Study of Electron Correlation in Helium-Like Systems Using an Exactly Soluble Model

The exact solution of a two-electron system in which the electron-electron interaction is Coulombic but the electron-nuclear attraction is a harmonic oscillator potential gives the following wave function: ₁₂f (r₁₂), where the 's are one-particle spherical harmonic oscillator wave functions. The exact f (r₁₂) has only a small curvature in r₁₂, the distance between the two electrons. This exactly soluble model is used to gain some insight into electron correlation in actual two electron atoms and into the usual approximations. A variational trial function, f (r₁₂) =1+r₁₂, where is a variable parameter, gives energies and even wave functions close to the exact solution. The correlation energy determined from an analytic Hartree-Fock solution and the average angle between the two electrons are somewhat less than in actual helium-like systems.