  We study the pi N -> pi pi N reaction around the N(1440) mass-shell energy.
Considering the total cross sections and invariant mass distributions, we
discuss the role of N(1440) and its decay processes. The calculation is
performed by extending our previous approach [Phys. Rev. C 69, 025206 (2004)]
to this reaction, in which only the nucleon and Delta(1232) were considered as
intermediate baryon states. The characteristics observed in the recent data for
the pi- p -> pi0 pi0 n reaction obtained by Crystal Ball Collaboration (CBC),
can be understood as a strong interference between the two decay processes:
N(1440) -> pi Delta(1232) and N(1440) -> N(pi pi)_S. It is also found that the
scalar-isoscalar pi pi rescattering effect in the NN*(pi pi)_S vertex, which
corresponds to the propagation of sigma meson, seems to be necessary for
explain ing the several observables of the pi N -> pi pi N reaction: the large
asymmetric shape in the pi0-pi0 invariant mass distributions of the pi- p ->
pi0 pi0 n reaction and the pi+ p -> pi+ pi+ n total cross section.
