Simplified model for the scattering of zero energy electrons by helium atoms

A local effective potential, H ex has been used to account for electron exchange, together with a model hamiltonian for the helium atom in Kohn's variational approximation to the electron helium scattering length, a. H ex was chosen to give agreement with the Born-exchange and static-exchange approximations. Correlation was introduced in the 84 term that trial function by using interelectronic coordinates. The method provides an upper bound to the 'model' scattering length and the value of 1.16a 0 was obtained in good agreement with more elaborate calculations and with experiment.