Analytic representation of the dipole oscillator-strength distribution. II. The normalization factor for electron continuum states in atomic fields

Abstract

We address ourselves to the question what analytic formula is the most suitable for fitting the dipole oscillator-strength distribution df/dε over a wide range of the kinetic energy ε of an electron ejected from an atom or molecule. A suitable expression will enable one to interpolate or extrapolate data reliably and to use them readily in applications such as the modeling studies in radiation physics. It is useful to distinguish two factors that together constitute df/dε. The first factor is defined in terms of the dipole matrix element with respect to a final-state eigenfunction whose amplitude near the origin is independent of ε. As we showed earlier, this factor is analytic at all finite ε except at a singularity at ε=−I, where I is the ionization threshold energy. The other factor arises from the energy-scale normalization of the final-state eigenfunction, and is the object of the present discussion from several angles. First, we present a survey of numerical data for the s,p, and d states with 0≤ε≤5 a.u. for all atoms with Z≤38, evaluated within the Hartree–Slater potential model. Next, we discuss analytic properties of the normalization factor, which include its relation to the phase shift, and its behavior near a resonance. We also elucidate the connection of the continuum normalization with the bound-state normalization. Finally, we illustrate the significance of our findings in the practical fitting of the df/dε data in the presence of a resonance, taking the valence-shell ionization of Ar as an example.