FORM OF ELECTRON-ATOM EXCITATION AMPLITUDES AT HIGH MOMENTUM-TRANSFERS IN THE FADDEEV-WATSON APPROXIMATION

A form of the off-shell Coulomb T matrix, which has a well defined on-shell limit, is used in the Fadeev-Watson multiple-scattering expansion for a direct three-body collision process. Using the excitation of atomic hydrogen by electron impact as an example, approximations to the second-order terms, which are valid for high momentum transfers of the incident electron, are derived. It is shown how the resulting asymptotic behaviour of the second-order Faddeev-Watson approximation is related to the high momentum transfer limit of the second Born approximation. The results are generalised to the excitation of more complex atoms. The asymptotic forms of the Faddeev-Watson and Born approximations are compared with other theories and with measurements of differential cross sections and angular correlation parameters for the excitation of H(2p) and He(21P). The results indicate that the Faddeev-Watson approximation converges more rapidly at high momentum transfers than does the Born approximation.