Wave Functions of Heliumlike Systems in Limiting Regions

Abstract

We find approximate analytical presentation of the solutions $\Psi(r_1, r_2, r_{12})$ of Schr\"odinger equation for two-electron system bound by the nucleus, in the space region $r_{1,2}=0$ and $r_{12}=0$ that are of great importance for a number of physical processes. The presentation is based on the well known behavior of $\Psi(r_1, r_2, r_{12})$ near the singulartriple coalescence point. The approximate functions are compared to the locally correct ones obtained earlier by the Correlation Function Hyperspherical Harmonic (CFHH) method for helium atom, light heliumlike ions and for the negative ion of hydrogen $H^-$. The functions are shown to determine a natural basis for the expansion of CFHH functions in the considered space region. We demonstrate, how these approximate functions simplify the calculations of the high energy ionization processes.