The Theory of Non-Relativistic and Relativistic Atomic Collisions

Using Massively Parallel Computers

Principal Investigators:

Michael S. Pindzola, Professor
Department of Physics, Auburn University
Phone: (334) 844-4127  Fax: (334) 844-4613  
E-mail: pindzola@physics.auburn.edu

David R. Schultz, Staff Scientist
Physics Division, Oak Ridge National Laboratory
Phone: (423) 576-9461  Fax: (423) 574-4745 
E-mail: schultz@orph01.phy.ornl.gov

Francis J. Robicheaux, Assistant Professor
Department of Physics, Auburn University
Phone: (334) 844-4366  Fax: (334) 844-4613  
E-mail: francisr@physics.auburn.edu

Donald C. Griffin, Professor
Department of Physics, Rollins College
Phone: (407) 646-2664 Fax: (407) 646-2600 
E-mail: griffin@rollins.edu

Energy Research Programs:

DOE Grant No. DE-FG05-96ER54348 with Auburn University
DOE Contract No. DE-AC05-96OR22464 with ORNL
DOE Grant No. DE-FG05-93ER54218 with Rollins College

Additional Authorized Users:

Phil Stancil, DOE Wigner Fellow, ORNL
Dan Plante, Instructor, Stetson University
John Shaw, DOE Post-doctoral student, Auburn University
Dario Mitnik, DOE Post-doctoral student, Auburn University

Introduction

The mission of the `Atomic Collision Physics'' program is to compute accurate collision cross sections and to develop new computational techniques in support of such calculations, relevant to the energy needs of the nation. Starting with a NERSC account on the Intel Paragons at the Center for Computational Sciences at ORNL, we have developed several working computer codes which directly solve the time-dependent Schrodinger equation on a partitioned lattice. Linear scaling up to 500 nodes was achieved for our investigation of the threshold law for the electron ionization of atoms. In the Spring of 1997 we changed from NX to MPI and within a couple of weeks our computer codes were running on the T3E-600 at NERSC under the early start program. Our photoionization codes are 12 times faster on the T3E than on the Paragons. The projects outlined below are ideal for massively parallel computers, several are currently making use of the T3E, and all have the potential for making significant advances in the field of atomic collision physics.

Electron-impact ionization of atomic ions

Using the NERSC account on the Intel Paragons at the Center for Computational Sciences at ORNL, we have completed a study of the threshold law for the electron-impact ionization of hydrogen [1,2]. The threshold law and the high energy Bethe limit determine the general shape of the ionization cross section for all atoms and molecules. On the Paragons we achieved 10 GFlops and linear scaling for our largest calculations on a 2500 x2500 lattice using 500 nodes. We are currently calculating ionization cross sections for atomic ions in the Li and Na isoelectronic sequences [3,4] using the T3E-600 at NERSC. We have found that experiment is 40\% higher than theory for the electron-impact ionization of Be^+, but agrees very well with theory for Mg^+.

Correlated photoionization of two-electron atomic systems

The time-dependent close-coupling codes used for electron-impact ionization have been extended to include radiative dipole coupling. The larger set of coupled partial differential equations can be used to calculate a wide variety of photoionization processes in two-electron atoms. Our correlated photoionization cross sections for helium [1], calculated on the T3E-600 at NERSC, agree very well with current synchotron experiments. We plan to extend the calculations to study photoionization from excited states of helium, double photoionization of H^- and Li^+, and multiphoton double ionization of helium.

Proton collisions with atoms and ions

We have carried out time-dependent lattice solutions of the Schrodinger equation for proton and antiproton collisions with hydrogen. The proton collisions were in 2d flatland space[1], while the antiproton collisions were in a full 3d space[2,3]. Using both finite difference and Fourier collocation methods, we plan to extend our full 3d calculations to include proton collisions with one-electron atomic systems. The T3E will enable us to extract excitation, capture, and ionization cross sections over a wide energy range for comparison with ongoing worldwide experimental efforts.

Positron collisions with atoms

The time-dependent close-coupling codes used for electron-impact ionization can be easily adapted to study positron collisions with atoms. Although exchange scattering is no longer present, positron collisions are in some ways more difficult than electron collisions due to the availability of the positronium formation channel. We have used the T3E-600 at NERSC to calculate the total transfer ionization cross section for positron collisions with hydrogen [1]. The inferred positronium formation cross section is in good agreement with current experimental measurements. We plan to extend the calculations to study positron collisions with alkali atoms.

Rydberg state dynamics in external fields

Technological advances have allowed the recent exploration of time dependent atomic dynamics. Experiments utilizing pulsed lasers or pulsed infrared radiation (FWHM of a few picoseconds) have initiated wave packets in strong electric fields. Experiments have also been performed where the electric field is pulsed (FWHM of roughly 500 femtoseconds). Direct calculations of the time dependent Schrodinger equations can take advantage of the parallel architecture of the T3E quite efficiently. The calculations can be quite large since these are two-dimensional waves. Calculations are performed by expanding the wave function in a basis set in spherical coordinates[1,2]. Linear speed-up is observed on ORNL Paragons [3] up to (and including) one angular momentum per processor. We ultimately want to address problems associated with three dimensional quantum waves. For example, the dynamics of a Rydberg electron in crossed electric and magnetic fields has not been explained quantum mechanically. There are several interesting issues that will be addressed including (1) calculations and explanations of photon-absorption cross sections of alkali atoms in crossed E- and B-fields and (2) why does it appear that the autoionization rate is independent of principle quantum number in crossed E- and B-fields. The graphic here shows a surface plot of the flux into a detector after exciting Cs with a pulsed laser. The time for the flux into the detector is in picoseconds and the average energy of the wave packet is in cm^-1. The Cs is in an electric field of 1 kV/cm. The laser pulse exciting the Cs from the ground state is polarized parallel to the electric field direction.

Electron-impact excitation of atomic ions

The close-coupled R-matrix method is used to solve the time-independent Schrodinger equation for electron-impact excitation cross sections for atomic ions of interest in laboratory and astrophysical plasma research. The numerical procedure is divided into several distinct stages: (1) radial integration of one and two body operators, (2) angular integration of one and two body operators, (3) matrix diagonalization of the electron-ion Hamiltonian within a box, and (4) close-coupled solution of the asymptotic equations of the S-matrix. We have adapted stage(4) to run on the ORNL Paragons[1]. We plan to change stage(4) from NX to MPI and begin test calculations on the T3E at NERSC, and convert stage(3) to parallel code.