Unified treatment of atomic excitation and ionization

A unified treatment of atomic excitation and ionization in ion-atom collisions is proposed. It is demonstrated that the state-resolved excitation cross sections multiplied by $n^3$, where $n$ is the principal quantum number of the excited state, and the corresponding partial singly differential ionization cross section form two parts of a single continuous function. This allows one to obtain the excitation cross section for any state including high-lying Rydberg states and the energy-differential ionization cross section at, and arbitrarily close to, the threshold. The proposed method can be used in any theoretical approaches to excitation and ionization and experimental measurements.