Atoms and Molecules in Strong External Fields Atoms and Molecules in Strong External Fields Edited by P. Schmelcher University of H eidelberg Heidelberg, Germany and W. Schweizer University of Tübingen Tübingen, Germany KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBookISBN: 0-306-47074-8 Print ISBN: 0-306-45811-X ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://www.kluweronline.com and Kluwer's eBookstore at: http://www.ebooks.kluweronline.com PREFACE This book contains contributions to the 172. WE-Heraeus-Seminar “Atoms and Molecules in Strong External Fields,” which took place April 7–11 1997 at the Physik- zentrum Bad Honnef (Germany). The designation “strong fields” applies to external static magnetic, and/or electric fields that are sufficiently intense to cause alterations in the atomic or molecular struc- ture and dynamics. The specific topics treated are the behavior and properties of atoms in strong static fields, the fundamental aspects and electronic structure of molecules in strong magnetic fields, the dynamics and aspects of chaos in highly excited Ryd- berg atoms in external fields, matter in the atmosphere of astrophysical objects (white dwarfs, neutron stars), and quantum nanostructures in strong magnetic fields. It is obvious that the elaboration of the corresponding properties in these regimes causes the greatest difficulties, and is incomplete even today. Present-day technology has made it possible for many research groups to study the behavior of matter in strong external fields, both experimentally and theoreti- cally, where the phrase “experimentally” includes the astronomical observations. Un- derstanding these systems requires the development of modern theories and powerful computational techniques. Interdisciplinary collaborations will be helpful and useful in developing more efficient methods to understand these important systems. Hence the idea was to bring together people from different fields like atomic and molecular physics, theoretical chemistry, astrophysics and all those colleagues interested in aspects of few-body systems in external fields. In combination or individually, the articles present a broad and timely review of the recent progress and the current state of the art in the theoretical, computational, and experimental studies of atoms and molecules in strong external fields. Astrophysical aspects related to magnetic white dwarfs and neutron stars are discussed. The com- putational problems in the strong field regime where the valence electrons experience electric and magnetic forces of comparable strength are discussed, and some new and effective methods based on discretization and finite element methods as well as novel basis set approaches are presented. New experiments of Rydberg states in strong external fields are reported and re- lated theoretical and computational aspects as well as the quest of quantum chaos are discussed. Attention is drawn to the non-separability of the center-of-mass for atomic and molecular systems in strong magnetic fields. This non-separability gives rise to effects important in the Rydberg as well as in the astrophysical region. But not only atoms and molecules in strong magnetic fields are reviewed; this book is rounded off by the discussion of quantum dots and shallow donor states in strong magnetic fields. Due to the scientific importance of the subject we hope that the articles presented v in this book will prove valuable to a wide scientific audience, ranging from the expe- rienced researcher to the newcomer. The 172. WE-Heraeus-Seminar brought together about 50 scientists from many countries. As scientific organizers, we wish to thank them for their participation, their presentation, and their enthusiasm, which created a very stimulating and scientifically fruitful atmosphere. We would like to express our thanks to Jutta Hartmann and Dr. Volker Schafer from the WE-Heraeus-Stiftung for the unbureaucratic procedure of funding, general organization and realization, and, of course, to the founders Dr. Wilhelm Heinrich Heraeus and Else Heraeus. We thank the Deutsche Forschungsgemeinschaft for their financial support for the East-European participants. Tübingen and Heidelberg W. Schweizer P. Schmelcher vi CONTENTS White Dwarfs for Physicists ................................................... 1 D. Koester Magnetic WhiteDwarfs: Observations in CosmicLaboratories ................... 9 S. Jordan Hydrogen in Strong Electric and Magnetic Fields and Its Application to Magnetic White Dwarfs.............................................................. 19 S. Friedrich, P. Faßbinder, I. Seipp and W. Schweizer Helium Data for Strong Magnetic Fields Obtained by Finite Element Calculations 25 M. Braun, W. Schweizer and H. Elster The Spectrum of Atomic Hydrogen in Magnetic and Electric Fields of White Dwarf Stars ................................................................. 31 Peter Faßbinder and Wolfgang Schweizer Neutron Star Atmospheres ........................................................ 37 G. Pavlov Hydrogen Atoms in Neutron Star Atmospheres: Analytical Approximations for Binding Energies ........................................................... 49 A. Y. Potekhin Absorption of Normal Modes in a Strongly Magnetized Hydrogen Gas ........... 55 T. Bulik and G. Pavlov Electronic Structure of Light Elements in Strong Magnetic Fields ................ 61 Patrice Pourre, Philippe Arnault and Francois Perrot From Field-Free Atoms to Finite Molecular Chains in Very Strong Magnetic Fields..................................................................... 69 M. R. Godefroid The National High Magnetic Field Laboratory — a Précis ........................ 77 J. E. Crow, J. R. Sabin and N. S. Sullivan Self-Adaptive Finite Element Techniques for Stable Bound Matter–Antimatter Systems in Crossed Electric and Magnetic Fields ........................... 83 J. Ackermann vii A Computational Method for Quantum Dynamics of a Three-Dimensional Atom in Strong Fields ........................................................... 89 V. S. Melezhik Discretization Techniques Applied to Atoms Under Extreme Conditions.......... 95 W. Schweizer, M. Stehle, P. Faßbinder, S. Kulla, I. Seipp and R. Gonzalez Computer-Algebraic Derivation of Atomic Feynman–Goldstone Expansions ...... 101 S. Fritzsche, B. Fricke and W.-D. Sepp Scaled-Energy Spectroscopy of Helium and Barium Rydberg Atoms in External Fields ....................................................................... 109 W. Hogervorst, A. Kips, K. Karremans, T. van der Veldt, G. J. Kuik and W. Vassen Atoms in Crossed Fields ......................................................... 121 J.-P. Connerade, K. T. Taylor, G. Droungas, N. E. Karapanagiati, M. S. Zhan, and J. Rao Hydrogen-Like Ions Moving in a Strong Magnetic Field........................... 135 V. G. Bezchastnov, G. G. Pavlov and J. Ventura Center-of-Mass Effects on Atoms in Magnetic Fields .............................. 141 D. Baye and M. Vincke Scaling Properties for Atoms in External Fields ................................... 153 H. Friedrich Time Independent and Time Dependent States of Atoms in Static External Fields 169 P. F. O’Mahony, I. Moser, F. Mota-Furtado and J. P. dos Santos Secular Motion of 3-D Rydberg States in a Microwave Field ...................... 181 A. Buchleitner Spontaneous Decay of Nondispersive Wave Packets............................... 187 K. Hornberger and A. Buchleitner lonization of Helium by Static Electric Fields and Short Pulses................... 193 A. Scrinzi Adiabatic Invariants of Rydberg Electrons in Crossed Fields...................... 199 J. von Milczewski and T. Uzer Highly Excited Charged Two-Body Systems in a Magnetic Field: A Perturbation Theoretical Approach to the Classical Dynamics ............................ 207 W. Becken and P. Schmelchcr Analysis of Quantum Spectra by Harmonic Inversion ............................. 215 J. Main, G. Wunner, V. A. Mandelshtam and H. S. Taylor Atoms in External Fields: Ghost Orbits, Catastrophes, and Uniform Semiclassical Approximations ............................................... 223 J. Main and G. Wunner viii Quadratic Zeeman Splitting of Highly Excited Relativistic Atomic Hydrogen ..... 233 D. A. Arbatsky and P. A. Braun Neutral Two-Body Systems of Charged Particles in External Fields .............. 241 L. S. Cederbaurn and P. Schmelcher Semiclassical Theory of Multielectron Atoms and the Molecular Ion in Intense External Fields ...................................................... 255 N. H. March On the Ground State of the Hydrogen Molecule in a Strong Magnetic Field ...... 265 P. Schmelcher and T. Detmer Hydrogen Molecule in Magnetic Fields: On Excited Sigma States of the Parallel Configuration.............................................................. 275 T. Detmer, P. Schmelcher, F. K. Diakonos and L. S. Cederbaum Electronic Properties of Molecules in High Magnetic Fields: Hypermagnetizabilities of .............................................. 283 K. Runge and J. R. Sabin Shallow DonorStatesinaMagneticField ....................................... 291 T. O. Klaassen, J. L. Dunn and C. A. Bates Quantum Dots in Strong Magnetic Fields........................................ 301 P. A. Maksym Density Functional Theory of Quantum Dots in a Magnetic Field ................ 313 M. Ferconi and G. Vignale An Analytical Approach to the Problem of an Impurity Electron in a Quantum Well in the Presence of Electric and Strong Magnetic Fields ................ 319 B. S. Monozon, C. A. Bates and J. L. Dunn List of Participants ................................................................ 327 Index .............................................................................. 333 ix Atoms and Molecules in Strong External Fields