Phase-shift analysis ofe-He scattering data and determination of the potential by inversion

A parametrized phase-shift analysis of the e-He scattering data of Andrick and Bitsch for energies below the first excitation threshold is carried out. This approach does not assume that the higher-order phase shifts are given by the Born approximation and allows a rigorous analysis of the statistical errors. We obtain better ${\chi }^2$ values for our fits to these data than do Andrick and Bitsch. As a by-product of our phase-shift analysis we can obtain the interaction potential with associated confidence limits. The tail of these potentials is consistent with the assumption of adiabatic polarization at energies below the first excitation threshold.