Bound and continuum state contributions to dipole oscillator strength sum rules: Total and orbital mean excitation energies for cations of C, F, Si, and Cl

We present dipole oscillator strength-dependent properties such as sum rules, dipole polarizability, mean excitation energy, and stopping cross section as a function of the ionic charge of C, F, Si, and Cl atoms. The excitation spectra and the dipole oscillator strengths are obtained by means of the time-dependent Hartree–Fock approximation. We report the sum rules, S_k, from −6 ≤ k ≤ 2 and the logarithmic sum rule L_k = dS_k/dk as a function of the ionic charge −1 ≤ q ≤ Z − 1 with Z being the nuclear charge. The contributions from the bound and continuum states to all sum rules are analyzed as a function of k and charge of the cation. The study allows us to determine a scaling behavior of the bound and continuum state contributions in terms of the cation number of electrons and nuclei charge for k ≤ 0. We propose a new way of determining orbital mean excitation energy as the difference between the mean excitation energy of two neighboring cationic states of an atom. This procedure allows to obtain all orbital mean excitation energy for the four atoms within the time-dependent Hartree–Fock approximation, thus effectively including electronic correlation in the orbital mean excitation energy. As a result, the mean excitation energy within a shell differs for each electron. Wherever possible, we compare with available data in the literature finding excellent agreement.