Calculation of the first-orders-wave optical potential in pionic atoms

A microscopic calculation of the first-order s-wave optical potential in pionic atoms which allows the inclusion of the off-shell dependence in momentum of the s-wave \ensuremath{\pi}N amplitude is carried out. Binding effects are also properly taken into account. The results obtained, together with those of the second-order optical potential, are in disagreement with phenomenological optical potentials. The results of the paper suggest the need of new and precise experiments on \ensuremath{\pi}N scattering at low energies and other experiments which can provide precise values of the \ensuremath{\pi}N scattering lengths.