Experimental differential scattering cross sections for excitation of helium by electron impact from its ground state to its $2{}_{}{}^1{}_{}{}^{}S$ state are presented at four incident electron energies in the range 26-55.5 eV for scattering angles between 10° and 70° and at 81.6 eV for scattering angles between 10° and 80°. These differential cross sections are normalized by using previously determined $2{}_{}{}^1{}_{}{}^{}P$ cross sections and measured $\frac{2{}_{}{}^1{}_{}{}^{}S}{2{}_{}{}^1{}_{}{}^{}P}$ cross-section ratios. These experimental cross sections and cross-section ratios are compared with results predicted by the Born approximation, the polarized Born approximation, and several other first-order approximations in which direct excitation is calculated in the Born approximation and exchange scattering in various Ochkur-like approximations. Calculations based on these approximations are also compared to the data of other experimenters at energies up to 600 eV. The effect on the small-angle scattering of several nonadiabatic dipole-polarization potentials is examined. For the 34-81. 6-eV energy range, it is shown that the inclusion of polarization is necessary for accurate predictions of the angle dependence of the $2{}_{}{}^1{}_{}{}^{}S$ cross sections at small angles. Cross sections resulting from the use of analytic self-consistent-field wave functions for both the ground and excited states are presented. They agree well with those obtained from more accurate correlated wave functions.

• Received 20 September 1971

DOI:https://doi.org/10.1103/PhysRevA.5.762