  A diagrammatic approach to quark exchange processes in meson-meson scattering
is applied to the case of inelastic reactions of the type
$(Q\barQ)+(q\barq)\rightarrow (Q\barq) + (q\barQ)$, where $Q$ and $q$ refer to
heavy and light quarks, respectively. This string-flip process is discussed as
a microscopic mechanism for charmonium dissociation (absorption) in hadronic
matter. The cross section for the reaction $J/\psi + \pi \to D+ \bar D$ is
calculated using a potential model, which is fitted to the meson mass spectrum.
The temperature dependence of the relaxation time for the $\J/Psi$ distribution
in a homogeneous thermal pion gas is obtained. The use of charmonium for the
diagnostics of the state of hot hadronic matter produced in ultrarelativistic
nucleus-nucleus collisions is discussed.
