Splitting of thePstates in heavy quarkonium systems and the nature of the spin-dependent potential

We consider the behavior of the splittings between the L=1 states in heavy quarkonium systems. With standard assumptions, the ratio of mass splittings, $R_{\chi }$=($M_2$-$M_1$)/($M_1$-$M_0$) is shown to grow slowly as we go from the lowest P states to their radial excitations, a behavior which is in accord with other theoretical calculations and is consistent with experiment. This behavior is the opposite of what is expected from a naive argument which we present. We show why the naive argument fails and how the phenomenological division of the potential into components which correspond to the exchange of a Lorentz scalar and vector can be made so as to obtain other behaviors.