Computational Challenges in Atomic and Molecular Physics
Organizers: Mitch Pindzola (Auburn), Bill McCurdy (LBL), Kate Kirby (ITAMP)
May 4-6, 2000
Dr. Anthony J. Baltz
Prof. Klaus Bartschat
Professor P. G. Burke
Prof. Shih-I Chu
Dr. Michael D. Crisp
Dr. Mark Edwards
Prof. Charlotte F. Fischer
Prof. Chris Greene
Dr. Robert J. Harrison
Prof. Martin Head-Gordon
Prof. Lars E. Hernquist
Prof. Jeffrey L.Krause
Dr. C. William McCurdy
Dr. Dario Mitnik
Dr. Esmond G. Ng
Prof. Michael S. Pindzola
Dr. Thomas N. Rescigno
Prof. Francis J. Robicheaux
Dr. Eric A. Rohlfing
Dr. Barry I. Schneider
Dr. Dave R. Schultz
Dr. Rick Stevens
Professor K. T. A. (Ken) Taylor
Prof. Jonathan Tennyson
Calculation of Pair Production and Ionization Induced by Relativistic Heavy Ions
Anthony J. Baltz
Early nonpertrubative coupled channels calculations of bound-electron positron pair production induced by heavy ion collisions showed an enhancement of some 2 orders of magnitude over corresponding perturbation theory calculations at small impact parameters for Pb +Pb reactions at relatively low relativistic energies (e.g. g = 2.3). These calculations aroused significant interest due to the anticipated large rates of pair production with an electron captured into a bound state of one of the pair of fully stripped ions in a collider such as the Brookhaven Relativistic Heavy-Ion Collider (RHIC) or the CERN Large Hadron Collider (LHC). The capture process provides an important limit on the beam lifetime since change of the charge of an ion leads to the loss of that ion from the beam.
An extensive investigation of bound-electron positron pair production in the coupled channels framework was undertaken at the ultrarelativistic energies of RHIC (g = 23,000). While a nonperturbative enhancement remained in calculations made with the largest basis size available, it decreased with basis size and was found to be only of order 10% of the total cross section.
The subsequent discovery that the ultrarelativistic electomagnetic heavy ion interaction takes a delta function form in the longitudinal light-cone coordinate has made possible exact semiclassical calculations for bound-electron positron pair production, single electron ionization, and continuum pair production. Calculations showed that in the ultrarelativistic limit there is no enhancement over perturbation theory for bound-electron positron pair production; there is in fact a small reduction in the exact calculation. The inferred failure of the coupled channels method in the ultrarelativistic limit leads one to question more generally the utility of coupled channels for calculating nonperturbative effects.
Exact semiclassical calculations of single electron ionization compared with previous calculations in the literature indicate that using exact Dirac wave functions for the bound states is at least as important as calculating nonperturbative effects. Comparison of theoretical calculations for ionization can be made with available fixed target data from CERN.
The exact amplitude for continuum pair production has been obtained in closed form. From the derived exact form, pair multiplicity rates are seen to differ from perturbation theory. Actual calculations by Hencken, Trautmann, and Baur making use of the closed form have shown that exact pair multiplicities are in fact smaller than perturbation theory.
Computer Simulations of Excitation, Ionization, and Ionization--Excitation in Electron--Atom Collisions
Department of Physics and Astronomy
Recent developments in the formal description and the numerical treatment of electron collisions with atoms and ions, together with the rapid growth in computer hardware, has opened the opportunity for benchmark comparisons between experimental data and theoretical predictions. For electron scattering from relatively simple (quasi-)one-electron and (quasi-)two-electron targets, the Schrödinger equation can now be solved with high accuracy by using time-independent close-coupling-type approaches with a large number of physical and pseudo-states or direct time-dependent lattice methods. While these approaches, particularly the "convergent close-coupling'' (CCC) and the "R-matrix with pseudo-states'' (RMPS) methods, have been very successful in the treatment of the collision processes mentioned above and therefore present a basis for attacking more challenging problems, the current situation is much less satisfactory for more complex targets such as the heavier noble gases, cesium, or mercury. Examples will be presented for these latter cases which demonstrate some success but also the need for further theoretical development. Even for collision systems where one-electron excitation seems to be well understood, ionization problems continue to present major challenges, particularly if the residual ion is left in an excited state or if multiple ionization occurs. Other challenges, of great practical importance for many applications, include ionization from excited initial states. For the latter processes, the currently available database for either experimental or theoretical results is very small. Furthermore, in the rare cases where a comparison is possible, there remain major discrepancies between experimental data and theoretical predictions. Finally, ways of visualizing the outcome of certain collision processes by using animated computer graphics to represent the charge cloud of collisionally excited atomic states (see http://bartschat.drake.edu/dloveall for details) will be shown.
*This work is supported by the National Science Foundation.
Atomic and Molecular R-matrix Calculations: Computational Challenges
P G Burke
Department of Applied Mathematics &
Over the last 25 years computer codes based on the R-matrix method have been used to describe a wide range of atomic, molecular and optical processes . This has enabled data of importance in many applications in astronomy, laser physics, atmospheric physics and plasma physics to be calculated. However in spite of this success many computational challenges of crucial importance in applications need to be addressed. These include:
(i) cross sections for electron and photon collisions with atoms, ions and molecules are urgently required at intermediate energies. A recently developed R-matrix with pseudo-states (RMPS) approach has been used with success for studying collisions with light atoms and ions  but requires the inclusion of hundreds or even thousands of coupled channels to obtain accurate results for complex targets;
(ii) electron collision strengths with complex ions are required in the analysis of many astronomical and laboratory plasmas. For example, lines of Fe II and Fe III are seen in many astrophysical spectra and transitions in Ni-like ions are the basis of proposed x-ray lasers. However both require the solution of hundreds of coupled channels for tens of thousands of energies to obtain converged rate coefficients;
(iii) multiphoton ionization rates for complex atoms, ions and molecules are required in the analysis of the interaction of super intense lasers with matter. Codes based on the R-matrix-Floquet approach  can lead to thousands of coupled channels for complex targets.
In order to address these challenges a major programme of research is underway at Belfast and the Daresbury Laboratory to develop a new generation of R-matrix codes that can take advantage of current and future MPPs and SMPs . In this talk the computational challenges in this area of atomic and molecular physics will first be discussed. Then the research underway to meet these challenges will be described.
 P G Burke and K A Berrington, Atomic and molecular processes: an R-matrix approach (Institute of Physics Publishing, Bristol and Philadelphia, 1993).
 K Bartschat, E T Hudson, M P Scott, P G Burke and V M Burke, Electron-atom scattering at low and intermediate energies using a pseudo-state/R-matrix basis, J.Phys.B:At.Mol.Opt.Phys. 29 115-123 (1996).
 P G Burke, P Francken and C J Joachain, R-matrix-Floquet theory of multiphoton processes, J.Phys.B:At.Mol.Opt.Phys. 24 761-90 (1991).
 A Sunderland, P G Burke, V M Burke and C J Noble, Parallelization of atomic R-matrix scattering programs in "High Performance Computing" Eds R J Allen et al (Kluwer Academic) Plenum Publishers, New York and London, 1999) 293-300.
New Time-Dependent Methods for Nonperturbative Treatments of Strong-Field Atomic and Molecular Processes
Department of Chemistry and
Several time-dependent methods recently developed at the University
of Kansas for high-
(a) Time-dependent generalized pseudospectral
method (with optimal nonuniform spatial grid discretization
of the Coulomb potential) for accurate and efficient numerical
solution of time-dependent Schroedinger equation in space and
time . Several applications of the procedure will be discussed:
(i) The study of high-resolution photoabsorption spectrum of
3D Rydberg atoms in static magnetic field  and in crossed
electric and magnetic fields . The results are in excellent
agreement with experimental spectra line by line, well within
the classically chaotic regimes. (ii) Study of coherent control
of multiple high harmonic generation (HHG) processes in intense
laser fields [1,4,5].
 X.M. Tong and S.I. Chu, Chem. Phys. 217, 119 (1997).
Computational Challenges in QED for Few-Body Systems
Gordon W. F. Drake
Department of Physics,
The calculation of nonrelativistic energies and lowest-order relativistic corrections can now be regarded as a solved problem for all practical purposes for heliumlike atoms. To a large extent, the same is also true for lithiumlike atoms, although there is still considerable work to be done in this area. This brings to the fore the need for the accurate calculation of QED corrections as the dominant source of uncertainty in comparisons with high precision measurements of transition frequencies. For many years, the calculation of Bethe's mean excitation energy (the Bethe logarithm) has posed one of the most difficult challenges in atomic physics. Until recently, results of useful accuracy were available only for a few low-lying S-states of helium. This problem has now been largely solved for helium and other three-body systems by the introduction of new variational basis sets capable of representing an enormous range of distance scales within a single basis set . The result is a vast improvement in computational efficiency relative to methods attempted in the past. Similar calculations for Li-like systems are now within reach, but considerably greater computer resources will be required. These same basis sets may also open new opportunities for applications in other areas where an enormous range of distance scales is involved.
 G.W.F. Drake and S.P. Goldman, Can. J. Phys. 77, 835 (1999).
Computational Challenges in Bose-Einstein Condensation
Charles W. Clark
Bose-Einstein condensates (BECs) that are optically manipulated
with laser light present an extreme computational challenge.
Laser light can be used to impart momentum to pieces of a condensate
causing some fraction of the BEC to be ejected. Often a space
Large Scale Atomic Structure Calculations
Charlotte Froese Fischer
Multiconfiguration variational techniques have been developed
for both non-relativistic (MCHF) methods, with lowest order relativistic
effects included in the Breit-Pauli approximation, and fully
relativistic (MCDF) methods with Breit and QED corrections.
This talk will describe briefly how both codes have been parallelized. We will then illustrate the use of systematic methods, where calculations of increasing accuracy within a model, are monitored for convergence. In the case of Breit-Pauli calculations for transition rates, estimates of uncertainties have been proposed. Since these are now sufficiently well understood, an "MCHF/MCDF Collection" has been started based on mass production processes where all energy levels for a certain portion of a spectrum are computed and also all transitions between these levels, allowing a computation also of the lifetime. Currently not all data is published but is available at a web site: http://www.vuse.vanderbilt.edu/~cff/mchf_collection
But progress also depends on the development of better algorithms.
Spline algorithms have been used successfully to investigate
the photoionization of negative ions to high energies. Recently
new algorithms were developed for all the Breit-Pauli integrals,
including the Slater integrals taking advantage of the fact that
the two-dimensional integrals are separable in off-diagonal regions.
Calculations were almost an order of magnitude faster but at
the same time had essentially machine precision. Thus the possibility
exists of reducing large amounts of radial data. A remaining
bottleneck is the large amount of angular data, particularly
for MCDF calculations. Some preliminary
* Research supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Science, Office of Science, US Department of Energy
Overcoming Computational Barriers in Describing
Addressing the Particle Number Bottleneck in Electronic Structure Theory
Department of Chemistry
Electronic structure theory has made tremendous strides during its first 70 years of existence. It has advanced from the formally exact but impractical framework of the postulates of quantum mechanics to the status of practical, predictive theoretical models that are routinely applied in almost every branch of chemistry. I will first briefly summarize the successes and the limitations of current electronic structure methods. This sets the stage for the focus of the talk, which is a look at the prospects for employing high performance computing to attack problems of far larger scale than has been traditionally possible. We shall see that to make meaningful progress on this problem, fundamental algorithmic progress on overcoming a particle number bottleneck to treating large systems is required. This problem,and its close connections to high performance computing, will be discussed in detail.
Parallel Computing on PC Clusters
Lars E. Hernquist
Harvard-Smithsonian Center for Astrophysics
During the past decade, large-scale numerical computations in astrophysics have been performed to an increasing extent on parallel computers. The available hardware has been dominated mainly by platforms supplied from traditional vendors, including the IBM SP, the Cray T3-E, and the SGI Origin 2000. Recently, however, a new parallel computing environment has emerged, based on commodity hardware, such as PCs. These clusters or "Beowulf" computers employ large numbers of PCs that are coupled together in such a way that they can run parallel applications.
In this talk, I review the history of this technology and
describe potential advantages of this type of architecture over
more conventional parallel supercomputers. Complications arising
from the requirements of a distributed memory are discussed,
and software issues relating
Computational Issues in Relativistic MBPT Calculations
Dynamics and Control of Atomic and Molecular Processes
Jeffrey L. Krause
University of Florida
Experiments and theory have now demonstrated that phase and amplitude tailored, ultrafast laser pulses can be used to control electronic dynamics in atoms, molecules and materials. In this talk I discuss briefly two systems under investigation in my group, Stark wave packets and quantum wells. In both cases we have shown that wave packets can be created and driven to maximum overlap with a target distribution at a desired position and a chosen time. Both systems also emit radiation in the THz regime, which can be controlled by varying the parameters of the excitation pulse. Modeling these systems is complex because the time and length scales vary over wide ranges. I discuss some of the theoretical and computational challenges that must be surmounted to make further progress in unraveling the dynamics in these systems, and in interpreting and designing future experiments.
The Computational Landscape for Atomic and Molecular Theory
C. William McCurdy
Lawrence Berkeley National Laboratory
The area of theoretical atomic and molecular physics has not been a significant participant in the national effort to exploit high-end computing as a new and defining enhancement to scientific inquiry across all disciplines. A number of other disciplines which have aggressively exploited these technologies have been able to demonstrate new scientific capabilities that have changed the role of theory and simulation in those areas. In these disciplines, the notion that high-end simulation is a tool for discovery, as opposed to simply a tool to guide, interpret and verify experiment, has been accepted as a major part of the strategy for future investments in fundamental theory. Theory in atomic and molecular physics has simply had no role in this trend. It has arguably suffered and will be disadvantaged as a result. This talk will be devoted to an analysis of the opportunities that are open to our discipline, and to pointing out how many of them have been ignored.
First, an analysis will be presented of the probable changes in computational technology available to researchers in atomic and molecular physics over the next ten years. The technical and financial underpinnings of Moore's law will be discussed, and the consequent prospects for improvements in computer processors will be summarized. The expected changes in computer architectures for both laboratory scale and supercomputer scale machines will be outlined. As a final perspective on computing technology itself, the plausible paths to petaflop scientific computing, and the technical issues they raise, will be outlined.
In addition to new developments in computational machinery, the intellectual products of modern computer science and numerical mathematics are reaching a point where their explicit incorporation in the strategy for atomic and molecular theory will accelerate the scientific success and improve the prospects of our field. I will briefly explore the potential role in our field of extending some developments in modern computer science to applications in atomic and molecular theory, including computational grids, new visualization technologies, new language environments, parallel programming tools, clusters, open software, etc. Also, some examples of areas where modern applied (numerical) mathematics has had a large and well-recognized impact, and which are applicable to atomic and molecular physics, will be given. It is perhaps in the area of applied and numerical mathematics that the most immediate opportunities exist.
Separate issues facing the theoretical atomic and molecular physics community include those of access to high-end facilities and the prospects for funding of computationally intensive research in this field. An overview of the expected changes in resources, and access to them, at national computing facilities over the next three years will be given. Finally, the current prospects for computational initiatives in which theoretical atomic and molecular physics might participate will be discussed.
What's New in Linear Equations Solver
Esmond G. Ng
Lawrence Berkeley National Laboratory
One of the common ingredients in large-scale scientific and engineering calculations is the solution of a matrix problem, which, just to name a few, can be a linear system, an eigenvalue problem, or matrix function. The success of such large-scale calculations consequently hinges on the efficiency of the solutions of these matrix problems. On the other hand, we have seen drastic improvements in many matrix algorithms in the last couple of decades. Some of the improvements are due to better understanding of the problems. Others are influenced by changes in computer architectures. In this talk, we will take linear equations solver as an example and survey the accomplishments that have been achieved. If time permits, we will speculate on where the field is heading.
Continuum Electronic Structure
T. N. Rescigno
Lawrence Berkeley National Laboratory and
With the exception of
modern Carr-Parrinello methods, all of chemical dynamics has
been treated with a two-step approach in which electronic structure
calculations are done first and the potential energy surfaces,
that are the output of that effort, form the basis for a separate
treatment of the dynamics. This paradigm does not work in low
energy electron-molecule collision problems, since the colliding
electrons are indistinguishable from those of the target. It
is thus impossible to distinguish target electron correlation
from correlation between the incident electron and the target
electrons: in low-energy electron scattering, structure and dynamics
are inseparable parts of a "continuum electronic structure"
Action Dependent Wave Packets
Francis J. Robicheaux
Department of Physics
Time dependent wave packets are composed of several energy eigenstates; the packets evolve in time so that the probability distribution moves in space in a manner reminiscent of the motion of a classical particle. Dispersion causes difficulties in the interpretation of time dependent wave packets. I will present the formalism for a completely new object: an "action dependent wave packet". The packets move through space as the action is changed in a manner reminiscent of a classical particle. However, the action dependent packets do not disperse. I will briefly discuss the application of a Beowulf cluster of workstations to the visualization of the action dependent wave packets.
Numerical Methods in Time-Dependent and Time-Independent Quantum Mechanics: An Example from Bose-Einstein Condensation in Trapped Gases
Barry I. Schneider
David L. Feder
Lee A. Collins
Lattice, Time-Dependent Schrödinger
The Computational Challenge of Laser-Driven Few-Electron Atoms and Molecules
K T Taylor, J S Parker, D Dundas, L R Moore and J F McCann
Department of Applied Mathematics and Theoretical
Over the past 6 years, stimulated by the steadily increasing
power available through advances in supercomputer technology,
we have, at Queen's University Belfast,
The initial work on laser-driven helium was made possible by the 256-processor Cray T3D newly available in 1994 to the UK academic community. This machine was replaced with a Cray T3E about 18 months ago. The T3E has more than twice as many processors as the T3D leading to 100 Gflops sustained performance on user code. Moreover, a total RAM in excess of 128 Gb on this Cray T3E is more than an 8-fold increase over that available on the Cray T3D.
The underlying spirit of our work has been to treat the electronic
motion of the systems
The talk will illustrate progress by means of results obtained
for various phenomena such as simultaneous double electron ionisation
of helium. It will also indicate certain important ranges of
laser intensity and wavelength for which atomic and molecular
l. E S Smyth, J S Parker and K T Taylor, Numerical integration
2. D Dundas, J M McCann, J S Parker and K T Taylor, Ionization dynamics of laser-driven H2+, submitted to J Phys B, March 2000.
Calculating Quantum States of Molecules at Dissociation
Department of Physics & Astronomy
A typical chemically bound triatomic molecule may have up to million bound states. Although the majority of these state are not accessible in current spectroscopy experiments, characterizing them is important for modeling radiative properties of hot molecules, in cool stellar atmospheres or rocket exhausts for example, and for predicting thermodynamic properties such as specific heats at high temperature. We have adapted discrete variable representation (DVR) based codes used for spectroscopic studies to run on a variety of MPP machines. Using these codes we have obtained all the bound levels of rotationally excited water up to dissociation .
A particular challenge is to represent quasibound states of these molecules which lie just above the dissociation limit. This region forms a bridge between high resolution spectroscopy and reaction dynamics. In particular there is spectroscopic data available on the H3+ molecule here which has defied interpretation for nearly two decades . Recently we have extended our codes to address this problem , latest results will be reported at the meeting.
 H Y Mussa and J Tennyson, J Chem Phys, 109, 10885 (1999).
 A. Carrington, J. Buttenshaw and R.A. Kennedy, Mol. Phys,
 H Y Mussa and J Tennyson, Computer Phys Comms (Special
8:15 a.m. Coffee; pick up workshop packets and nametags
Session 1: Resources and Architectures
Chair: K. Kirby
Session 2: Bose-Einstein Condensation
Chair: K. Kirby
Session 3: e+Atom
Chair: M. Pindzola
Session 4: Wavepackets and Relativistic Effects
Chair: M. Pindzola
5:30 p.m. Wine and Cheese Reception (Perkin Lobby)
Session 5: Algorithm Development and Numerical Techniques
Chair: C.H. Greene
Session 6: Molecular Excitation and Scattering
Chair: C.H. Greene
Session 7: Atoms in Strong fields
Chair: C. W. McCurdy
Session 8: Heavy Particle
Chair: C. W. McCurdy
Session 9: Structure
Chair: F. Robicheaux
Session 10: Future Initiatives