Multiple-Scattering Expansions for Nonrelativistic Three-Body Collision Problems. VII. Differential Cross Section for Elastic Scattering

The energy and angular dependences of the differential elastic scattering cross section are investigated in the first-order Faddeev-Watson multiple-scattering (FWMS) approximation for a number of three-body atomic systems. The anomalies in the first-order Born approximation are not present in the first-order FWMS approximation. Significant differences are found between the elastic ($e^{-}$, H) and ($e^{+}$, H) scattering at energies as high as 10 keV. The elastic ($e^{+}, e^{-}{e}^{+}$) and ($p^{+}, e^{-}{e}^{+}$) scattering cross sections which are incorrectly predicted to be zero in the first-order Born approximation are calculated. The forward-angle peaking of the elastic scattering cross section is accounted for in the first-order FWMS approximation by allowing the system to participate in the intermediate inelastic scatterings. In general, significant differences are found in the magnitude of the cross sections obtained in the first-order FWMS and Born approximations at energies where the first-order Born approximation has been extensively used for normalizing experimental results. The energy for the first-order Born approximation, to be accurate, can be determined experimentally by locating the energy above which the difference between the ($e^{-}$, H) and ($e^{+}$, H) scatterings ceases to be appreciable.