C. William McCurdy, Daniel A. Horner, Zhiyong Zhang, and Wim Vanroose, Lawrence Berkeley National Laboratory
Thomas N. Rescigno, Lawrence Berkeley National Laboratory and Lawrence Livermore National Laboratory
Mark Baertschy, University of Colorado/JILA
William Isaacs, Lawrence Livermore National Laboratory

Wave functions for a quantum mechanical system of a charged particle colliding with a model two-electron atom. The vertical axis represents the coordinate of the incident particle, and the other two axes are the electron coordinates. In the left panel, the collision energy is lower than the breakup threshold; in the center panel, the collision energy is sufficient to singly ionize the atom; in the right panel, the energy is sufficient to cause complete fragmentation of the system.

Computational Approach
Our approach builds on the algebraic variational formalisms (the Complex Kohn variational method) we have been developing to study electron-atom and electron-molecule scattering. These approaches have now been extended to include complex optical potential interactions, a scattered-wave/flux operator formalism, and a variety of techniques based on analyticity. These techniques allow us to treat a broad range of problems, from low-energy electron-molecule collisions using elaborate variational wave functions to direct solutions of the Schrödinger equation for simple atomic targets that provide detailed ionization cross sections.

Accomplishments
We developed a new procedure for computing impact ionization amplitudes that provides a direct and efficient route to computing the breakup cross sections. This provided an independent check on the fundamental correctness of the results we had initially obtained by numerically extrapolating the quantum mechanical flux. The computational approach we have developed has, to date, provided the only complete solution to the quantum mechanical three-body Coulomb at low collision energies.

We have also developed a new technique for computing the scattered wave function that does not require the solution of large systems of complex linear equations. This is accomplished by writing the scattered wave function as the Fourier transform of a time-propagated initial state that can be computed using a discrete variable representation in conjunction with a split-operator method.

We have completed the second phase of our work on electron-CO₂ scattering, exploring resonant vibrational excitation in the 4 eV energy region and carrying out time-dependent wavepacket studies in three dimensions. This study represents the first time that all aspects of an electron-polyatomic collision, including not only the determination of the fixed-nuclear electronic cross sections but also a treatment of the nuclear dynamics in multiple dimensions, has been carried out entirely from first principles.

Significance
Electron collision processes are central to the problems of interest to DOE, playing a key role in such diverse areas as fusion plasmas, plasma etching and deposition, and waste remediation. Electron-molecule collisions play a central role in the plasma processing of silicon chips, but the understanding and modeling of these low-temperature plasmas is severely hampered by the lack of a database of electron-molecule collision cross sections; this project will significantly add to that base of knowledge. In mixed radioactive waste, the primary radioactive decay events produce showers of secondary electrons which initiate the chemistry that produces a mixture very different from the one that was present originally. The tools we are developing will make it possible to understand and model this kind of electron-initiated chemistry. Central to understanding plasma formation are the fundamental studies of electron and positron impact ionization of simple atoms. We developed the first complete method for treating electron-impact ionization of atoms from first principles, solving a fundamental problem in atomic physics that had resisted solution for more than 40 years. We are now working extensions of the computational approach that will allow us to study systems containing more than two electrons.

Publications
M. Baertschy, T. N. Rescigno, and C. W. McCurdy, "Accurate amplitudes for electron impact ionization," Phys. Rev. A 64, 022709 (2001).

M. Baertschy, T. N. Rescigno, C. W. McCurdy, J. Colgan, and M. S. Pindzola, "Ejected-energy differential cross sections for the near threshold electron-impact ionization of hydrogen," Phys. Rev. A 63, 050701 (2001).

W. A. Isaacs, M. Baertschy, C. W. McCurdy, and T. N.Rescigno, "Doubly differential cross sections for the electron impact ionization of hydrogen," Phys. Rev. A 63, 030704(R) (2001).

www.lbl.gov/cs/amo_theory/