  We propose a semiclassical approach to calculate multiparticle cross sections
in scalar theories, which have been strongly argued to have the exponential
form $\exp(\lambda^{-1}F(\lambda n,\epsilon))$ in the regime $\lambda\to0$,
$\lambda n$, $\epsilon=$ fixed, where $\lambda$ is the scalar coupling, $n$ is
the number of produced particles, and $\epsilon$ is the kinetic energy per
final particle. The formalism is based on singular solutions to the field
equation, which satisfy certain boundary and extremizing conditions. At low
multiplicities and small kinetic energies per final particle we reproduce in
the framework of this formalism the main perturbative results. We also obtain a
lower bound on the tree--level cross section in the ultra--relativistic regime.
