Formulae for Enhanced Cross Sections Induced by Unusual Resonant Poles

Abstract We extend the traditional effective range theory, which can explain the low-energy scattering phenomena by a real potential in neutron plus target systems, to describe the scattering by a complex potential. The extension is achieved based on an analytic Jost function, and we construct analytic formulae to describe enhanced cross sections in neutron scattering originating from unusual resonant states, such as an antiresonant state and an unstable bound state, appearing around zero momentum. The formulae are checked by comparing them with numerical calculations, and we find that the analytic formulae are quite valid in reproducing the cross sections for shape elastic scattering and compound nucleus formation in low-energy neutron scattering.