Statistical electron correlation coefficients for the five lowest states of the heliumlike ions

Statistical correlation coefficients were introduced by Kutzelnigg, Del Re, and Berthier to provide overall measures of the difference between the electron pair density and the product of one-electron densities in atoms and molecules. Some properties of these coefficients are discussed, and it is shown that an angular correlation coefficient is experimentally accessible. Radial and angular correlation coefficients are computed from highly accurate wave functions for the 1¹S, 2³S, 2¹S, 2³P, and 2¹P states of the heliumlike ions from He through Mg¹⁰⁺. It is found that positive angular correlation coefficients occur in the 2¹P state of the two-electron positive ions but not in neutral helium. Moreover, the angular correlation coefficients for the 2¹S and 2³S states of the positively charged two-electron ions show that a previously proposed reformulation of Hund's rule is incorrect.