Effect of charge polarization on inelastic scattering: differential and integral cross sections for excitation of the 21S state of helium by electron impact

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.