Collinear configuration of the helium atom and two-electron ions

Collinear configurations of the helium-like atomic systems, relevant, e.g., for the quasifree mechanism of the double photoionization of helium, are studied, parameterized by the single scalar parameter -1 <= lambda <= 1 (collinear parameter) where lambda = 0 corresponds to the electron-nucleus (e-n) coalescence and lambda = 1 corresponds to the electron-electron (e-e) coalescence. In general, lambda 0 corresponds to the n-e-e configuration, and lambda < 0 to the e-n-e configuration. Simple mathematical representations of the expectation values of the Dirac delta function relevant for the collinear configurations are derived and calculated from fully three-body dynamics without approximation for the twoelectron atomic wave functions with nuclear charge 1 <= Z <= 5. Simple formulas for calculating the expectation values of the kinetic and potential energy operators in collinear configurations are derived. Unusual physical properties of the n-e-e collinear configurations found for certain ranges of lambda are presented. The first few angular Fock coefficients for collinear configurations are derived as functions of lambda. Highly accurate model wave functions describing the ground states of the two-electron atoms with a collinear arrangement of the particles are constructed. All results are illustrated in tables and figures. (C) 2020 Elsevier Inc. All rights reserved.