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A systematical investigation of the electron-impact ionization cross sections of Sn$^+$ and Sn$^+$ ions has been performed by employing a crossed-beams technique, Single- and Double-Ionization cross sections for these ions were measured within energy ranges from the ionization threshold to 1000 eV. The study uncovers contributions from indirect ionization processes, involving the ionization or excitation of inner electron subshells. These insights and are valuable for advancing the understanding of electron-ion interactions and supporting plasma modeling efforts, as well as applications in extreme ultraviolet (EUV) lithography. The findings underscore the critical role of accurate experimental data in refining theoretical models for complex atomic systems. Configuration-Averaged Distorted Wave (CADW) direct ionization cross section calculations using the Los Alamos National Laboratory (LANL) were performed for comparison. The Classical Trajectory Monte Carlo (CTMC) method was used to determine the electron impact single ionization cross sections for Sn$^+$; the CTMC simulations were made in the three-body approximation. These two theoretical calculations included the excitations from inner shells as well as the ground state. Both theoretical approaches show qualitative agreement with the total experimental cross-sections.