Regularized perturbative series for the ionization potential of atomic ions

We study N-electron atoms with nuclear charge Z. It is well known that, in the cationic (Z > N) large-Z region, the atom behaves as a weakly interacting system. The anionic (Z < N) regime, on the other hand, is characterized by an instability threshold at , below which the atom spontaneously emits an electron. We construct a regularized perturbative series (RPS) for the ionization potential that is based on the behaviors for large Z and Z near Zc. The large-Z expansion coefficients are analytically computed from perturbation theory, whereas the slope of the energy curve at Z = N - 1 is computed from a kind of zero-range forces theory that uses as input the electron affinity and the covalent radius of the neutral atom with N - 1 electrons. Relativistic effects in the one-particle Hamiltonian are considered at the level of first-order perturbation theory. Our RPS formula is to be used to check the consistency of the ionization potential values for atomic ions contained in the NIST database.