Near-threshold quantization and level densities for potential wells with weak inverse-square tails

A previous study detailed the near-threshold quantization rule for strongly attractive inverse square tails. No attempt has been made to address this rule for potential wells with weakly attractive or repulsive inverse-square tails. This paper presents a comprehensive overview over the nature of near-threshold quantization rules and level densities for any strength of the 1/r² term in the potential tail.