Investigation of the pion--pion interaction at low energies in. pi. N. --> pi pi. N reactions near the threshold

Investigations of the ..pi pi.. interaction in ..pi..N..--> pi pi..N reactions near the threshold are briefly reviewed. The experimental data were obtained mainly on the synchrocyclotron of the Laboratory of Nuclear Problems at the Joint Institute for Nuclear Research. The experimental data on the scattering lengths and phase shifts of s-wave ..pi pi.. scattering and also the total cross sections of ..pi..N..--> pi pi..N reactions near the threshold are analyzed in the framework of the theory of broken chiral symmetry. The obtained results show that it is fruitful to use chiral theory to describe the ..pi pi --> pi pi.. and ..pi..N..--> pi pi..N processes at low energies.