Fredholm Determinants Applied to Electron-Hydrogen Scattering

The properties of the Fredholm determinant for the electron-hydrogen atom system are discussed. These properties are used to derive formulas for the elastic-scattering phase shifts. $S$- and $P$-wave phase shifts are calculated for low energies and the results are compared with other recent calculations. Exchange effects are fully accounted for in the formalism, and a formula is given for the scattering amplitude when two exit channels are present.