Visualization of electron correlation in a series of helium S states

Electron correlation has been studied for a series of helium S states represented by a variety of wavefunctions, the best of which are accurate Hylleraas—Kinoshita functions. The states studied are the ground state, the lowest excited ¹S and ³S states, and the (2s)² and (2p)² doubly-excited ¹S states. Primary data is obtained from graphs of the conditional probability density as a function of the radial distance r₂ and the interelectronic angle θ₁₂, given that r₁ is fixed at various distances. Such graphs make clear the extent to which characteristics such as angular and radial correlations, and Fermi and Coulomb holes, are consequences of the relative motion of electrons in two-electron atoms.