Excitation and ionization by electron impact in transition and super-transition arrays

This study investigates the ionization and excitation processes induced by electron impact between two configurations or superconfigurations. Rate coefficients are calculated for transition arrays or super-transition arrays rather than level-to-level transitions. Special attention is given to a series of oxygen-like ions relevant to inertial confinement fusion, specifically silicon, germanium, argon, and krypton. Calculations are performed over a wide temperature range, from 50 to 3000 eV. To facilitate the determination of rates at any temperature and ion charge, the computed rates are fitted with a two-dimensional Chebyshev polynomial expansion, yielding a set of coefficients for practical applications. Additionally, an extension of the Clenshaw algorithm to two dimensions, using the Chebyshev coefficients, is proposed to address numerical challenges and enhance computational efficiency.