Quarkonia potential by a numerical inversion method with given end-point behavior

From observables we construct a unique spin-averaged quarkonia potential consistent with specified end-point behavior. At small quark-antiquark separation, we assume asymptotic freedom and at large separation, linear confinement. At intermediate radii the potential is expressed in terms of Fourier coefficients. Spin-averaged $\psi$ and $\Upsilon$ energy levels and relative leptonic widths determine a unique flavor-independent potential and $c$- and $b$-quark masses.