Effect of the Imprisonment of Resonance Radiation on Excitation Experiments

The theory of the imprisonment of resonance radiation developed by Holstein and by Bieberman is applied to the analysis of experimental measurements of excitation cross sections for the resonance ($n{}_{}{}^1{}_{}{}^{}P$) states of helium. The transport equation for the density of atoms in the resonance state is solved numerically for the case of a thin sheet of exciting electrons between parallel plane electrodes. The fraction of the resonance atoms producing visible radiation is then calculated for parallel plane geometry and estimated to within five percent for cylindrical geometry with an axial electron beam. Predictions of the theory are compared with the available experimental data for helium. The theory shows that at the helium pressures commonly used (${10}^{-3\mathrm{}}$ to ${10}^{-1\mathrm{}}$ mm of Hg) the observed visible radiation may easily be a factor of ten greater than that expected when imprisonment effects are neglected. As a result, the cross sections for the excitation of the $n{}_{}{}^1{}_{}{}^{}P$ states given in the literature are much too large. For example, our analysis of the available experimental data suggests that the cross section for excitation by electrons to the $3{}_{}{}^1{}_{}{}^{}P$ state of helium at 100 electron volts is 3×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ instead of 4×${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ as given in the literature.