The fine and hyperfine structure and dipole transitions of charmonium and bottonium in the two-step potential model

The fine and hyperfine structure and dipole transitions of the charmonium (cc-bar) and bottonium (bb-bar) systems are investigated in a simple quark-confining, analytically solvable, nonrelativistic quark-antiquark (two-step) potential, V = Vsub(V) + Vsub(S) where Vsub(V) is the fourth component of a vector potential and Vsub(S) is a scalar potential. Our predictions for the splittings of the P-state multiplets and for the absolute masses of the various 3Psub(J)(chi) states of cc-bar and bb-bar systems are in good agreement with the data. For the hyperfine splittings of bb-bar system they are obtained Msub(GAMMA) - Msub(etasub(b))' = 42 MeV and Msub(GAMMA') -Msub(etasub(b))' = 34 MeV, which are comparable with the other theoretical predictions. Our results for the dipole transition rates are also comparable with the available experimental data and with other theoretical predictions