  Using the color-singlet free energy F_1 and total internal energy U_1
obtained by Kaczmarek et al. for a static quark Q and an antiquark Qbar in
quenched QCD, we study the binding energies and wave functions of heavy
quarkonia in a quark-gluon plasma. By minimizing the grand potential in a
simplified schematic model, we find that the proper color-singlet Q-Qbar
potential can be obtained from the total internal energy U_1 by subtracting the
gluon internal energy contributions. We carry out this subtraction in the local
energy-density approximation in which the gluon energy density can be related
to the local gluon pressure by the quark-gluon plasma equation of state. We
find in this approximation that the proper color-singlet Q-Qbar potential is
approximately F_1 for T ~ T_c and it changes to (3/4)F_1+(1/4)U_1 at high
temperatures. In this potential model, the J/psi is weakly bound above the
phase transition temperature T_c, and it dissociates spontaneously above 1.62
T_c, while chi_c and psi' are unbound in the quark-gluon plasma. The bottomium
states Upsilon, chi_b and Upsilon' are bound in the quark-gluon plasma and they
dissociate at 4.10 T_c, 1.18 T_c, and 1.38 T_c respectively. For comparison, we
evaluate the heavy quarkonium binding energies also in other models using the
free energy F_1 or the total internal energy U_1 as the Q-Qbar potential. The
comparison shows that the model with the new Q-Qbar potential proposed in this
manuscript gives dissociation temperatures that agree best with those from
spectral function analyses. We evaluate the cross section for
sigma(g+J/psi->c+cbar) and its inverse process, in order to determine the J/psi
dissociation width and the rate of J/psi production by recombining c and cbar
in the quark gluon plasma.
