Off-diagonal potentials in the distorted-wave expansion for electron-atom scattering

A formal discussion of the distorted-wave expansion is presented for the case of arbitrary optical distorting potentials. The authors show that the use, without further modifications, of such potentials of order greater than n in a DW expansion limited to order n results in multiple counting. Several local approximations to the second-order off-diagonal potential are examined. These potentials, along with the partial-wave amplitudes to which they give rise, are compared with the results of an exactly equivalent potential treatment for the 1s to 2s excitation of atomic hydrogen at energies of 100 eV and above.