Chapter 3 The Semiempirical Deutsch-Märk Formalism. A Versatile Approach for the Calculation of Electron-Impact Ionization Cross Sections of Atoms, Molecules, Ions, and Clusters

Collisions of electrons with matter causing ionization are among the most fundamental processes in collision physics. The knowledge of cross sections for electron-impact ionization is of basic importance to our understanding of collision physics and critical to many applications such as low-temperature processing plasmas, fusion edge plasmas, gas discharges, planetary, stellar, and cometary atmospheres, radiation chemistry, mass spectrometry, and chemical analysis. While much progress has been made in the experimental determination of cross sections for atomic and molecular targets, rigorous quantum mechanical calculations of ionization cross sections are scarce and exist only for some simple atoms in their electronic ground state. The need to incorporate ionization cross sections for these targets in modeling codes in many applications has stimulated a renewed interest in the use of less rigorous approaches to the calculation of ionization cross section ranging from simplistic additivity rules to semirigorous methods that incorporate aspects of established collision theories and some quantum mechanically calculated target properties. Here we present a review of the status of calculations of absolute electron-impact ionization cross sections using the Deutsch-Märk (DM) formalism for a variety of targets ranging from ground-state atoms to atoms in excited states to molecules, free radicals and clusters, and to positive and negative ions. The main emphasis is on demonstrating the versatility of the DM formalism as its range of applicability has been extended over the years, both in terms of range of impact energies covered and range of target species studied. Extensive comparisons will be made with available experimental data and, to the extent possible, with results from other cross-section calculations to demonstrate the accuracy, reliability, and predictive potential of the DM formalism.