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

Abstract

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.

The Triple Differential Cross Sections for Electron Impact Ionization of Metastable 3s State Hydrogen Atoms with Exchange Effect

“…We have considered here the triple differential cross-sections (TDCS) with exchange effects for the ionization of metastable 3S-state hydrogen atoms by electrons for the incident electron energy of 250 eV i E = and ejected electron energies 1 5 eV E = and 50 eV. The final continuum state of the present work shows a similar but shifted amplitude in the recoil lobe position as the earlier result of hydrogenic ground state second born approximation [21].…”

“…Dash curve shows the second born 2P state result [47]. Short dash curve focuses hydrogenic ground state second born result [21]; Dash-dotted curve shows hydrogenic ground state BBK model [34] and filled round shows hydrogenic ground state experiments [15]. [48].…”

“…Electron-hydrogen ionization from ground state theoretical results of Dal et al [21], the BBK model of Brauner et al [34] and the experimental results of Ehrhardt et al [15] are presented here for comparisons. The earlier works of hydrogenic 2S-state [38] ionization results.…”

“…The triple differential cross-section (TDCS) in electron hydrogen atom ionization collision has become increasingly interesting over the last four to five decades both theoretically and experimentally for relativistic [2]- [9] as well as for non-relativistic energies [10]- [21]. Triple differential cross-section (TDCS), measured in (e, 2e) coincidence experiment investigated first by Ehrhardt et al [22] and Amaldi et al [23].…”

“…A few theoretical calculations for the TDCS of metastable 2S and 2P [45]- [50] state hydrogen atoms by electron exchange are observed. The theoretical results of Del et al [21], BBK model [34], and the absolute data [15] for the ionization of hydrogen atoms by electrons from ground state have been considered in the present work for comparison.…”