Ionization cross sections and contributions of continuum to optical characteristics of Rydberg states

Simple analytical properties of ionization cross sections allow high-precision evaluations of contributions from integrals over continuum to sum rules for oscillator-strength moments and to the blackbody-radiation-induced shifts of atomic levels. The contributions from continuum and from infinite sums over discrete states are presented in terms of the cross section for the threshold photoionization. General properties of the indicated contributions are determined for bound states with small angular momenta (l <= 3) in hydrogen atoms. Asymptotic presentations for the contributions from continuum to the sums of oscillator-strength moments are proposed for highly excited Rydberg states. The estimate is given to the accuracy of determining the infinite sum over discrete states by a sum of a finite number of terms.