Inverse scattering problem for quarkonium systems. II. Applications to ψ and ϒ families

The inverse scattering formalism for reflectionless potentials is extended to the reconstruction of central potentials in three space dimensions. An approximate interquark potential is derived from the ψ(3.095) and ψ^'(3.684) levels and leptonic decay widths. Remaining ambiguities are discussed in detail. Consequences for the Υ family and prospects for refining the interquark potential are explored.