  The propagator in the instanton background in the -lambda phi^4 scalar model
in four dimensions is studied. Leading and sub-leading terms of its asymptotics
for large momenta and its on-shell double residue are calculated. These results
are applied to the analysis of the initial state and initial-final state
corrections and the calculation of the next-to-leading (propagator) correction
to the exponent of the cross section of multiparticle scattering processes.
