Supercomputing, Collision
Processes, and Applications
PHYSICS OF ATOMS AND MOLECULES
Series Editors
P. G. Burke, The Queen’s University of Belfast, Northern Ireland
H. Kleinpoppen, Atomic Physics Laboratory, University of Stirling, Scotland
Editorial Advisory Board
R. B. Bernstein (New York, U.S.A.)
J. C. Cohen-Tannoudji (Paris, France)
R. W. Crompton (Canberra, Australia)
Y. N. Demkov (St. Petersburg, Russia)
C. J. Joachain (Brussels, Belgium)
W. E. Lamb, Jr. (Tucson, U.S.A.)
P.-O. Löwdin (Gainesville, U.S.A.)
H. O. Lutz (Bielefeld, Germany)
M. C. Standage (Brisbane, Australia)
K. Takayanagi (Tokyo, Japan)
Recent volumes in this series:
COINCIDENCE STUDIES OF ELECTRON AND PHOTON IMPACT IONIZATION
Edited by Colm T. Whelan and H. R. J. Walters
DENSITY MATRIX THEORY AND APPLICATIONS, SECOND EDITION
Karl Blum
ELECTRON MOMENTUM SPECTROSCOPY
Erich Weigold and Ian McCarthy
IMPACT SPECTROPOLARIMETRIC SENSING
S. A. Kazantsev, A. G. Petrashen, and N. M. Firstova
INTRODUCTION TO THE THEORY OF X-RAY AND ELECTRONIC SPECTRA OF FREE
ATOMS
Roman Karazjia
PHOTON AND ELECTRON COLLISION WITH ATOMS AND MOLECULES
Edited by Philip G. Burke and Charles J. Joachain
PRACTICAL SPECTROSCOPY OF HIGH-FREQUENCY DISCHARGES
Sergei A. Kazantsev, Vyacheslav I. Khutorshchikov, Günter H. Guthöhrlein, and Laurentius
Windholz
SELECTED TOPICS ON ELECTRON PHYSICS
Edited by D. Murray Campbell and Hans Kleinpoppen
SUPERCOMPUTING, COLLISION PROCESSES, AND APPLICATIONS
Edited by Bell, Berrington, Crothers, Hibbert, and Taylor
THEORY OF ELECTRON-ATOM COLLISIONS, PART I: POTENTIAL SCATTERING
Philip G. Burke and Charles J. Joachain
VUV AND SOFT-X-RAY PHOTOIONIZATION
Edited by Uwe Becker and David A. Shirley
A Chronological Listing of Volumes in this series appears at the back of this volume.
A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume
immediately upon publication. Volumes are billed only upon actual shipment. For further information please
contact the publisher.
Supercomputing, Collision
Processes, and Applications
Edited by
Kenneth L. Bell, Keith A. Berrington,
Derrick S. F. Crothers, Alan Hibbert,
and Kenneth T. Taylor
The Queen’s University of Belfast
Belfast, Northern Ireland
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Preface
Professor Philip G. Burke, CBE, FRS formally retired on 30 September
1998. To recognise this occasion some of his colleagues, friends, and former
students decided to hold a conference in his honour and to present this
volume as a dedication to his enormous contribution to the theoretical
atomic physics community. The conference and this volume of the invited
talks reflect very closely those areas with which he has mostly been associated and his influence internationally on the development of atomic physics
coupled with a parallel growth in supercomputing.
Phil’s wide range of interests include electron-atom/molecule collisions,
scattering of photons and electrons by molecules adsorbed on surfaces,
collisions involving oriented and chiral molecules, and the development of
non-perturbative methods for studying multiphoton processes. His development of the theory associated with such processes has enabled important
advances to be made in our understanding of the associated physics, the
interpretation of experimental data, has been invaluable in application to
fusion processes, and the study of astrophysical plasmas (observed by both
ground- and space-based telescopes).
We therefore offer this volume as our token of affection and respect to
Philip G. Burke, with the hope that it may also fill a gap in the literature in
these important fields.
K. L. Bell
K. A. Berrington
D. S. F. Crothers
A. Hibbert
K. T. Taylor
v
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Contents
1. Fifty Years of Atomic and Molecular Collision Theory
1
A. Dalgarno
2. Electron-Atom Resonances
F. H. Read
9
3. Recent Progress in Electron-Atom Scattering
I. Bray
15
4. Benchmark Studies in Electron-Impact Excitation of Atoms
K. Bartschat
33
5. A Model Adiabatic Potential to Study Shapes and Locations
of Single Particle Resonances: The Case of Electron-Ozone
Scattering
F. A. Gianturco, R. R. Lucchese, and N. Sanna
6.
Aspects of an Ab Initio Approach to Electron Scattering
by Small Molecules
T. N. Rescigno
7. Atoms in Intense Laser Fields
C. J. Joachain
51
67
77
8. Manipulating Small Molecules with Intense Laser Fields
J. H. Posthumus, K. Codling, and L. J. Frasinski
105
9. Matrix Methods
I. S. Duff
119
vii
10. Elastic Electron Collision with Chiral and Oriented
Molecules
K. Blum, M. Musigmann, and D. Thompson
137
11. Positron Scattering by Atoms
B. H. Brandsen
155
12. From Positron to Positronium Scattering
G. Laricchia, A. J. Garner, and K. Paludan
171
13. Embedding and R-Matrix Methods at Surfaces
J. E. Inglesfield
183
14. Negative Ion Resonance of Molecules on Surfaces:
From Spectroscopy to Dynamics
L. Šiller and R. E. Palmer
197
15. BERTHA—4-Component Relativistic Molecular Quantum
Mechanics
I. P. Grant
213
16. JET Applications of Atomic Collisions
H. P. Summers, R. W. P. McWhirter, H. Anderson,
C. F. Maggi, and M. G. O’Mullane
225
17. Radiation Pressure and Element Diffusion in Stellar Interiors
M. J. Seaton
249
18. Atomic Physics of Muon-Catalyzed Fusion
I. Shimamura
269
Index
279
FIFTY YEARS OF ATOMIC AND MOLECULAR COLLISION THEORY
A. Dalgarno
Harvard-Smithsonian Center for Astrophysics
60 Garden Street
Cambridge, MA 02138
USA
Atomic, Molecular and Optical (AMO) Physics is about photons, electrons and positrons,
positive and negative ions, atoms and molecules and their mutual interactions. There are two
major strands of inquiry in AMO Physics: studies of spectra and studies of collisions. In
spectroscopic measurements, ions, atoms and molecules emit or absorb electromagnetic
radiation. Electromagnetic radiation consists of light waves and waves have wavelengths that
can be measured by spectroscopic instruments. Our eyes are spectroscopic instruments with
which we can distinguish colours increasing in wavelength from the violet to the red.
Butterflies see in the ultraviolet which lies at the short wavelength side of the violet. At much
shorter wavelengths are X-rays and
At wavelengths longer than red are the infrared,
millimetre and radio waves. The major impetus for the revolution in scientific thought that
culminated in the formulation of quantum mechanics was driven by measurements of the
spectrum of radiation emitted by hydrogen atoms. To explain the observation that narrow
features appeared at specific wavelengths, Niels Bohr in 1913 gave up classical mechanics
and in its place he invoked the idea that the electron in a hydrogen atom occupies only certain
discrete orbits in its motion about the central nucleus, in contrast to classical mechanics
according to which all orbits are allowed. Then radiative transitions between these stationary
states of the electron produce spectral lines at specific wavelengths as observed. Earlier,
Planck’s theory of the thermal radiation emitted by a hot object had invoked the idea of
discrete quantized energy modes but no one, least of all Planck, envisaged the theory as more
than a temporary empirical fix that was needed to reproduce the measurements that had been
made at long wavelengths. However, Planck’s quantum theory of radiation is correct and it
helped to establish a fundamental concept of quantum mechanics, the duality of particles and
waves; in the case of electromagnetic waves, the particles are photons.
Spectroscopy is the major diagnostic probe in science. The wavelength of a spectral line
is a unique property of the emitting or absorbing ion, atom or molecule and its presence in the
spectrum identifies definitively the species. By measuring the spectra of an object, near or
remote, the elements of which the object is made can be determined. The Astrophysical
Journal was launched in 1895 with the subtitle “An International Review of Spectroscopy and
Astronomical Physics”.
The spectral line positions depend on the velocity of the emitter or absorber.
Measurements of spectral lines emitted by stars in external galaxies reveal shifts in the
wavelengths. The lines are red-shifted from which we conclude that all galaxies are moving
away from us and the space of the Universe is expanding.
The other major strand of research in AMO Physics and indeed other disciplines of
Physics is the study of the collisions of beams of particles. One of the most famous
experiments in physics was the measurement by Rutherford of the angular distribution of a
beam of
scattered by a thin foil. It demonstrated that at the centre of an atom lies a
Supercomputing, Collision Processes, and Applications
edited by Bell et al., Kluwer Academic / Plenum Publishers, New York, 1999
1
heavy nucleus. Once we had learnt to control beams of particles—for charged particles like
electrons and positive ions, electric and magnetic fields could be used—it became possible to
explore the properties of atoms and molecules by using them as targets and measuring what
happens when the beams collide with them. The quantization of the electron orbits in atoms,
indicated by the spectroscopic data, was confirmed by the measurement of discrete energy
losses in collisions of an electron beam with atoms. The duality of particles and waves was
confirmed by experiments in which electrons showed wave-like properties of interference and
diffraction. With continued technical improvements and a better understanding of the
behaviour of particle beams, measurements of the collision of one particle beam with another
could be performed. Particle beams have provided a general exploratory tool of enormous
power and versatility that has greatly extended our knowledge of physical processes and has
led to new technologies. Today collisions at extremely high energies generated in accelerators
are the principal experimental tool for investigations of elementary particles and the
fundamental laws and symmetries of physics. Led by Brian Gilbody, Queen’s University has
housed a distinguished research program, studying collisions of high energy multicharged ion
beams.
Spectroscopy and collisions are not independent and each may be intimately involved in
the other. Collisions taking place in the presence of radiation fields can be modified by them,
raising the possibility of controlling the outcome of reactions by judicious use of photon
beams. Photoionization, a process in which photons are absorbed and electrons are ejected
and photodissociation, a process in which photons are absorbed and the molecules are broken
into their constituent atoms, are examples of collision processes initiated by radiation, of
particular interest today with the advent of laser sources that generate intense electromagnetic
fields.
Spectroscopy and collisions are combined in investigations of ionized gases which are
gases in which some of the atoms have lost electrons and exist as positive ions and some may
have gained an electron and exist as negative ions. Spectral lines can be used to establish
which of the ionization stages are present. Ionized gases are plasmas and they range from
weakly ionized of the kind investigated at Queen’s by Bill Graham and his collaborators to
very nearly fully ionized as in fusion plasmas. The Universe can be regarded as ionized
plasma, embedded in which are galaxies, stars and planets.
Historically the study of plasmas began with the exploration of electrical discharges in
gases which led Thompson to the discovery of the electron one hundred years ago. Today
plasma processing technologies comprise a substantial industrial activity of major economic
importance.
Plasmas are extraordinarily complex and interesting phenomena and we are far from
achieving a fully quantitative picture of them. They exist or can be produced in a wide range
of physical conditions of composition, temperature, density and radiation fields. To model
their behaviour involves the identification of the multitude of atomic, molecular and optical
processes that together are responsible. The efficiency with which the processes occur must
then be determined quantitatively by experimental measurement or by theoretical calculations.
AMO Physics has changed dramatically over the past fifty years. In 1948, Volumes 60
and 61 together occupying 1000 pages were published in the Proceedings of the Physical
Society of London. They dealt with all of Physics The articles were mostly concerned with
measurements of the properties of materials in solid and liquid form. An example is a
measurement of the dielectric constant of water at centimetre wavelengths reported by C.H.
Collie, J. B. Hasted and D.M. Ritson. I mention it in particular because John Hasted was one
of the experimenters who led in the resurgence of AMO physics that has taken place in the last
half century. Volume 60 of the Proceedings contained short papers on the spectra of the alkali
metal pairs
and NaK, on the dissociation energy of nitric oxide and on the structure of
carbon monoxide and a long paper on collision-broadening of ammonia in gases. There were
three theoretical papers by Charles Coulson and his collaborators on momentum distributions
in atoms and on the electronic structure of the conjugated molecules napthalene, anthracene,
coronene and pirene, which happen to be of current astrophysical interest because of the
possible existence of polycyclic aromatic hydrocarbons (PAHs) in the interstellar space of our
Galaxy. The volume included one paper on gas discharges by L.B. Loeb, discussing the
mechanism of spark breakdown. Setting aside the discussions of PAHs as chemistry, other
than gas discharge physics AMO Physics occupied 36 pages of volume 60. Volume 61 is
noteworthy because of a paper by R. H. Sloane and C. S. Watt presenting some intriguing
results on the negative ions emitted from oxide-coated cathodes. The measurements were
2
carried out in the Department of Physics here. Both Sloane and Watt became long term
members of the faculty at Queen’s. Volume 61 included a paper on the initiation of low
pressure glow discharges by J. D. Craggs and J. H. Meek. These two papers took 32 pages.
The only other paper in AMO Physics is a Letter of two pages on the spectrum of silver iodide
by R. F. Barrow and M. F. R. Mulcahy. Thus in 1948, the Proceedings of the Physical
Society devoted a total of 38 pages out of 1000 to AMO physics, if I exclude papers on gas
discharges, 70 if I include them.
In 1949, it was decided to split the journal into parts A and B. Part A included quantum
theory, atomic physics, molecules and spectra. The areas of application of AMO physics,
electric discharges, astrophysics, radio, geo- and ionosphere physics and solar physics were
to be in Part B. The total AMO content in 1949 in Part A was 38 pages again, mostly on
measurements of molecular spectra and quantum mechanical calculations of momentum wave
functions. Part B, though ostensibly not dealing with atomic physics or spectra, contained a
paper on spectroscopic observations of pyrotechnic glows and a paper describing experiments
on photoionization in gases. Including them, AMO physics occupied 55 pages of Volume 62.
Ten years later, in 1958, it was decided that the separation of the subject matter of
Physics into two sections had led to an undesirable fragmentation and Parts A and B were
reunited into a single publication. Volumes 71 and 72 of the Proceedings of the Physical
Society were published that year. The number of pages was 2200 pages of which 312 were
AMO Physics. The number of pages may not seem large but for AMO Physics it represented
an increase by a factor of six in ten years. It signaled perhaps the end of an era in which it
had been possible for an individual to pick up an issue of the journal and expect to read all the
papers it contained on AMO Physics. I note in passing that amongst the authors of papers in
Volumes 71 and 72 those forty years ago were Brian Bransden, Benno Moisewitsch, Michael
Seaton, Arthur Kingston and myself, all present at this conference.
The growth continued and in 1968 the editors of the Proceedings gave up the unequal
struggle and the Proceedings was again separated into sections. The Journal of Physics B
emerged as the section devoted to Atomic and Molecular Physics. It contained 1250 pages, an
increase in ten years by a factor of four. In 1978, there were 5000 pages. The number of
pages remained at about 5000 through to 1988. In 1988, the title was enlarged to Journal of
Physics B (Atomic, Molecular and Optical Physics) to reflect the changing distribution of
research brought about by the use of lasers and other sophisticated optical techniques. The
number of pages then increased steadly and in 1998, we can expect 7000 pages. The
comparable journal in the United States, Physical Review A, will contain about 10,000 pages,
but the pages are larger. There has also occurred a proliferation of more specialised journals.
We now have time barely to read the titles of papers. The expansion in AMO Physics is
surely not over. The fundamental discoveries and the technological applications that will arise
from explorations of coherence and control, ultracold atoms and molecules, Bose-Einstein
condensation, hollow atoms, atom interferometry, atom manipulation, atom lasers, X-ray
lasers, intense fields, quantum computation and plasma manipulation and not least
enhancements in computer power ensure the continued growth of AMO Physics.
Although physics and indeed most of science is driven by experiments, theory has a
central role to play in providing a simplifying, logical framework, into which the results of
different experiments can be incorporated and which provides a prescription for the prediction
of physical phenomena. The theory is expressed as laws or principles, written in the form of
mathematical equations. It is the responsibility of theory not only to write down the equations
but also to solve them. Only by comparing the solutions with measurements can we be sure
the equations are in fact correct and complete. Indeed, many advances in physics have
stemmed from small differences found between theoretical predictions and experimental
measurements. Theory is needed also for practical reasons. The data base of AMO processes
required for applications to other sciences and technologies is so vast it cannot be supplied by
experiments. Experiments provide crucial tests of the accuracy of theoretical predictions, but
theory must be the principal future source of AMO data.
Fifty years ago saw the stirrings of the revolution that was to be brought about by the
realisation of the electronic digital computer. Before and during the war, calculations were
done mainly by pencil and paper aided by tables of mathematical functions and by a manual
analogue computing device called a slide rule. Much effort had to be given to the ongoing
detection and correction of errors as they inevitably occurred, because of the heavy price that
would be paid if an error were to propagate deeply into the serial computation. The entire
calculation from the point at which the error occurred would have to be repeated, hand
3
operation by hand operation.
Slide rules were often used. They had the advantage of being readily transportable. In a
biographical memoir, Sir David Bates mentions Sir Harrie Massey’s custom of travelling with
a slide rule and a notepad, computing as he went.
Electric analogue computers in the form of differential analysers existed but they were
complicated to assemble and unreliable in operation. They met with some success in solving
differential equations. Sir Harrie Massey and Sir David Bates used a differential analyzer built
in the Physics Department at Queen’s in 1938 by a highly skilled technician, John Wyler, to
solve equations arising in the theory of the photoionization of atomic oxygen.
By 1948, manually operated mechanical calculating machines were widely available. The
more fortunate individuals had access to versions with electric motors but computation
remained an extraordinarily tedious activity. But it had to be done. Experiments are
ultimately presented as numbers and numbers are what theory must provide for comparison.
To inject some interest into the process, students would sometimes indulge in races to see
who could, for example, solve correctly a selected differential equation in the shortest time.
In these competitions, the error rate increased rapidly with computing speed and the race often
went to the slowest. Fortunately for the sanity of theorists, the period between electric and
electronic machines was mercifully short, or so it seems in retrospect.
The emphasis in theoretical research in AMO Physics was on the invention of
approximations and methods that whilst preserving the physical content of the problem
yielded mathematical expressions and procedures that were computationally tractable. In a
sense this is still the emphasis and still the challenge, but the speed, scale and complexity of
what is practicable have been enormously enhanced with no end yet in sight. There has
occurred a corresponding increase in the rapidity and flexibility of communication.
Computers can be accessed remotely and computers at different locations can be brought to
bear simultaneously on a common research problem. National and international networks,
both formal and informal, have become a powerful unifying force in scientific research.
The challenges in responding to these dramatic changes in the computing environment
and exerting control over its direction have been formidable. In AMO Physics, many have
contributed but we would all agree that Philip Burke has been an intellectual leader at the many
fronts of the enterprise. He has exhibited sophisticated skills and creativity in mathematical
and numerical analysis, designing new mathematical approaches and numerical procedures in
a mutual relationship that has been uniquely productive. Philip began his career with
pioneering studies of the scattering of nuclei but soon took up what was to be his major
interest, the much more versatile field of electron and photon collisions with atoms, ions and
molecules.
His work is measured not only by his publications, extensive though they are, but also
by the personal influence he has had on the research of his fellow scientists throughout the
world and on the training of the next generation. I leave aside Philip’s services in
administrative capacities and his participation as a member of advisory committees, except to
remark that his wise counsel been of the utmost importance in ensuring scientific access in the
United Kingdom to the developing computer power as it came into being.
The history of the theory of scattering is one of increasingly elaborate formulations in
which more and more of the physical mechanisms were included, but it had to be done in such
a way that the resulting mathematical expressions were accessible to numerical computation.
It began with the Born approximation. Scattering is characterised by cross sections which
depend on the initial and final states of the target and which depend on the velocity of the
projectile electron. In the Born approximation for excitation or ionization of the target, it is
assumed that the transition is driven by a single direct interaction of the electron as it passes
the target. There is a change in the momentum of the electron but its path is not disturbed by
the target. If the electron is moving rapidly, the physical description, represented
mathematically by the Born approximation, is accurate. Given the initial and final target
wavefunctions, the Born approximation cross sections can be obtained by numerical
quadrature. For elastic scattering there is no change in the electron momentum during the
collision. The Born approximation again reduces to a simple quadrature. Quadrature is a
relatively simple numerical exercise.
Electrons are fermions and in scattering, the projectile electron and any one of the
electrons of the target can interchange places. Antisymmetrising the total wave function yields
the Born-Oppenheimer approximation. The resulting expression can still be evaluated by
quadrature but the formula has severe defects and the results are unreliable. There is a
4
modification called the Born-Ochkur approximation that leads to some improvement and is
easier to calculate. The Born approximation often failed at low collision energies, yielding
cross sections that were much too large. The worst of its excesses could be restrained by an
extension that preserved the unitarity of the scattering matrix, as noted by Michael Seaton and
Valerie Burke, or by the use of the eikonal Born series as developed by Fred Byron and
Charles Joachain.
More of the physics is contained in another approximation, the distorted wave
approximation. It takes account of the modification in the path of the electron arising from its
interaction with the electrostatic distribution of the target. In its antisymmetrised version, it
becomes the exchange distorted wave approximation. It is an extension of the single
configuration Hartree-Fock method for bound states to the continuum. The mathematics can
be reduced to ordinary second order differential equations which can with some effort be
solved by numerical integration. Variational methods could be used in place of direct
numerical integration and they offered the prospect of a more elaborate description of the
physics whilst being somewhat easier to implement
A significant improvement to the theory for electron scattering by complex atoms was the
extension by Michael Seaton of multiconfiguration Hartree-Fock theory. However, HartreeFock omits some physics that is important at low energies. The slowly moving electron
polarises the target and the polarised target acts back on the motion of the electron, producing
an attractive long range polarization force. The inclusion in the physics of polarization and
exchange forces led to the successful explanation of the mysterious Ramsauer effect in which
the scattering cross section is observed to pass through a minimum as the electron energy is
increased.
The distorted wave approximation works well for weak interactions but it does not allow
for the transition to reverse during the transit of the electron. That requires a balanced
approximation in which the initial and final states are treated with equal accuracy. Studies of
the coupled equations in limiting circumstances had been reported by Massey and Mohr and
by Seaton in the Proceedings of the Physical Society, which demonstrated the importance of
coupling in the excitation mechanism, but numerically we are faced with a demanding task.
Still more demanding is the problem if we take the obvious conceptual step of expanding to a
multi-state description which allows physically for the possibility of excitation by virtual
transitions into and out of many states.
Progress would have been limited except for the advent of electronic digital computers.
Responding to the new opportunity, in 1960 and 1961 Philip Burke, Kenneth Smith, Valerie
Burke, Ian Percival, Ronald McCarroll and Harry Schey used the early electronic digital
computers, the IBM 704 and the English Electric DEUCE machines, to solve by direct
numerical integration the close-coupled set of equations that arises in the multistate
formulation of the scattering of electrons by hydrogen atoms. The results were published in
the Proceedings of the Physical Society and the Physical Review. This achievement
transformed the theoretical study of electron and photon collisions with atoms and ions into a
different kind of activity. In place of an effort to understand the principal mechanism at work
in a particular process, a systematic investigation could be undertaken of the possibilities by
exploring numerically the effects of different choices of basis sets. The calculations raised the
hope that theory could have a predictive capacity, a hope that has been amply demonstrated by
Michael Seaton’s Opacity Project and by the talks presented at this conference.
Theory can also predict new phenomena.The close-coupling equations quickly revealed
the presence of structure in cross sections that could be attributed to long-lived resonance
states formed during the collision by the capture of the electron in temporary bound states that
subsequently decayed. Thus numerical studies, rather than being simply a support of
established theory, stimulated the discovery of new concepts needed for the physical
interpretation of the features revealed by the calculations. With the extension of the closecoupling methods to complex ions and atoms, the dominating role of these resonance states in
electron impact excitation was demonstrated. Resonance states lead to the processes of
autoionization and dielectronic recombination which affect the ionization balance in plasmas.
The close-coupling method was soon extended by Philip Burke and Sydney Geltman by
the addition of pseudo-states to the multi-state expansion. Suitably chosen pseudo-states
provide a correct account of correlation and polarization. However because the final state has
two continuum electrons, electron impact ionization poses a more severe theoretical problem
which is still under active investigation.
Setting up the close-coupled equations for a complex system, especially when relativistic
5
effects are included, is a demanding mathematical exercise, but still greater difficulties attend
the construction of a reliable convergent procedure for the numerical integration of the
equations. A method of great power and capable of generalization to a wide range of atomic
and molecular problems is the R-matrix method introduced into AMO Physics by Philip
Burke, Alan Hibbert and Derek Robb. A much greater variety of processes can occur when
photons and electrons interact with molecules. Molecules lack spherical symmetry, the nuclei
also move, and the theoretical problems are formidable. Nevertheless, the R-matrix method
has been extended to molecular systems and substantial progress has been made in developing
numerical codes that combine methods of scattering theory and quantum chemistry.
The power of the R-matrix method and the super power of supercomputers open up new
areas of investigation to direct numerical attack. The R-matrix method has been extended to
treat the behaviour of atoms and molecules in intense radiation fields and to include the
additional dimension of time. Time-dependent studies in which systems can be followed as
they evolve from different initial conditions will enlarge and deepen our understanding of the
physics of AMO processes and open new pathways of research.
AMO Physics is integral to a broad range of scientific and technological disciplines and
its growth in the past fifty years has been matched by its increased utility as a diagnostic probe
and as an instrument for predicting the response of materials to disturbances induced by
electric fields, radiation fields and dynamical interactions.
Rather than attempt a necessarily superficial summary of the vast array of the applications
of AMO Physics, I will take a specific example from my own particular interests and consider
the physics of the supernova 1987a. On February 23, 1987, the core of a blue supergiant star
in the Large Magellanic Cloud collapsed and the star exploded. It was the brightest supernova
since the invention of the telescope, the first from which neutrinos were detected and the first
for which molecules were found in the ejecta. The progenitor star had also been observed.
The event was a major happening in astronomy. Supernovae are believed to be the source of
the elements heavier than iron found on Earth and the source of the energetic cosmic rays that
bombard the Earth. SN 1987a enabled a decisive test to be made of theories of
nucleosynthesis in stellar explosions.
Other than the neutrinos, all our information about the supernova comes from the
electromagnetic radiation emitted by the object and the supernova can be regarded as an
evolving laboratory of atomic and molecular physics. The light curve, which is the total
energy emitted in the optical and infrared regions of the spectra, established that the principal
source of luminous energy is the decay of radioactive 56Co which is itself a product of the
decay of 56Ni. The decay time of 56 Co is 111.26 days which closely matches the decay of
the light curve. At times beyond 1200 days, it is replaced by 57Co which has a lifetime of
1.07 years. After 1500 days, the decay of radioactive 44Ti which has a lifetime of
years takes over as the main source of energy. The decay products are
and positrons.
The
scatter in collisions with the free and the bound electrons, producing X-rays and
fast electrons. The electrons and the positrons collide with the ions, atoms and molecules in
the ejecta, producing the light that is observed. Several years into the evolution of the ejecta,
the steadily diminishing particle density allows the
to escape and the main energy
source is the positrons, which slow down in collisions and annihilate, producing the 511 keV
line. Spectral analysis of the light reveals features that can be identified with specific elements.
Thus H, He, Ni, Co, Fe, O, Si, Mg, Na and Ca have all been identified in SN 1987a, the
detection of Ni and Co confirming their role in energising the ejecta.
Of unique value is the evolutionary nature of the object. Changes in the emission
spectrum can be followed over long periods of time. Because of the expansion of the ejecta
and the loss of energy by radiation, the material cools with age and there has been a shift of
the thermal part of the emission to longer wavelengths. The emission line of FeII at a
wavelength of 715.5 nm, strong in the beginning, is now no longer detectable.
The spectrum shows that the elements are present as neutral atoms and singly ionized.
The high ionization stages produced in the initial blast must have been removed by radiative
and dielectronic recombination and by charge transfer recombination, once some neutral
material had formed.
The ionization of the atoms arises from collisions with the fast electrons and positrons
and the relative abundances of neutral and ionized material is determined by the ionization
across sections. The excitation of the levels emitting the spectra that are measured has three
sources. Low-lying levels are populated by thermal collisions. High-lying levels are
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populated by electron recombination and by direct impact excitation by the electrons and
positrons. Given reliable cross sections we can infer the element abundances and test the
models of nucleosynthesis. The physics has similarities to the physics of terrestrial auroras.
Thus the oxygen doublet at 630.0 nm and 636.4 nm is a characteristic feature of the spectrum
and it is produced mostly by electron impact. The doublet of ionized oxygen near 372.7 nm,
produced in auroras by simultaneous excitation and ionization of neutral oxygen, is also seen
in the supernova. A striking example of the importance of reliable AMO data is provided by
the observation that the sodium doublet at 589 nm has a strength comparable to the oxygen red
lines. Yet the nuclear models suggest that oxygen will be two orders of magnitude more
abundant than sodium. The resolution must be that the excitation cross section for electron
impact excitation of sodium is one hundred times larger than that for oxygen.
The spectra contain information about the progenitor star, the supernova explosion, the
nucleosynthesis of the elements, the chemistry of molecule and dust formation, the dynamics
of the expanding ejecta and possibly the contribution to the energy supply from the neutron
star left behind by the explosion. AMO Physics, particularly of the kind discussed at this
conference, is central to finding the answers to the many questions that remain.
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ELECTRON-ATOM RESONANCES
Frank H Read
Department of Physics and Astronomy
University of Manchester
Manchester M13 9PL, UK
THE FIRST OBSERVATIONS OF ELECTRON-ATOM RESONANCES
Prof. Philip Burke has been a leader in the subject of electron-atom scattering resonances
since the beginning of the subject in 1961. He provided (with Schey) the first clear
theoretical evidence1 for the existence of such resonances, as shown in Fig. 1. Using a closecoupling approximation it was found that the s-wave phase shift for scattering of electrons by
hydrogen atoms increases steeply just below the energy of the first excited state. This was
interpreted as being due to a narrow ‘Breit-Wigner’ resonance. About three months earlier
Smith et al2 had published a less conclusive result -the single critical point that showed a
significant increase in the elastic scattering cross section below the first excited state had been
slow to converge (taking 10hrs of computing time).
The first published experimental evidence for the existence of an electron-atom
resonance is that of Schulz3, reproduced in Fig. 2. A clear dip in the elastic scattering cross
section, followed by a peak, is observed at an energy of approximately 19.4eV, below the
energy of the first excited state at 19.8eV. Soon afterwards Fleming and Higginson4
published a less precise observation of this resonance, using a simpler transmission
experiment.
The asymmetric shape of the e-He resonance structure is analogous to that observed
earlier by Silverman and Lassettre (although not published openly until 19645) in electron
impact excitation of autoionizing states of helium, which had been interpreted by Fano6 as the
interference of a resonant and a direct (ie non-resonant) scattering mechanism, giving the
now-famous ‘Fano profile’.
The first theoretical and experimental observations of electron-atom resonances all
appear to have been ‘accidental’, in the sense that they were not being looked for, although
scattering resonances were at that time well known in nuclear physics and also the existence
of broad peaks in the scattering of low-energy electrons by molecules such as
had been
known for many years. It is told for example that Schulz observed the e-He resonance when
he was looking for a cusp at the energy of the first excited state, which he was unable to see
Supercomputing, Collision Processes, and Applications
edited by Bell et al., Kluwer Academic / Plenum Publishers, New York, 1999
9
(and much later Cvejanovic et al7 accidentally obtained the first clear observation of this cusp
when they were looking at the resonance).
RECENT RESULTS
The subject continues to be well studied, and the Belfast group continues to maintain a
leading position8,9. A new generation of high resolution studies has started in which laser
excitation of atomic negative ions is used, for example in helium to reach narrow quartet
resonance states from a metastable quartet state10. In the Manchester group we have recently
completed a thorough exploration of the He doublet states in neutral helium that lie below the
(N=3) threshold, by inelastic electron scattering from the He ground state. There is
considerable overlapping of these states and so to deduce their individual energies and widths
it is necessary to use a range of different incident energies and scattering angles. A
representative result is shown in Fig. 3. It has been possible to deduce the energies and
widths of 13 states in this energy region, most of which have not previously been measured.
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