Approximating the Green's Function in Evaluating Second-Order Amplitudes

POSTER

Abstract

It is well established that second-order effects are often important for electron impact ionization processes. Due the complexity of evaluating second order amplitudes, approximations are typically made in their evaluation. One of the approximations that have been used is accounting only for the imaginary part of the Green's function, so that the second-order amplitude reduces to a sum of products of two first-order terms. To check the validity of this approximation, we performed second-order distorted-wave calculations, in which the first-order amplitudes were evaluated by a convergent $R$-matrix with pseudostates (close-coupling) model to describe the initial bound state and the ejected-electron--residual-ion interaction. The results obtained without making any approximations are compared with those obtained by simplifying the Green's function for electron impact ionization of helium to He$^{+}$(1s) and He$^{+}$(2s,2p). The approximation is found to be reasonably good for direct ionization to He$^{+}$(1s) at incident energies greater than about 600 eV. The accuracy decreases with decreasing incident electron energy.

Authors

  • Zhangjin Chen

  • Don Madison

    Laboratory for Atomic and Molecular Research, University of Missouri-Rolla, Rolla, MO 65401

  • Shunji Kuroiwa

    PSAC/NIE/NTU, Singapore, School of Physics, The University of Sydney, Sydney NSW 2006, Australia, Nantes University, France, Varian Semiconductor Equipment Associates, Gloucester, MA01930, USA, Institute of Physics, POB 68, 11080 Zemun, Belgrade, Serbia and Montenegro, Department of Aeronautics and Astronautics, Kyoto University, Japan, Institut fur Kernphysik, Universitat Frankfurt, University of Missouri - Rolla, University of Maryland, Department of Physics, Department of Physics and Astronomy, Drake University, Des Moines, Iowa 50311, USA, CSIRO Molecular Science, Organic Chemistry Institute, University of Heidelberg, Centre for Molecular Simulation and School of Information Technology, Swinburne University of Technology, Department SBG, Limburgs Universitair Centrum, The Open University, Department of Mechanical Engineering, University of Minnesota, INP-Greifswald-Germany, LACE-Lyon-France, California State Polytechnic University, Pomona, Dublin City University, Ireland, OSRAM GmbH, D-81536 Munich, Germany, Institute of Low Temperature Plasma Physics, 17489 Greifswald, Institut of Physics, University of Greifswald, Germany, Instituto de Ciencias Nucleares, UNAM, UAM, Acopotzalco, Centro de Ciencias F\'{i}sicas, UNAM, Eindhoven University of Technology, Sandia National Lab, Air Force Research Laboratory WPAFB, School of Electrical Engineering, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia and Montenegro, Advanced Energy Incorporated, Applied Materials Incorporated, National Centre for Plasma Science and Technology, Dublin City University, Ireland, Institute for Plasma and Atomic Physics, Ruhr-University Bochum, Germany, Institute for Plasma and Atomic Physics, Ruhr University Bochum, Germany, OSRAM Sylvania, HanYang University, Ruhr-University of Bochum, Nagoya University, Stanford University, Department of Physical Electronics -- Masryk University, Brno, Czech Republic, Hypertherm Inc., University of Minnesota, Los Alamos National Laboratory, LPTP Ecole Polytechnique 91120 Palaiseau, LACE UCB-Lyon1 UMR CNRS 5634 blvd 11Nov.1918 69100 Villeurbanne France, Lawrence Berkeley National Laboratory, University of California, Davis, Multicharged Ions Spectra Data Center of VNIIFTRI, Advanced Photon Research Center, Japan Energy Research Institute, Applied Physics Division, Los Alamos National Laboratory, Theoretical Division Los Alamos National Laboratory, Gaseous Electronics Inst., Nagoya Institute of Technology, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720-1770, Science Institute, University of Iceland, Reykjavik, Iceland, Australian National University, Flinders University, KAIST, Plasmart Co., Samsung Electronics, St Petersburgh State University-Russia, Trinity College Dublin, Ireland, School of Physics, The University of Sydney, Australia, INP Greifswald, F.-L.-Jahn-Str. 19, 17489 Greifswald, Germany, Sungkyunkwan University, Korea, National University of Ireland, Maynooth, Ireland, Applied Materials, Tokyo Institute of Technology, LPTP, Ecole Polytechnique, LPTP, Ecole Polytechnique, 91128 Palaiseau, France, School of Physics, University of Sydney, Physics Dept, Macquarie University, Australia, Department of Applied Science, University of California at Davis, Stevens Institute of Technology, Department of Electrical Engineering and Computer Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan, Shibaura Mechatronics Corp.