  Quenched lattice data for the quark-antiquark interaction (in terms of heavy
quark free energies) in the color singlet channel at finite temperatures are
fitted and used within the nonrelativistic Schroedinger equation formalism to
obtain binding energies and scattering phase shifts for the lowest eigenstates
in the charmonium and bottomonium systems in a hot gluon plasma. The partial
dissociation rate due to the Bhanot-Peskin process is calculated using
different assumptions for the gluon distribution function, including free
massless gluons, massive gluons, and massive damped gluons. It is demonstrated
that a temperature dependent gluon mass has an essential influence on the heavy
quarkonia dissociation, but that this process alone is insufficient to describe
the heavy quarkonia dissociation rates.
