WAVE FUNCTIONS OF HELIUM-LIKE SYSTEMS IN LIMITING REGIONS
Drukarev E.G., Amusia M.A., Liverts E.Z., Krivec R., Mandelzweig V.B.

Received: June 12, 2006

PACS: 32.80.Fb, 31.15.Ja

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We find an approximate analytic forms for the solutions Ψ(r₁, r₂, r₁₂) of the Schrodinger equation for a system of two electrons bound to a nucleus in the spatial regions r₁=r₂=0 and r₁₂=0 that are of great importance for a number of physical processes. The forms are based on the well-known behavior of Ψ(r₁, r₂, r₁₂) near the singular triple coalescence point. The approximate functions are compared to the locally precise ones obtained earlier by the correlation function hyperspherical harmonic (CFHH) method for the helium atom, light helium-like ions, and the negative ion of hydrogen H^-. The functions are shown to determine a natural basis for the expansion of CFHH functions in the considered spatial region. We demonstrate how these approximate functions simplify calculations of high-energy ionization processes.