The second Born approximation for the single and double ionization of atoms by electrons and positrons

• Published in: Journal of physics. B, Atomic, molecular, and optical physics Vol. 44; no. 1; p. 015204
• Main Authors: Dal Cappello, C, Haddadou, A, Menas, F, Roy, A C
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 14.01.2011; Institute of Physics
• Subjects: Approximation; Atomic and molecular collision processes and interactions; Atomic and molecular physics; Atomic excitation and ionization by electron impact; Born approximation; Cross sections; Distortion; Electron scattering; Exact sciences and technology; Helium; Ionization; Mathematical analysis; Mathematical models; Physics; Positron scattering; Positron-atom collisions; Numerical integration; Electron impact ionization; Differential cross sections; Theoretical study; Positron impact ionization; Helium; Born approximation; Electron-atom collisions; Continuum; Multiple ionization; Hydrogen Atoms; Positrons; Wave functions; Comparative study; Physical Sciences
• ISSN: 0953-4075; 1361-6455
• DOI: 10.1088/0953-4075/44/1/015204

Recently, Lahmam-Bennani et al (2010 J. Phys. B: At. Mol. Opt. Phys. 43 105201) have shown that the second Born approximation is necessary to describe the experimental results of the double ionization of atoms and molecules. The second Born approximation needs a difficult triple numerical integration and often many authors find some controversial results. We now investigate, in greater detail, the application of the second Born approximation for the easier case: the ionization of atomic hydrogen by electrons. The ionization of atomic hydrogen allows us to check accurately this approximation because the wavefunctions describing the target are known exactly. Moreover, sophisticated models such as convergent close coupling (CCC) and the continuum distorted wave eikonal initial state (CDW-EIS) exist and give closer results leading to easier comparisons. We report accurate second Born results for differential cross sections for the ionization of atomic hydrogen using a basis including 100 discrete states, and another basis including 32 discrete states and pseudo-states. The results of the present method are compared with other calculations and experiment. The single ionization of helium is also investigated in order to answer an old controversy between two different theoretical results. Finally, an application of the second Born approximation to the double ionization of helium has been performed.