Study of correlation effects in an exactly solvable model two-electron system

The correlation energies for a system of two electrons moving under mutual Coulomb repulsion augmented by a linear interparticle potential and bound to a central harmonic oscillator potential are studied through an exact analytical solution proposed recently by the authors. The same are also obtained for a related model with no linear term through numerical solution. Several plots of the local as well as averaged correlation holes for varying strengths of the binding potential for both the models provide insight into the shape and radius of the holes. The effect of correlation on the single particle density is manifested through reduction of the probability density near the center with a consequent increase in the outer region.