LAUSR

Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using several fully three-body methods of variational and direct types, the ground state wave functions Ψ of the helium-like atomic systems with nucleus charge 1 ≤ Z ≤ 5 are calculated in a few coordinate systems including the hyperspherical coordinates R,α,θ. The wave functions Ψav(R) of the hyperspherical radius R are calculated numerically by averaging Ψ over the hyperspherical angles α and θ. The exact analytic representations for the relative derivatives Ψav′(0)/Ψav(0) and Ψav′′(0)/Ψav(0) are derived. Analytic approximations very close to Ψav(R) are obtained. Using the Pekeris-like wave functions Ψ, the one-electron densities ρ(r) are calculated as functions of the electron–nucleus distance r. The relevant derivatives ρ′(0)/ρ(0) and ρ″(0)/ρ(0) characterizing the behavior of ρ(r) near the nucleus are calculated numerically. Very accurate analytical approximations, representing the one-electron density both near the nucleus and far away from it, are derived. All the analytical and numerical results are supplemented with tables and graphs.Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using several fully three-body methods of variational and direct types, the ground state wave functions Ψ of the helium-like atomic systems with nucleus charge 1 ≤ Z ≤ 5 are calculated in a few coordinate systems including the hyperspherical coordinates R,α,θ. The wave functions Ψav(R) of the hyperspherical radius R are calculated numerically by averaging Ψ over the hyperspherical angles α and θ. The exact analytic representations for the relative derivatives Ψav′(0)/Ψav(0) and Ψav′′(0)/Ψav(0) are derived. Analytic approximations very close to Ψav(R) are obtained. Using the Pekeris-like wave functions Ψ, the one-electron densities ρ(r) are calculated as functions of the electron–nucleus distance r. The relevant derivatives ρ′(0)/ρ(0) and ρ″(0)/ρ(0) characterizing the behavior of ρ(r) near the nucleus are calculated numerically. Very accurate analytical approximations, representing the one-elect...