Experimentally favoured potential for mesons

We show first that a natural potential to be used in a semirelativistic wave equation for theS=1,J=J _max light and heavy mesons is, forr?1 Fermi,V(r)=ar+b/r withb??π/2, forr?1 Fermi,V(r)=cln(r/r ₀). Next we show that this particularb value favours in fact a QCD-like potential forr?1 Fermi so that a logarithmic potential is only an effective one in a smallr region.