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 1 s n l 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 1 s density of the helium cation, while D > ( r ) extracts the n l density of the hydrogen atom from D ( r ) . The radial separation 〈 | r 1 − r 2 | 〉 , 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 ) .