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In frame of a phenomenological approach based on Compton-like Feynmanamplitudes, we study multi-pion production in antiproton nucleon collisions.The main interest of this reaction is related to the possibility to study theproperties of the presumable $\bar N N$ atom and of its resonances. For thecase of formation of a scalar or pseudoscalar resonant state, with$I^G(J^{P})=1^-(0^{\pm}),~0^+(0^-)$ numerical results are obtained. Thedifferential cross section in an experimental set-up where the pions invariantmass is measured, is given with explicit dependence on the lepton pair andpions invariant mass.

Study of resonant processes for multi-pion production in $\bar p +p\to\ell ^++\ell^- +n_\pi \pi$ annihilation