in Atoms 2nd Edition By N. B. Delone and V. P. Krainov

14 Atoms in Plasmas By V. S. Lisitsa

15 Excitation of Atoms and Broadening of Spectral Lines 2nd Edition By I. I. Sobel'man, L. Vainshtein, and E. Yukov

16 Reference Data on Multicharged Ions By V. G. Pal'chikov and V. P. Shevelko

17 Lectures on Non-linear Plasm Kinetics By V. N. Tsytovich

18 Atoms and Their Spectroscopic Properties By V. P. Shevelko

19 X-Ray Radiation of Highly Charged Ions By H. F. Beyer, H.-J. Kluge, and V. P. Shevelko

20 Electron Emission in Heavy Ion-Atom Collision By N. Stolterfoht. R. D. DuBois. and R. D. Rivarola

21 Moleeules and Their Spectroscopic Properties By S. V. Khristenko, A. I. Maslov. and V. P. Shevelko

22 Physics of Highly Excited Atoms and Ions By V. S. Lebedev and I. L. Beigman

23 Atomic Multielectron Processes By V. P. Shevelko and H. Tawara

24 Guided Wave Produced Plasmas By H. Schlüter, Y. M. Aliev, and A. Shivarova

25 Quantum Statistics of Strongly Coupled Plasmas By D. Kremp, W. Kraef!. und M. Schlanges

26 Atomic Physics witb Heavy Ions By H. F. Beyer and V. P. Shevelko

N.B. Delone V.P. Krainov

Multiphoton Processes in Atoms

Second Enlarged and Updated Edition

With 122 Figures and 11 rabies

Springer

Professor Nikolai B. Delone General Physics Institute

Professor Vladimir P. Krainov Oepartment of Theoretical Physics

Russian Academy of Sciences. 38 Vavilov Street 117942 Moscow. Russia

Moscow Institue of Physics and Technology 141700 Oolgoprudny Moscow Region. Russi ..

Series Editors:

Professor Dr. Günter Ecker . Ruhr-Universität Bochulll. Fakultät für Physik und Astronomie. Lehrstuhl Theoretische Physik I. Universitätsstrasse 150. 0-44801 Bochum. Germany

Professor Peter Lambropoulos, Pb. D. Max-Planck-Institut für Quantenoptik. 0-85748 Garehing, Germany. and Foundation for Research and Technology - Hellas (FO.R.T.H.), Institute of Electronic Structure & Laser (IESL), University ofCrete. PO Box 1527. Heraklion, Crete 71110, Greece

Professor Jürgen Mlynek Universität Konstanz. Universitätsstr. 10 0-78434 Konstanz. Germany

Professor Dr. Herbert WaItber Sektion Physik der Universität München, Am Coulombwall I, 0-85748 Garching/München. Germany

Library of Congress Cataloging-in-Publication Oata

Oelone, N. B. Multipholon processes in atoms I N.B. Oelone, V.P. Krainov. - 2nd enl. and updatet ed. p. cm. - (Springer series on atoms + plasmas. ISSN 0177-6495: (3) Includes bibliographieal referenees and index. ISBN 978-3-642-62969-3 (alk. paper) I. Mulliphoton proeesses. 2. Atoms. I. Krainov, V.P. (Vladimir Pavlovich). 1938- . 11. Title. 111. Series. QC793.5.P42045 1999 539.7 -- dc21 99-39037

CIP ISSN 0177-6495 ISBN 978-3-642-62969-3 ISBN 978-3-642-57208-1 (eBook) DOI 10.1007/978-3-642-57208-1

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© Springer-Verlag Berlin Heidelberg 1994.2000 Originally published by Springer-Verlag Berlin Heidelberg New York in 2000

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Preface to Second Edition

The first edition of this book had been written by us in the end of 1992. During the next five years the investigations of interaction between intense laser radiation and atoms produced a lot of new and important results. The goal of this second edition is to generalize these new results.

The second edition does not differ substantially from the first on in contents and distribution of the thematics among the chapters. Only one change should be noted: The new Chapter 9 "Atoms in Super-Intense Laser Fields" has been written instead of the old three Chapters 9-11. It contains a review of the new experimental and theoretical data obtained during the last five years. New results appeared practically in all directions of investigations. However, most of these results had been obtained with super-intense laser fields. We describe these results in the new Chapter 9.

We stress once more that the title of this book is more general than it should be, since it is devoted to multiphoton ionization processes only. The volume of this book would be twice as large if the physics of multi photon excitation of atoms and the nonlinear scattering of light by atoms is to be included.

We express our deep gratitude to many colleages for valuable discussions of various problems considered in this book. Systematical discussions of the laser­atom physics at the Moscow Weekly Seminar for Multiphoton Processes at the General Physics Institute of the Russian Academy of Sciences were very useful for us.

Moscow, January 1999 N.B. Delone, V.P. Krainov

Preface to First Edition

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 applica­tions 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 Laser­Atom 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 multiphoton 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 applicability 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 problems 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

VIII Preface to First Edition

dealing with weak electromagnetic fields, then moderate, and 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 excitation and multi photon 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

Table of Contents

1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 AC-Stark Shift of Atomic Levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11 2.1 Single-Level Quantum System. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 12 2.2 The Linear Stark Shift for a Hydrogen Atom

in an Oscillating Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 14 2.3 Atomic Response to an External Oscillating Field .... . . . . . . . .. 15 2.4 The Perturbation of Non-Degenerate Atomic States

in a Weak Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 17 2.5 Perturbation of the Hydrogen Atom Spectrum in a Strong Field.. 22 2.6 Perturbation of Rydberg States in a Weak Field . . . . . . . . . . . . . .. 25 2.7 Stark Effect in a Super-Atomic Radiation Field ............... 28 2.8 The Stark Atom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 33 2.9 AC-Stark Shift in Negative Ions. . . . . . . . . . . . . . . . . . . . . . . . . . .. 34 2.10 Dynamical Stark Resonance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37 2.11 AC-Stark Shift and Ionization ............................. 40

3 Ionization of a Particle with a Short-Range Potential Well. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 43 3.1 The Keldysh-Faisal-Reiss Approximation. . . . . . . . . . . . . . . . . . .. 44

3.1.1 The Keldysh Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 45 3.1.2 The Reiss Approach ............................. .. 46 3.1.3 Other S-Matrix Approaches. . . . . . . . . . . . . . . . . . . . . . . .. 48 3.1.4 Above-Threshold Ionization in Keldysh-Type Approaches. 49

3.2 Model One-Particle Potentials of Negative Ions. . . . . . . . . . . . . .. 50 3.2.1 Multiphoton Detachment of an Electron from H- ....... 51 3.2.2 Multiphoton Detachment of Electrons from Complex

Negative Ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 54 3.3 Residual Interaction Between Electrons. . . . . . . . . . . . . . . . . . . . .. 57 3.4 Removal of Internal Electrons from Negative Ions. . . . . . . . . . . .. 59 3.5 Numerical Solutions for the Strong-Field Case. . . . . . . . . . . . . . .. 60 3.6 Experiments on Multiphoton Detachment of Negative Ions. . . . .. 62

3.6.1 Integral Rates and Cross Sections. . . . . . . . . . . . . . . . . . .. 62 3.6.2 Angular Distributions of Electrons. . . . . . . . . . . . . . . . . . .. 65

X Table of Contents

3.6.3 AC-Stark Shift of Photodetachment Thresholds ......... 65

4 Tunneling Ionization of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69 4.1 Landau-Dykhne Adiabatic Approximation ................... 69 4.2 Rates of Tunneling Ionization for Atoms and Ions. . . . . . . . . . . .. 71 4.3 Energy Spectrum of Electrons ............................. 73

4.3.1 Linearly Polarized Radiation ........................ 73 4.3.2 Circularly Polarized Radiation . . . . . . . . . . . . . . . . . . . . . .. 73 4.3.3 Non-Monochromatic Radiation. . . . . . . . . . . . . . . . . . . . . .. 74 4.3.4 Ponderomotive Acceleration of Electrons. . . . . . . . . . . . .. 74 4.3.5 Angular Distributions of Ejected Electrons . . . . . . . . . . . .. 76

4.4 Above-Barrier Decay of Atoms ........... . . . . . . . . . . . . . . . .. 77 4.5 Experimental Data and Interpretation. . . . . . . . . . . . . . . . . . . . . . .. 78 4.6 Relativistic Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81

5 Direct (Nonresonant) Multiphoton Ionization of Atoms. . . . . . . . . .. 85 5.1 Multiphoton Ionization of Hydrogen Atom. . . . . . . . . . . . . . . . . .. 87

5.1.1 Method of Sturrnian Green's Functions. . . . . . . . . . . . . . .. 88 5.1.2 Other Methods for Calculation of Multiphoton Cross

Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92 5.1.3 WKB Approximation for Multiphoton Ionization. . . . . . .. 95 5.1.4 Experimental Multiphoton Cross Sections of Direct

Ionization of Hydrogen Atom. . . . . . . . . . . . . . . . . . . . . . .. 98 5.1.5 Polarization Dependence of Multiphoton Cross Sections.. 99 5.1.6 Photoelectron Angular Distributions .................. 101

5.2 Alkali Atoms ........................................... 102 5.2.1 Perturbation Theory Calculations of Multiphoton Cross

Sections .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 103 5.2.2 Experimental Multiphoton Cross Sections .............. 104 5.2.3 Polarization Dependence of Multiphoton Cross Sections .. 106 5.2.4 Dependence of Multiphoton Cross Sections

on the Electron Ejection Angle ...................... 107 5.3 Atoms with Many Valence Electrons ........................ 110

5.3.1 Structure of Many-Electron Atoms ................... 110 5.3.2 Experimental Multiphoton Ionization Cross Sections for

Alkaline-Earth Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 111 5.3.3 Experimental and Theoretical Multiphoton Cross Sections

for Atoms of Noble Gases .......................... 113 5.3.4 Nonperturbational Numerical Calculations ............. 116 5.3.5 Residual Interactions Between Valence Electrons ........ 117 5.3.6 Polarization Dependence of Multiphoton Cross Sections .. 119 5.3.7 Electron Angular Distributions ....................... 120

6 Resonance-Enhanced Ionization ............................... 123 6.1 Resonance-Enhanced Ionization in a Weak Field .............. 124

Table of Contents XI

6.2 Field Effects in Resonance-Enhanced Ionization ............... 125 6.2.1 Hydrogen Atom ................................... 125 6.2.2 Alkali Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 127 6.2.3 Atoms of Noble Gases ............................. 128 6.2.4 Rabi Oscillations in Resonance Transitions ............. 129 6.2.5 Non-Monochromatic Fields ......................... 132

6.3 Angular Distributions of Photoelectrons ..................... 133 6.4 Exotic Resonances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 135

6.4.1 Quadrupole Resonances ............................ 136 6.4.2 Forbidden Resonances. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 137 6.4.3 Non-Resonant Excitation of Intermediate Resonances .... 139

6.5 Resonances with Autoionizing States ........................ 140 6.5.1 Structure of Autoionizing States. . . . . . . . . . . . . . . . . . . . .. 140 6.5.2 Multiphoton Ionization via Autoionizing States ......... 141 6.5.3 Excitation of an Autoionizing State by a Weak

Electromagnetic Field .............................. 143 6.5.4 Excitation of an Autoionizing State by a Strong

Electromagnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 145 6.5.5 Experimental Studies ............................... 146

6.6 Further Experiments ..................................... 150

7 Above-Threshold Ionization of Atoms . ......................... 151 7.1 The Nature of Above-Threshold Multiphoton Ionization ........ 151 7.2 Compound Matrix Elements for Processes of Kth and (K + l)th

Orders ................. , ............................... 152 7.3 WKB Estimates of Dipole Matrix Elements .................. 154 7.4 A Critical Field ......................................... 156 7.5 Two-Photon Above-Threshold Ionization of a Hydrogen Atom ... 156 7.6 Multiphoton Above-Threshold Ionization .................... 159 7.7 Experimental Aspects .................................... 161

7.7.1 Non-Uniform Space-Time Distribution of the Laser Radiation ........................................ 162

7.7.2 Laser Pulse Length ................................ 162 7.7.3 The Ponderomotive Force in a Long Laser Pulse ........ 164 7.7.4 Charge Density ................................... 164 7.7.5 Laser Intensity .................................... 164

7.8 Experimental Data for I < Ie .............................. 165 7.8.1 Appearance Intensity ............................... 165 7.8.2 Nonlinear Power for Electron Production

in Various Above-Threshold Maxima ................. 165 7.8.3 Ratio of the Rates for (K + I)-Photon

and K-Photon Processes ............................ 166 7.8.4 Electron Angular Distributions in Above-Threshold

Maxima. Comparison to Threshold Ionization Peaks Predictions ....................................... 166

XII Table of Contents

7.9 Theoretical Description of Above-Threshold Ionization at I < Ie 169 7.10 Experimental Data for I < Ie and Their Interpretation. . . . . . . . .. 171

7.10.1 Electron Energy Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . .. 171 7.1 0.2 Electron Angular Distributions. . . . . . . . . . . . . . . . . . . . . .. 172 7.10.3 Dependence of Electron Energy Spectra

on the Laser Polarization ........................... 173 7.11 Theoretical Interpretation of Electron Energy Spectra for I > Ie .. 176

7.11.1 Predictions of the Keldysh-Reiss Approach ............. 176 7.11.2 Role of the Atomic Potential ........................ 178 7.11. 3 Numerical Calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 178 7.11.4 Method of Essential States . . . . . . . . . . . . . . . . . . . . . . . . .. 179 7.11.5 Method of Multichannel Above-Threshold Ionization .... 182 7.11.6 Coulomb-Volkov Approximation. . . . . . . . . . . . . . . . . . . .. 182

7 .12 Above-Threshold Ionization by Ultra-Short Laser Pulses. . . . . . .. 182 7.13 Other Effects .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 184

7.13.1 Saturation of Above-Threshold Ionization. . . . . . . . . . . . .. 184 7.13.2 Tunneling Limiting Case. . . . . . . . . . . . . . . . . . . . . . . . . . .. 185 7.13.3 Nonlinear Photodetachment of an Electron

from a Negative Ion ............................... 185 7.13.4 Excitation of Higher Harmonics ...................... 186

8 Multiple Ionization of Atoms ................................. 189 8.1 Mechanisms of Multiple Ionization ......................... 190 8.2 Stepwise Production of Multiply Charged Ions ............... : 196

8.2.1 Doubly Charged Ions of Alkaline-Earth Atoms ......... 196 8.2.2 Multiply Charged Ions of Noble Gases ................ 204 8.2.3 Theoretical Description of the Stepwise Production

of Multiply Charged Ions ........................... 213 8.2.4 Principal Conclusions on Stepwise Ionization ........... 221

8.3 Simultaneous Detachment of Several Electrons ................ 221 8.3.1 Experimental Data ................................. 222 8.3.2 Theoretical Description of Simultaneous Detachment

of Several Electrons ............................... 226 8.3.3 General Conclusions on Simultaneous Detachment

of Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 8.4 Detachment of Electrons from Inner Shells of Atoms and Ions ... 233 8.5 Multiple Ionization of Atoms in the Tunneling Limit ........... 241 8.6 Summary .............................................. 244

9 Atoms in Super-Intense Laser Fields . .......................... 247 9.1 Multiphoton Ionization ................................... 247 9.2 Above-Barrier Ionization .................................. 251

9.2.1 New Experimental Data ............................ 251 9.2.2 Rescattering Effects in AT! .......................... 252 9.2.3 Plateau in AT! Spectra ............................. 254

Table of Contents XIII

9.3 Tunneling and Barrier-Suppression Ionization ................. 257 9.3.1 Rescattering of Tunneling Electrons ................... 257 9.3.2 Barrier-Suppression Ionization ....................... 260 9.3.3 Relativistic Effects ................................ 265 9.3.4 New Experimerital Data and Their Interpretation ........ 269

9.4 Ionization by Superintense Laser Fields ...................... 274 9.4.1 Classification of Possible Stabilization ................. 275 9.4.2 Numerical Calculations ............................. 278 9.4.3 The Kramers-Henneberger Approximation ............. 279 9.4.4 Interference Stabilization of Rydberg Atoms ............ 284 9.4.5 Experimental Data ................................. 289

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Subject Index .................................................. 313