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Wavefunctions of helium-like systems in limiting regions
Authors:E G Drukarev  M Ya Amusia  E Z Liverts  R Krivec  V B Mandelzweig
Institution:(1) Konstantinov Petersburg Nuclear Physics Institute, Russian Academy of Sciences, Gatchina, St. Petersburg, 188300, Russia;(2) Racah Institute of Physics, The Hebrew University, 91904 Jerusalem, Israel;(3) Ioffe Physicotechnical Institute, St. Petersburg, 194021, Russia;(4) Department of Theoretical Physics, Josef Stefan Institute, 1001 Ljubljana, Slovenia
Abstract:We find an approximate analytic form for the solution ψ(r 1, r 2, r 12) of the Schrödinger equation for a system of two electrons bound to a nucleus in the spatial regions r 1 = r 2 = 0 and r 12 = 0, which are of great importance for a number of physical processes. The forms are based on the well-known behavior of ψ(r 1, r 2, r 12) near the singular triple coalescence point. The approximate functions are compared to the locally exact 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.
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