Bethe Surface and Inelastic and Elastic Differential Cross Sections for Helium Obtained by Use of 25-keV Incident Electrons

The complete electron-impact spectra, including the elastic scattering, for He have been obtained at the scattering angles 1°, 1.5°, 2°, 3°, 4°, 5°, 7°, and 10° using 25-keV incident electrons. The data cover the momentum-transfer region from 0.8 to 7.5 in atomic units (a.u.). Measured intensities were converted approximately to relative generalized oscillator strengths for different values of energy transfer, and placed on an absolute scale by use of the Bethe sum rule. Although sum-rule normalization using the energy-loss spectrum at a fixed angle is not rigorous, it is justified in the large-angle high-energy limit. Comparison of the results with the theory proved that use of sum-rule normalization was justified at angles as small as 1°. The first-Born theory was shown to be in agreement with experiment over the complete data range. In the case of the binary-encounter theory, good agreement with experiment was obtained from momentum-transfer values greater than 4 a.u. Below 4 a.u. substantial deviations were observed, especially in regions removed from the maximum of the spectral distribution. Sums of the generalized optical-oscillator strength, the x-ray incoherent-scattering factor $S\left(K\right)\mathrm{}$,, the elastic differential, and total scattering cross sections were all computed from the experimental data. The experimental values of $S\left(K\right)\mathrm{}$ and the elastic differential cross section agreed with accurate theoretical calculations to an average accuracy of 2%. Compton profiles obtained at 5°, 7°, and 10° were found to be in excellent agreement with previous electron-impact, x-ray, and $\gamma$-ray measurements. The unresolved autoionizing double excitations ($2s2p$, $2p^{ 2}$, etc.) at an energy loss of 60 eV were observed at both 1° and 2.7°. The $2{}_{}{}^1{}_{}{}^{}P\leftarrow 1{}_{}{}^1{}_{}{}^{}S$ transition at 21.2 eV was also a prominent feature of the Bethe surface and could still be observed at angles as large as 4°.