“…The data from Refs. [24,25,26] for π + p → π + π + n, [27,28,29,30,31,32,33,34,35,36] for π − p → π + π − n, and [37,38,39,40,41] for π − p → π 0 π 0 n. section indicates the increase by about 25 % with R N ∆ = 0.4 and 65 % with R N ∆ = 0.8 around T π = 300 MeV. These two channels exhibit large influence of the π∆∆ interaction on the total cross section.…”