Abstract
A field-theoretic study of the simultaneous electron-photon excitation (SEPE) and direct electron excitation (DEE) is done for the He $1{}^{1}\stackrel{\ensuremath{\rightarrow}}{S}2{}^{3}S$ transition by spin polarized electrons in the field of soft photons. The ratio of SEPE to DEE is found to lie around $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ for the 0.117-eV photon and incident electron of energy ${E}_{i}$ between 19.817 and 20 eV. The present result is compared with the existing experimental data.
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