Abstract Two potentials are called equivalent if they give the same asymptotic phase shift for elastic scattering. A study was made of the equivalent local potentials (ELP) derived from nonlocal potentials produced by Hartree-Fock (HF) and Brueckner-Hartree-Fock calculations. The methods used to derive these ELP are analytic. Application has been made to low energy elastic scattering from closed shell nuclei. Both the ELP and the damping function vary slowly with energy within the range from 0 to 6 MeV. The range of the ELP increases with A in approximate agreement with the nuclear size, but the functional form becomes less smooth, an effect most likely due to truncation effects in the original HF calculation.