Astronomy-Inspired Atomic and Molecular Physics

252 Pages·2003·6.354 MB·English

by  A. R. P. Rau (auth.)

ASTRONOMY-INSPIRED ATOMIC AND MOLECULAR PHYSICS
ASTROPHYSICS AND
SPACE SCIENCE LIBRARY
VOLUME 271
EDITORIAL BOARD
Chairman
W. B. BURTON, National Radio Astronomy Observatory, Charlottesville, Virginia, U.S.A.
[email protected];
University of Leiden, The Netherlands
[email protected]
Executive Committee
J. M. E. KUIJPERS, Faculty of Science, Nijmegen, The Netherlands
E. P. J. VAN DEN HEUVEL, Astronomical Institute, University of Amsterdam,
The Netherlands
H. VAN DER LAAN, Astronomical Institute, University ofUtrecht,
The Netherlands
MEMBERS
I. APPENZELLER, Landessternwarte Heidelberg-Königstuhl, Germany
J. N. BAHCALL, The Institute for Advanced Study, Princeton, U.S.A.
F. BERTOLA, Universitá di Padova, Italy
J. P. CASSINELLI, University ofWisconsin, Madison, U.S.A.
C. J. CESARSKY, Centre d’Etudes de Saclay, Gif-sur-Yvette Cedex, France
O. ENGVOLD, Institute of Theoretical Astrophysics, University of Oslo, Norway
R. McCRAY, University of Colorado, JILA, Boulder, U.S.A.
P. G. MURDIN, Institute of Astronomy, Cambridge, U.K.
F. PACINI, Istituto Astronomia Arcetri, Firenze, Italy
V. RADHAKRISHNAN, Raman Research Institute, Bangalore, India
K. SATO, School of Science, The University ofTokyo, Japan
F. H. SHU, University of California, Berkeley, U.S.A.
B. V. SOMOV, Astronomical Institute, Moscow State University, Russia
R. A. SUNYAEV, Space Research Institute, Moscow, Russia
Y. TANAKA, Institute of Space & Astronautical Science, Kanagawa, Japan
S. TREMAINE, CITA, Princeton University, U.S.A.
N. O. WEISS, University of Cambridge, U.K.
ASTRONOMY-INSPIRED
ATOMIC
AND MOLECULAR PHYSICS
by
A.R.P. RAU
Department of Physics and Astronomy,
LouisianaState University, BatonRouge, U.S.A.
KLUWER ACADEMIC PUBLISHERS
NEW YORK,BOSTON, DORDRECHT, LONDON, MOSCOW
eBookISBN: 0-306-47820-X
Print ISBN: 1-4020-0467-2
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Contents
Preface ix
1. ATOMIC STRUCTURE 1
1 Beginnings 1
2 The Hydrogen Atom 3
2.1 Eigenstates in the spherical representation 3
2.2 High symmetry of the hydrogen atom,
separation in parabolic coordinates 6
3 The Two-electron Atom 8
3.1 The ground state of helium 9
3.2 Excited states 12
3.3 Configuration interaction 16
4 Heavier Atoms 17
4.1 Configurations and states 17
4.2 Simple screening pictures 20
4.3 The Thomas-Fermi self-consistent field model 22
4.4 Exact treatments: Hartree-Fock and
configuration interaction 28
5 Line Spectra and Their Uses 30
5.1 Atomic spectra in astronomy 30
5.2 Doppler shifts ofspectral lines 34
Problems 37
2. COUPLING OF ATOMS TO RADIATION 41
1 Introduction 41
2 Photoabsorption and Photoemission 42
2.1 The Oscillator strength 43
v
vi ASTRONOMY-INSPIRED ATOMIC AND MOLECULAR PHYSICS
2.2 Alternative forms of the dipole
matrixelement 46
2.3 Selection rules 49
2.4 Moments and sum rules 53
3 Charged-particle Collisions 55
3.1 The Generalized Oscillator strength 55
3.2 Total cross-section 59
4 The Negative Ion of Hydrogen 60
4.1 The ground state of 61
4.2 Photodetachment of 63
4.3 Radiative capture 64
Problems 66
3. ATOMS IN WEAK, STATIC FIELDS 69
1 Introduction 69
2 External Electric and Magnetic Fields 70
2.1 Coupling to external fields 70
2.2 Time-independent perturbation theory 71
2.3 The Stark effect 76
2.4 The Zeeman effect 78
3 Internal Perturbations in an Atom 82
3.1 Relativistic mass correction 82
3.2 Spin-orbit coupling 83
3.3 Other corrections 84
Problems 85
4. ATOMS IN STRONG MAGNETIC FIELDS 87
1 Introduction 87
1.1 Free electrons in a magnetic field 88
2 Excited States in a Magnetic Field 91
2.1 Basic Hamiltonian and spectrum 91
2.2 Degenerate perturbation theory in
an 97
2.3 Large-scale numerical calculations 106
2.4 Quasi-classical JWKB analysis 110
2.5 Rydberg diamagnetism in other atoms 114
3 Strong Field Effects on Low-lying States 114
3.1 Introduction 114
3.2 Hydrogen in an ultrastrong magnetic field 115
Contents vii
3.3 Complex atoms in ultrastrong fields 122
3.4 Complex atoms in very strong,
but not ultrastrong, fields 126
4 Strong Magnetic Fields in Astronomy 131
Problems 133
5. ELECTRON CORRELATIONS 135
1 Introduction 135
2 Electron Correlations 136
2.1 Qualitative picture 136
2.2 The spectrum of He and 137
2.3 Experimental observation 141
3 Hyperspherical Coordinates 142
3.1 Coulomb potential and hyperspherical
harmonics in six dimensions 149
3.2 Adiabatic hyperspherical method 151
3.3 Description of resonances 156
3.4 High-lying doubly-excited states and double
ionization 161
4 Dielectronic Recombination 164
Problems 167
6. DIATOMIC MOLECULES 169
1 Introduction 169
2 Structure of Diatomic Molecules 170
2.1 Basic mechanism and nomenclature
of covalent bonds 170
2.2 Molecular orbitals and states of simple
diatomic molecules 173
2.3 The Born-Oppenheimer approximation 176
2.4 Rotations and vibrations of the internuclear axis 179
2.5 Anharmonicities and rotation-vibration
coupling 182
2.6 Parity of molecular states 184
2.7 Effect of nuclear spin 185
3 Molecular Spectra 187
3.1 Rotational spectra 187
3.2 Vibrational spectra 189
3.3 Raman spectra 192
3.4 Electronic spectra 193
viii ASTRONOMY-INSPIRED ATOMIC AND MOLECULAR PHYSICS
3.5 External field effects on molecular spectra 199
3.6 Collisional processes 199
4 Astrophysical Applications 200
Problems 205
7. POLYATOMIC MOLECULES 207
1 Introduction 207
2 Structure and Spectra of Polyatomic Molecules 207
2.1 Born-Oppenheimer approximation and
electronicstructure 207
2.2 Rotation of polyatomic molecules
and spectra 211
2.3 Vibrations of polyatomic molecules 215
2.4 Degeneracies and rovibronic couplings 221
3 Astrophysical Applications 224
Problems 227
References 229
Index 233
Preface
This book deals with topics in atomic and molecular structure and
dynamics that are important to astronomy. Indeed, the topics selected
are of central interest to the field of astronomy, many having been ini-
tiated by the needs of understanding worlds other than ours. Except
for some lunar surface material returned by the Apollo missions, and
material naturally delivered to us by cosmic rays, comets, and mete-
ors, our only access to the other worlds of our astronomical Universe is
through our observations of electromagnetic radiation from them. (Very
recently, neutrinos from the Sun and supernovae have also been studied,
and there are hopes for observations of gravitational waves in the next
decades.)
Overwhelmingly, therefore, our knowledge of the astronomical world is
derived from the emission, absorption, and scattering of electromagnetic
radiation from atoms and molecules. We “touch” and discern the mate-
rial content of these distant objects only through such absorptions and
emissions. As a result, there is a strong coupling between the subjects
of astronomy and atomic and molecular physics. Indeed, a major theme
for this book is that at several times, both in the beginnings of these sub-
jects and continuing today, atomic and molecular problems have been
directly stimulated, even initiated, by the needs of astronomy. In turn,
of course, they have proved vital to astronomy. It seemed appropriate,
therefore, to compile a primer on atomic and molecular physics within
this context of astronomy. The focus is on the basic physics of atoms and
molecules with a sample of their astronomical applications. This book
is designed as a possible textbook for a course in atomic physics for
students in astronomy programs, either at the senior undergraduate or
first-year graduate school level in U.S. universities, or their equivalents.
The only preparation presumed is of knowledge of quantum physics at
the level of a one semester- or year-long undergraduate course. Each
ix