Polarizability Pathology of the Fermi-Omont Pseudopotential

Any realistic electron-atom or ion-atom potential energy function contains a long range contribution from the atomic polarizability which gives a 1/r^4 long-range tail. For orbital momenta L>0, this is well-known to modify the Wigner threshold law, causing scattering phaseshifts to vary linearly in energy instead of as k^(2L+1). As a result, the L>0 Fermi-Omont zero-range pseudopotentials are erroneously divergent at zero energy, due to this modification, a divergence deriving from very long range physics that should not be incorporated into a Dirac delta function. Here we investigate some alternative scenarios for repairing this pathological behavior, with some accurate benchmarking tests for comparison.