Simple local potentials for elastic scattering of electrons by noble-gas atoms

We study the performance of a simple l-dependent but otherwise local electron--noble-gas potential consisting of the direct electrostatic terms plus a 1/r⁴ polarization potential, which merges into a constant for r{≤}r₀, r₀ depending on the target atom and the partial wave. This simple one-parameter potential reproduces low-energy elastic-scattering data by helium, neon, and argon, as well as the most advanced and sophisticated ab initio calculations. In a partial wave containing at least one occupied single-particle state in the target atom, the condition that the highest-lying bound state in the local potential has maximum overlap with the corresponding Hartree-Fock single-particle state of the atom, may serve as criterion for determining r₀.