A theoretical explanation of the observed splittings among the $P$ states of charmonium is given with the use of a nonsingular potential model for heavy quarkonia. We also show that the recently observed mass difference between the center of gravity of the ${}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}$ states and the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state of $c\overline{c}$ does not provide a direct test of the color hyperfine interaction in heavy quarkonia. Our theoretical value for the mass of the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state is in agreement with the experimental result, and its $E1\mathrm{}$ transition width is 341.8 keV. The mass of the ${\eta }_c^{\prime }$ state is predicted to be 3622.3 MeV.

• Received 24 September 1993

DOI:https://doi.org/10.1103/PhysRevD.49.1551