Pion-helium potential by inverse scattering method

The inverse scattering formalism is applied to the case of the pion-helium system to obtain the real and imaginary parts of a local phenomenological potential from π^-{{{-}}}⁴$He partial wave phase shifts at a fixed energy. The phase shifts and inelasticities for all partial waves up to angular momentum l=9 are extracted from the differential cross-section data by parametrizing the nuclear amplitude. The method has been tried for a number of incident pion energies between 51 and 110 MeV. The real and imaginary parts of the potential are seen to compare well with the commonly used pion-nucleus Laplacian potential.