  We develop a new method for taking into account the interference
contributions to proton-proton inelastic cross-section within the framework of
the simplest multi-peripheral model based on the self-interacting scalar \phi^3
field theory, using Laplace's method for calculation of each interference
contribution.
  We do not know any works that adopted the interference contributions for
inelastic processes. This is due to the generally adopted assumption that the
main contribution to the integrals expressing the cross section makes
multi-Regge domains with its characteristic strong ordering of secondary
particles by rapidity. However, in this work, we find what kind of space
domains makes a major contribution to the integral and these space domains are
not multi-Regge. We demonstrated that because these interference contributions
are significant, so they cannot be limited by a small part of them. With the
help of the approximate replacement the sum of a huge number of these
contributions by the integral were calculated partial cross sections for such
numbers of secondary particles for which direct calculation would be
impossible.
  The offered model qualitative agrees with experimental dependence of total
scattering cross-section on energy {\sqrt s} with a characteristic minimum in
the range {\sqrt s \approx 10} GeV.
  However, quantitative agreement was not achieved; we assume that due to the
fact that we have examined the simplest diagrams of \phi^3 theory.
