  The annihilation of heavy particles close to thermal equilibrium, which plays
a prominent role in the chemical equilibration of heavy quarks in the
Quark-Gluon Plasma (QGP) as well as in many classic dark matter scenarios, is
reexamined. We derive a scattering amplitude that resums near-threshold
attractive interaction of the annihilating particles in terms of the
non-relativistic scattering $T$-matrix and Green's function, thereby capturing
the pertinent Sommerfeld enhancement from both nonperturbative scattering state
and bound state solutions. The derived formula is of such generality that it
applies to arbitrary partial wave processes of two-particle annihilation, and
enables to incorporate finite widths of the annihilating particles. In a
screened potential model, the non-perturbative scattering amplitude is computed
and the Sommerfeld enhancement is identified for heavy quark-antiquark
annihilation in the QGP.
