Inverse scattering problem for quarkonium systems. II. Applications toψandϒfamilies

Abstract

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 $\psi \mathrm{}\left(3.095\right)\mathrm{}$ and ${\psi }^{\prime }\mathrm{}\left(3.684\right)\mathrm{}$ levels and leptonic decay widths. Remaining ambiguities are discussed in detail. Consequences for the $\Upsilon$ family and prospects for refining the interquark potential are explored.