ABSTRACT We demonstrate a new technique for calculating proton-proton inelastic cross-section, which allows one by application of the Laplace' method replace the integrand in the integral for the scattering amplitude in the vicinity of the maximum point by expression of Gaussian type. This, in turn, allows us to overcome the computational difficulties for the calculation of the integrals expressing the cross section to sufficiently large numbers of particles. We have managed to overcome these problems in calculating the proton-proton inelastic cross-section for production (n ≤ 8) number of secondary particles in within the framework of φ3 model. As the result the obtained dependence of inelastic cross-section and total scattering cross-section on the energy √s are qualitative agrees with the experimental data. Such description of total cross-section behavior differs considerably from existing now description, where reggeons exchange with the intercept greater than unity is considered.
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I. Sharf, A. Tykhonov, G. Sokhrannyi, M. Deliyergiyev, N. Podolyan and V. Rusov, "Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 2," Journal of Modern Physics, Vol. 3 No. 1, 2012, pp. 16-27. doi: 10.4236/jmp.2012.31003.
 I. Sharf, G. Sokhrannyi, A. Tykhonov, K. Yatkin, N. Po-dolyan, M. Deliyergiyev and V. Rusov, “Mechanisms of Proton-Proton Inelastic Cross-Section Growth in Multi-Peripheral Model within the Framework of Perturbation Theory. Part 1,” Journal of Modern Physics, Vol. 2, No. 12, 2011, pp. 1480-1506.
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