ITAMP Workshop

Computational Challenges in Atomic and Molecular Physics

Organizers: Mitch Pindzola (Auburn), Bill McCurdy (LBL), Kate Kirby (ITAMP)

May 4-6, 2000

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 Online Talks

Participants

Abstracts

Schedule of Talks

Online Talks

Baltz

Bartschat

Burke

Chu

Drake

Edwards

Fischer

Greene

Hernquist

Johnson

Krause

MMcCurdy

Ng

Rescigno

Robicheaux

Schneider

Schultz

Participants

 

Dr. Anthony J. Baltz
Division of Nuclear Physics, SC-23
U.S. Deprtment of Energy
19901 Germantown Road
Germantown, MD 20874-1290
anthony.baltz@science.doe.gov

Prof. Klaus Bartschat
Department of Physics and Astronomy
Drake University
Des Moines, IA 50311
klaus.bartschat@drake.edu

Professor P. G. Burke
Dept of Applied Mathematics and Theoretical Physics
The Queen's University of Belfast
Belfast, BT7 1NN, Northern Ireland, UK
p.burke@qub.ac.uk

Prof. Shih-I Chu
Department of Chemistry
University of Kansas
Lawrence, KS 66045-0046
sichu@kuhub.cc.ukans.edu

Dr. Michael D. Crisp
U.S. Department of Energy
Office of Energy Research
19901 Germantown Road
Germantown, MD 20874-1290
MICHAEL.CRISP@science.doe.gov

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Dr. Gordon W. F. Drake
University of Windsor
Department of Physics
Windsor, ON, N9B 3P4, Canada
gdrake@uwindsor.ca

Dr. Mark Edwards
Georgia Southern University and
NIST
100 Bureau Drive, Stop 8410
Gaithersburg, MD 20899
edwards@amo.phy.gasou.edu

Prof. Charlotte F. Fischer
Electrical Engineering and Computer Science
Box 1679B
Vanderbilt University
Nashville TN, 37235
cff@vuse.vanderbilt.edu

Prof. Chris Greene
JILA, CB 440
University of Colorado
Boulder, CO 80309
chg@jilacg.colorado.edu

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Dr. Donald C. Griffin
Department of Physics
Rollins College
Campus Box 2743
1000 Holt Avenue
Winter Park, FL 32789-4499
griffin@vanadium.rollins.edu

Dr. Robert J. Harrison
Pacific Northwest National Laboratory
Mail Stop K1-83
PO Box 999
Richland WA 99352
robert.harrison@pnl.gov

Prof. Martin Head-Gordon
University of California Berkeley
Chemistry Department
215 Hildebrand
Berkeley, CA 94720
mhg@bastille.cchem.berkeley.edu

Prof. Lars E. Hernquist
Harvard-Smithsonian Center for Astrophysics
60 Garden St., MS 51
Cambridge, MA 02138
lhernquist@cfa.harvard.edu

Prof. Walter R. Johnson
Department of Physics
225Nieuwland Science Hall
Notre Dame University
Notre Dame, IN 46556
johnson@nd.edu

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Prof. Jeffrey L.Krause
University of Florida
Quantum Theory Project
P.O. Box 118435
Gainesville, FL 32611-8435
krause@qtp.ufl.edu

Dr. C. William McCurdy
Lawrence Berkeley National Laboratory
One Cyclotron Road, MS 50B-4230
Berkeley, CA 94720
cwmccurdy@lbl.gov

Dr. Dario Mitnik
Department of Physics
Auburn University
Auburn, AL 36849
dario@physics.Auburn.EDU

Dr. Esmond G. Ng
Lawrence Berkeley National Laboratory
One Cyclotron Road, MS-50F
Berkeley, CA 94720
egng@lbl.gov

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Prof. Michael S. Pindzola
Auburn University
Department of Physics
Auburn, AL 36849
pindzola@physics.auburn.edu

Dr. Thomas N. Rescigno
LawrenceBerkeley National Laboratory
One Cyclotron Road, MS 50F
Berkeley, CA 94720
tnr@llnl.gov

Prof. Francis J. Robicheaux
Department of Physics
Auburn University
Auburn, AL 36849
francisr@physics.auburn.edu

Dr. Eric A. Rohlfing
U.S. Department of Energy
Office of Basic Energy Sciences, SC-14
19901 Germantown Road
Germantown, MD 20874-1290
eric.rohlfing@science.doe.gov

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Dr. Barry I. Schneider
National Science Foundation
Physics Department
4201 Wilson Blvd.
Arlington, VA 22230
bis@bohr.mps.nsf.gov

Dr. Dave R. Schultz
Oak Ridge National Laboratory
Bldg. 6003, P.O. Box 2008
Oak Ridge, TN 37831-6373
schultz@ornl.gov

Dr. Rick Stevens
Mathematics and Computer Science Division
Argonne National Laboratory
9700 South Cass Avenue
Argonne, IL 60649
stevens@mcs.anl.gov

Professor K. T. A. (Ken) Taylor
Dept of Applied Mathematics and Theoretical Physics
David Bates Building
The Queen's University of Belfast
Belfast, BT7 1NN, Northern Ireland, UK
email k.taylor@qub.ac.uk

Prof. Jonathan Tennyson
Department of Physics & Astronomy
University College London
Gower Street
London WC1E 6BT, UK
j.tennyson@ucl.ac.uk

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Abstracts

Baltz

Bartschat

Burke

Chu

Drake

Edwards

Fischer

Greene

Head-Gordon

Hernquist

Johnson

Krause

McCurdy

Ng

Rescigno

Robicheaux

Schneider

Schultz

Taylor

Tennyson

 

Calculation of Pair Production and Ionization Induced by Relativistic Heavy Ions

Anthony J. Baltz

Physics Department
Brookhaven National Laboratory
Upton, New York 11973, USA

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.

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 Computer Simulations of Excitation, Ionization, and Ionization--Excitation in Electron--Atom Collisions

Klaus Bartschat

Department of Physics and Astronomy
Drake University
Des Moines, IA 50311, USA

klaus.bartschat@drake.edu

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.

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Atomic and Molecular R-matrix Calculations: Computational Challenges

P G Burke

Department of Applied Mathematics & Theoretical Physics
Queen's University Belfast

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 [1]. 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 [2] 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 [3] 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 [4]. 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.

[1] P G Burke and K A Berrington, Atomic and molecular processes: an R-matrix approach (Institute of Physics Publishing, Bristol and Philadelphia, 1993).

[2] 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).

[3] 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).

[4] 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.

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 New Time-Dependent Methods for Nonperturbative Treatments of Strong-Field Atomic and Molecular Processes

Shih-I Chu

Department of Chemistry and
Kansas Center for Advanced Scientific Computing
University of Kansas
Lawrence, Kansas 66045

Several time-dependent methods recently developed at the University of Kansas for high-
precision nonperturbative treatments of the structure, multiphoton dynamics, and high-resolution spectroscopy of atomic, molecular, and Rydberg systems in external fields will be presented. These include:

(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 [1]. Several applications of the procedure will be discussed: (i) The study of high-resolution photoabsorption spectrum of 3D Rydberg atoms in static magnetic field [2] and in crossed electric and magnetic fields [3]. 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].

(b)   Self-interaction-free time-dependent density functional theory (TDDFT) for nonperturbative treatments of multiphoton processes of (many-electron) atomic and molecular systems in strong fields [5-8].

References

[1] X.M. Tong and S.I. Chu, Chem. Phys. 217, 119 (1997).
[2] S.I. Chu and X.M. Tong, Chem. Phys. Lett. 294, 31 (1998).
[3] X.M. Tong and S.I. Chu, Phys. Rev. A 61, 031401 (Rapid Comm) (2000).
[4] X.M. Tong and S.I. Chu, J. Phys. B 32, 5593 (1999).
[5] X.M. Tong and S.I. Chu, Phys. Rev. A 61, 021802 (Rapid Comm) (2000).
[6] D. Telnov and S.I. Chu, Chem. Phys. Lett. 264, 466 (1997); Int. J. Quantum Chem. 69, 305 (1998); Phys. Rev. A 58, 4749 (1998).
[7] X. M. Tong and S.I. Chu, Phys. Rev. A 57, 452 (1998); Phys. Rev. A 58, R2656 (1998).
[8] X. Chu and S.I. Chu, ICOMP8 Conference Proc. (2000).

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 Computational Challenges in QED for Few-Body Systems

Gordon W. F. Drake

Department of Physics,
University of Windsor,
Windsor, Ontario, N9B 3P4

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 [1]. 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.

[1] G.W.F. Drake and S.P. Goldman, Can. J. Phys. 77, 835 (1999).

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 Computational Challenges in Bose-Einstein Condensation

Mark Edwards
Georgia Southern University and
NIST

Charles W. Clark
NIST

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
grid is used to represent the solution of the basic equation that describes such systems, the Gross-Pitaevskii (GP) equation. To capture all of the physics contained in such an experiment requires a grid spacing that is small compared to an optical wavelength with a grid length larger than a centimeter in some cases. I will describe some recent experiments involving laser light interacting with a BEC and discuss some of the computational techniques that have been used in place of direct numerical integration of the GP equation. I will also discuss prospects for modeling future experiments.

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Large Scale Atomic Structure Calculations

Charlotte Froese Fischer

Vanderbilt University
Nashville TN 37215 USA

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.
The Breit-Pauli approach is the simpler, less computationally intensive method, but for heavy or highly ionized systems a fully relativistic approach is essential.

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
ideas will be presented.

* Research supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Science, Office of Science, US Department of Energy

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Overcoming Computational Barriers in Describing
Condensates and Clusters

Chris H. Greene

JILA
University of Colorado
Boulder, CO 80309

The description of a Bose-Einstein condensate at the simplest Hartree-Fock level can already be challenging, particularly when the geometry of the trap is fully three-dimensional or when there are multiple spin components in the condensate. Going beyond the Hartree-Fock or Gross-Pitaevskii description is required to describe higher excited states of the condensate. Some related issues arise in the treatment of excited states of clusters of rare gas atoms, and I will address some progress in treating such higher vibrational modes at the workshop.

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 Addressing the Particle Number Bottleneck in Electronic Structure Theory

Martin Head-Gordon

Department of Chemistry
University of California, Berkeley, and
Chemical Sciences Division
Lawrence Berkeley National Laboratory
Berkeley CA 94720

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.

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 Parallel Computing on PC Clusters

Lars E. Hernquist

Harvard-Smithsonian Center for Astrophysics
60 Garden St., MS 51
Cambridge, MA 02138

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
to operating systems and libraries are outlined. Finally, I describe an ongoing project here at the CfA to develop a PC cluster employing hundreds of processors for studies of the origin of galaxies and large-scale structure in the Universe.

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Computational Issues in Relativistic MBPT Calculations of
Atomic Structure

Walter R. Johnson

Department of Physics
225 Nieuwland Science Hall
Notre Dame University
Notre Dame, IN 46556

Calculation of transition matrix elements for alkali-metal atoms is discussed as an
illustration of computational issues faced in applications of relativistic many-body
perturbation theory.

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Dynamics and Control of Atomic and Molecular Processes

Jeffrey L. Krause

University of Florida
Quantum Theory Project
Gainesville, FL 32611-8435

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.

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 The Computational Landscape for Atomic and Molecular Theory

C. William McCurdy

Lawrence Berkeley National Laboratory
Berkeley, CA 94720

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.

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What's New in Linear Equations Solver

Esmond G. Ng

Lawrence Berkeley National Laboratory
Berkeley CA 94720

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.

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Continuum Electronic Structure

T. N. Rescigno

Lawrence Berkeley National Laboratory and
Lawrence Livermore National Laboratory
Berkeley, CA 94720

      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" problem.
      Over the past fifteen years, several first principles methods have been developed and applied to a variety of electron-polyatomic scattering problems. Significantly, all of these techniques are algebraic variational methods and, while they make use of some tools found in electronic structure codes in various aspects of their formulation, it has generally been the case that quantum chemistry codes are used to calculate the wave functions for the electronic states of the target molecule as well as various additional matrix elements, and then those quantities are fed into a separate suite of scattering codes. The difficult electronic continuum problem for polyatomics has been formulated outside the context of bound state electronic structure, and components of modern quantum chemistry technology have been grafted onto it.
      The opportunity now exists to build the next generation of electron scattering codes and theories within the current context of the rich infrastructure of bound state quantum chemistry. I will describe the current implementation of a variational approach - the complex Kohn method - that has been successful in treating electron collisions with a number of polyatomic targets. I will then describe several modifications that can make the method even more powerful, which we have explored in preliminary studies, but which we have not yet fully implemented. A principal difficulty in any variational formulation of electron-molecule scattering is the calculation of two-electron matrix elements involving continuum functions - the so-called bound-free and free-free matrix elements. A new algorithm for computing bound-free integrals has been developed that allows for the rapid, quasi-analytic, evaluation of continuum bound-free matrix elements. This technique has been fully tested and parallelized. By incorporating these routines into a modern structure code, collision integrals can be computed, processed and transformed just as standard bound-bound integrals are handled. It is now feasible to drop the use of separable approximations and to treat all aspects of exchange effectively exactly.
      The other significant development in the evolution of the complex Kohn method that has taken place is a reformulation of the basic method along the lines suggested by "time-independent wave packet" approaches. The result is a continuous-energy version of the complex Kohn approach that allows cross sections to be rapidly evaluated over a range of collision energies after a single intensive computational setup. In that sense, the method shares a key advantage of the R-matrix method without the need for matrix elements computed over a finite volume; it is, in a sense, an "R-matrix theory without a box".

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Action Dependent Wave Packets

Francis J. Robicheaux

Department of Physics
Auburn University
Auburn, AL 36849

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.

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 Numerical Methods in Time-Dependent and Time-Independent Quantum Mechanics: An Example from Bose-Einstein Condensation in Trapped Gases

Barry I. Schneider
NSF

David L. Feder
NIST

Lee A. Collins
LANL

Charles W. Clark
NIST



There are many computationally challenging problems in time-dependent and time-
independent quantum mechanics. These require solving large-scale eigenvalue problems and/or linear systems, or propagating solutions of the Schroedinger equation in real or imaginary time. The equations are often non-linear or integro-differential, which can complicate the numerics even further. Using the non-linear, time-dependent, Gross-Pitaevski equation as a model, I will discuss how a suitable choice of representation, namely the Discrete Variable Method, can simplify the problem. I will explore how ideas developed in the quantum chemistry community may be suitably modified for this and related applications. The remaining computational challenges will be discussed and
possible solutions outlined.

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 Lattice, Time-Dependent Schrödinger Equation
Solution for Ion-Atom Collisions*

David R. Schultz

Physics Division
Oak Ridge National Laboratory
Oak Ridge, TN 37831-6373

It has long been a goal in the study of physics on the atomic scale to develop methods to solve the Schr\"odinger equation as directly as possible in order to circumvent difficulties and uncertainties introduced through various theoretical and computational approximations. For so-called "single center' problems (e.g. the electronic structure of atoms and ions) exquisite levels of precision have been obtained, even for many-electron systems. However, for dynamical problems such as ion-atom collisions, even for systems with only one or a few electrons, such a high precision description of observables has not often been achieved. The necessity to thoroughly describe the possibly multielectron, multicenter continuum, the need to represent processes driven through channels involving states on more than one center, or involving the interaction among electrons, are examples of inherent complexities that limit their accuracy and precision. Therefore, to treat ion-atom collisions, a many theoretical approaches have been devised which are applicable in various regimes.

The aim of recent work has been to develop an approach which can overcome many of the difficulties associated with these methods (e.g. the need for somewhat arbitrary 'electron translation factors' in molecular orbital close coupling, the limitations of treating the interactions perturbatively when they are in fact strong, the lack of a dense representation of the two-center continuum in atomic or molecular close coupling, etc.) by solving the time-dependent Schrödinger equation (TDSE) as directly as possible on a numerical lattice.

Applications to be described here include demonstrations of the utility of the lattice techniques not only in achieving significant improvements in the accuracy of the results over a wide range -- and therefore a wide span of the various approximation methods -- but also its usefulness in illuminating underlying physical mechanisms. Examples will include early two-dimensional (2D) lattice solutions which served as proof-of-principle of the new techniques and new computational platforms [1], latter 3D calculations for antiproton [2] and proton [3] impact of H and He+, explication of ubiquitous but previously unexplained oscillations [4] in low-energy ion-atom collisions, and ongoing 4D calculations for antiproton-He collisions and few-fermion quantum dot structures.

Thus, I hope to demonstrate in this presentation that lattice solution of the TDSE provides a new and powerful toolkit for addressing ion-atom and other atomic scale phonemena. Close collaborations over the years with Chris Bottcher, Mitch Pindzola, Jack Wells, Michael Strayer, and Don Madison on the presently described or related projects is gratefully acknowledged.

*Work supported by the U.S. Department of Energy, Office of Fusion Energy Sciences and Office of Basic Energy Sciences, at ORNL which is managed by UT-Battelle under contract DE-AC05-00OR22725.

References

1. P. Gavras, M.S. Pindzola, D.R. Schultz, and J.C. Wells, Phys. Rev. A 52, 3868 (1995).

2. D.R. Schultz, P.S. Krstic, C.O. Reinhold, and J.C. Wells, Phys. Rev. Lett. 76, 2882 (1996); J.C. Wells, D.R. Schultz, P. Gavras, and M.S. Pindzola, Phys. Rev. A 54, 593 (1996); D.R. Schultz, J.C. Wells, P.S. Krstic, and C.O. Reinhold, Phys. Rev. A 56, 3710 (1997).

3. D.R. Schultz, M.R. Strayer, and J.C. Wells, Phys. Rev. Lett. 82, 3976 (1999); A. Kolakowska, M.S. Pindzola, F. Robicheaux, D.R. Schultz, and J.C. Wells, Phys. Rev. A {\bf 58}, 2872 (1998); A. Kolakowsaka, M.S. Pindzola, and D.R. Schultz, Phys. Rev. A 59, 3588 (1999).

4. D.R. Schultz, C.O. Reinhold, and P.S. Krstic, Phys. Rev. Lett. 78, 2720 (1997).

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 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 Physics
The Queen's
University of Belfast
Belfast, BT7 1NN, UK

Over the past 6 years, stimulated by the steadily increasing power available through advances in supercomputer technology, we have, at Queen's University Belfast,
made considerable strides in solving the fundamental, time-dependent, three-body
problem presented by laser-driven helium and, latterly, that which arises in
laser-driven H2+ when vibrational dissociation is allowed to take place. Moreover
we have very recently started transferring the experience gained in developing
algorithms, numerical methods and massively parallel computer codes for these systems [1,2] to an attack on laser-driven H2. This molecule presents a three- or four-body problem depending on whether or not inter-nuclear vibrational motion is taken into account.

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
in full-dimensionality and the nuclear motion in appropriate lower-dimensionality. Thus with helium driven by a linearly-polarised laser, the two electrons share 5 degrees of freedom between them and the very small amplitude motion of the massive nucleus can be safely neglected. With the inter-nuclear axis of laser driven H2+ aligned along the laser's
polarisation axis the electronic motion has 2 degrees of freedom and nuclear dissociative motion brings in one extra dimension. Finally, for H2 similarly aligned, the two electrons share 5 degrees of freedom as in helium and nuclear vibrational motion, when allowed for, introduces another.

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 response is
at present computationally inaccessible but which the newest supercomputers are opening up.

l. E S Smyth, J S Parker and K T Taylor, Numerical integration of the
time-dependent Schrödinger equation for laser-driven helium, Comput Phys Commun 114, 1 (1998).

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.

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Calculating Quantum States of Molecules at Dissociation

Jonathan Tennyson

Department of Physics & Astronomy
University College London,
London WC1E 6BT, UK

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 [1].

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 [2]. Recently we have extended our codes to address this problem [3], latest results will be reported at the meeting.

[1] H Y Mussa and J Tennyson, J Chem Phys, 109, 10885 (1999).

[2] A. Carrington, J. Buttenshaw and R.A. Kennedy, Mol. Phys,
45, 753 (1982).

[3] H Y Mussa and J Tennyson, Computer Phys Comms (Special issue on
Parallel Computing), in press.

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Schedule of Talks

 Thursday, May 4, 2000 [Pratt Conference Room ALL DAY]

8:15 a.m. Coffee; pick up workshop packets and nametags

Session 1: Resources and Architectures

Chair: K. Kirby

 8:30 a.m. C.W. McCurdy: The Computational Landscape for Atomic and Molecular Theory
 9:15 a.m L. Hernquist: Parallel Computing on PC Clusters
 9:50 a.m. Coffee break

Session 2: Bose-Einstein Condensation

Chair: K. Kirby

 10:10 a.m. M. Edwards: Computational Challenges in Bose-Einstein Condensation
 10:45 a.m. C.H. Greene: Overcoming Computational Barriers in Describing
Condensates and Clusters
11:20 a.m. B. I. Schneider: Numerical Methods in Time-Dependent and Time-Independent Quantum Mechanics: An Example from Bose-Einstein Condensation in Trapped Gases
11:55 a.m. Lunch

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Session 3: e+Atom

Chair: M. Pindzola

 2:00 p.m. P.G. Burke: Atomic and Molecular R-matrix Calculations: Computational Challenges
 2:35 p.m. K. Bartschat: Computer Simulations of Excitation, Ionization, and
Ionization-Excitation in Electron-Atom Collisions
3:10 p.m. Break

Session 4: Wavepackets and Relativistic Effects

Chair: M. Pindzola

 3:40 p.m. F. Robicheaux: Action Dependent Wave Packets
 4:15 p.m. J. L. Krause: Dynamics and Control of Atomic and Molecular Processes
4:50 p.m. G.W.F. Drake: Computational Challenges in QED for Few-Body Systems

5:30 p.m. Wine and Cheese Reception (Perkin Lobby)

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 Friday, May 5, 2000 [Phillips Auditorium]

Session 5: Algorithm Development and Numerical Techniques

Chair: C.H. Greene

 8:30 a.m. R. Stevens: Future Directions in High-Performance Computing Architecture for Computational Science
 9:20 a.m. E. Ng: What's New in Linear Equations Solver
9:55 a.m. W.R. Johnson: Computational Issues in Relativistic MBPT Calculations of Atomic Structures
10:30 a.m. Coffee

Session 6: Molecular Excitation and Scattering

Chair: C.H. Greene

 11:00 a.m. J. Tennyson: Calculating Quantum States of Molecules at Dissociation
 11:35 a.m. T.N. Rescigno: Continuum Electronic Structure
12:15 p.m. Lunch

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  [Pratt Conference Room]

Session 7: Atoms in Strong fields

Chair: C. W. McCurdy

 2:00 p.m. K. Taylor: The Computational Challenge of Laser-Driven Few-Electron Atoms and Molecules
 2:35 p.m. S-I. Chu: New Time-Dependent Methods for Nonperturbative Treatments of Strong-Field Atomic and Molecular Processes
3:10 p.m. Break

Session 8: Heavy Particle

Chair: C. W. McCurdy

 3:40 p.m. D. R. Schultz: Lattice, Time-Dependent Schrödinger Equation
Solution for Ion-Atom Collisions
 4:15 p.m. A. J. Baltz: Calculation of Pair Production and Ionization Induced by Relativistic Heavy Ions
4:50 p.m. D. Griffin and M. Pindzola: Discussion on algorithms and access

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 Saturday, May 6, 2000 [Phillips Auditorium]

Session 9: Structure

Chair: F. Robicheaux

 9:00 a.m. M. Head-Gordon: Addressing the Particle Number Bottleneck in Electronic Structure Theory
 9:35 a.m. R.J. Harrison: TBA
10:10 a.m. C.F. Fischer: Large Scale Atomic Structure Calculations
10:45 a.m. Coffee

Session 10: Future Initiatives

11:15 a.m. B. Schneider
11:40 a.m. K. Kirby, C. W. McCurdy, and M.S. Pindzola: Challenges discussion
 1:00 p.m. End of workshop

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