Abstract
Inelastic unitarity contribution to the pion-nucleon ${S}_{\frac{1}{2}}$, $T=\frac{1}{2}$ zero-energy scattering length has been determined following the modified $\frac{N}{D}$ formalism due to Froissart. The fixed-energy dispersion relations and the experimental information for the $s$-wave inelastic parameter have been used to solve the resulting dispersion equations in the effective-range approximation method of Bal\'azs. We find a large positive scattering length, indicating that the inclusion of inelastic effects generates an attractive interaction in the $s$ wave.
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