LAUSR

Abstract 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 ≤ λ ≤ 1 (“collinear parameter”) where λ = 0 corresponds to the electron-nucleus ( e − n ) coalescence and λ = 1 corresponds to the electron–electron ( e − e ) coalescence. In general, λ > 0 corresponds to the n-e-e configuration, and λ 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 two-electron 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 λ are presented. The first few angular Fock coefficients for collinear configurations are derived as functions of λ . 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.