Tests of Born Approximations: Differential and Total Cross Sections for Elastic Scattering of 100- to 400-eV Electrons by Helium

The angular dependence of elastic scattering of 100- to 400-eV electrons by helium atoms has been measured for scattering angles of 5\ifmmode^\circ\else\textdegree\fi{} to 30\ifmmode^\circ\else\textdegree\fi{} with a high-resolution electron spectrometer. The observed relative differential cross sections were converted to an absolute basis by measuring their ratio to known cross sections for excitation to the $2^{1}P$ state. Integration over angles yielded total elastic scattering cross sections. Large deviations from the Born approximation are found, especially for small electron energies and small scattering angles. Experimental and theoretical results are analyzed and compared in some detail. Exchange and polarization are chiefly responsible for deviations from the Born approximation. The Ochkur (Bonham) approximation is shown to be almost equivalent to the first-order exchange approximation for electron energies of 350 and 500 eV. Analytical series expansions for differential and total Born cross sections are given. Our experimental results are in qualitative agreement with results of earlier experiments, but are quantitatively different and extend to smaller scattering angles.