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 $1{}_{}{}^1{}_{}{}^{}S$, $2{}_{}{}^3{}_{}{}^{}S$, $2{}_{}{}^1{}_{}{}^{}S$, $2{}_{}{}^3{}_{}{}^{}P$, and $2{}_{}{}^1{}_{}{}^{}P$ states of the heliumlike ions from He through ${\mathrm{Mg}}^{10+}$. It is found that positive angular correlation coefficients occur in the $2{}_{}{}^1{}_{}{}^{}P$ state of the two-electron positive ions but not in neutral helium. Moreover, the angular correlation coefficients for the $2{}_{}{}^1{}_{}{}^{}S$ and $2{}_{}{}^3{}_{}{}^{}S$ states of the positively charged two-electron ions show that a previously proposed reformulation of Hund's rule is incorrect.