Correlation Energies and Auger Rates in Atoms with Inner-Shell Vacancies

Many-body perturbation theory is used to calculate the correlation energy of an atom with an inner-shell vacancy. Numerical calculations are given for neon with either a $1s$ or a $2s$ vacancy. For the case of the $1s$ vacancy, the energy has an imaginary part which is proportional to the Auger rate. Our results are compared with semiempirical determinations of the correlation energy and with experimental results for the fluorescence yield.