  The doubly differential cross sections for the $^4$He$(\pi^+,\pi^-) 4p$
reaction were calculated using both a two-nucleon sequential single charge
exchange model and an intranuclear cascade code. Final state interactions
between the two final protons which were the initial neutrons were included in
both methods. At incident pion energies of 240 and 270 MeV the low-energy peak
observed experimentally in the energy spectrum of the final pions can be
understood only if the contribution of pion production is included. The
calculated cross sections are compared with data.
