Inner and outer radial density functions in singly-excited 1snl states of the He atom

The one-electron radial density function D(r) has recently been found to be separable into inner D_<(r) and outer D_>(r) radial density functions. The inner D_<(r) and outer D_>(r) densities are studied for 28 singly-excited 1snl singlet and triplet states (0≤l<n≤5) of the He atom at a correlated level. Theoretical structures of D_<(r) and D_>(r) are discussed within the Hartree-Fock framework. Comparison of correlated D_<(r) and D_>(r) with hydrogenic radial densities based on the modal characteristics and Carbó’s similarity index clarifies that D_<(r) represents the 1s density of the helium cation, while D_>(r) extracts the nl density of the hydrogen atom from D(r). The radial separation 〈|r₁−r₂|〉, which constitutes a lower bound to the standard deviation of D(r), is shown to be estimated from the location of the outermost maximum of D_>(r).