PHENOMENOLOGICAL PI-N-]PI-PI-N AMPLITUDE AND ANALYSIS OF LOW-ENERGY DATA ON TOTAL CROSS-SECTIONS AND 1-D DISTRIBUTIONS

We develop the phenomenological amplitude of the pi N --> pi pi N reac tion taking into account the exchanges of Delta and N-() along with t he OPE mechanism and the polynomial background derived with the accoun t of isotopic, crossing, C, P and T symmetries of strong interactions. The data base consisting of total cross sections in the energy region 0.300 less than or equal to P-Lab less than or equal to 500 MeV/c and 1D distributions from the bubble-chamber experiments was used to dete rmine free parameters of the amplitude. For the first time there was f ound an amplitude equally well describing the broad variety of differe nt data in all reaction channels. The best solutions are characterized by chi(DF)(2) The isobar exchanges are found to be more important tha n OPE at the considered energies. Despite this the parameters of OPE a re statistically significant; however, the pi pi-scattering lengths ap pear different in different solutions.