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

The one-electron radial density function D(r)D(r) has recently been found to be separable into inner D<(r)D<(r) and outer D>(r)D>(r) radial density functions. The inner D<(r)D<(r) and outer D>(r)D>(r) densities are studied for 28 singly-excited 1snl1snl singlet and triplet states (0≤l(r)D>(r) are discussed within the Hartree–Fock framework. Comparison of correlated D<(r)D<(r) and D>(r)D>(r) with hydrogenic radial densities based on the modal characteristics and Carbó’s similarity index clarifies that D<(r)D<(r) represents the 1s1s density of the helium cation, while D>(r)D>(r) extracts the nlnl density of the hydrogen atom from D(r)D(r). The radial separation 〈|r1−r2|〉〈|r1−r2|〉, which constitutes a lower bound to the standard deviation of D(r)D(r), is shown to be estimated from the location of the outermost maximum of D>(r)D>(r).