Analytic representation of the dipole oscillator-strength distribution

It is possible to represent an essential factor of the dipole oscillator-strength distribution for a single-electron continuum in terms of a compact expression involving a polynomial of several degrees in a suitable variable. The factor, which may be called the reduced oscillator-strength distribution, is defined in terms of the radial dipole matrix element with respect to the final-state wave function normalized in an energy-independent way near the origin. The key variable is g = ε/(ε+I), where ε is the kinetic energy of the ejected electron and I is the ionization threshold energy. The structure of the analytic representation has been identified through a study of the analytic properties of the dipole matrix element as a function of ε. For illustration, H, He, Li, and Na atoms are treated explicitly. Implications of our results to molecules and multichannel cases are also indicated. The present findings will be especially useful for interpolation and extrapolation of experimental data.