  We analyze a model of interacting particles and strings described by a path
integral with the Dirichlet boundary conditions. Such model is a natural
framework to examine the processes involving the center-of-mass motion of
string theory D0-branes: recoil, annihilation and pair production. We
demonstrate that, within the proposed formalism, the exclusive
annihilation/pair-production amplitudes admit a saddle point evaluation. Even
though the saddle point equation cannot be solved analytically, it allows to
extract valuable information on the coupling constant dependence of the
amplitudes. In particular, D0-brane pair production turns out to be suppressed
as exp[-O(1/g_{st}^2)], much stronger than the naive expectation
exp[-O(1/g_{st})]. All our derivations generalize rather immediately to the
case of unstable D0-brane decay. In conclusion, we briefly comment on the
possible implications our results may have for the conventional
soliton-anti-soliton annihilation.
