Energy level inequalities in a open-quote open-quote wrinkled close-quote close-quote quarkonium potential

The open-quote open-quote concave close-quote close-quote downward property of the standard static q bar q potentials leads to the energy level inequalities En+2-En+1<En+1-En in the quarkonium mass spectrum. However, this inequality is experimentally observed to be reversed for n=2 in charmonium and n=3 in bottomonium, a fact that is inexplicable in terms of any known concave downward potential. We attempt to explain this by allowing for the violation of the concavity condition in a small interval, i.e., a open-quote open-quote wrinkle close-quote close-quote in some recently proposed quarkonium potentials. copyright 1996 The American Physical Society