The cross sections for the production of ${\mathrm{He}}^{+}$ ion in the $4S$ state by single-electron collisions with neutral helium atoms in the ground state have been calculated by the Born approximation at various incident-electron energies from 200 to 450 eV. These cross sections range from 8.2×${10}^{-21\mathrm{}}$ to 6.6×${10}^{-21\mathrm{}}$ ${\mathrm{cm}}^2$. By using the ionization-excitation cross sections of the $4P$ and $4D$ states calculated by Dalgarno and McDowell and by extending their calculations to $4F$, the cross sections of the excitation of the $n=4\mathrm{}\to n=3\mathrm{}$ transitions of ${\mathrm{He}}^{+}$(4686 Å) have been computed. It was found that the transition $4S\to 3P$ contributes about 90% of the total radiation of the various members of the $n=4\mathrm{}\to n=3\mathrm{}$ group. The theoretical cross sections of the 4686-Å radiation agree with the experimental values to within 15%. It is concluded that the observed 4686-Å radiation can be ascribed mainly to direct ionization-excitation to the $n=4\mathrm{}$ states of ${\mathrm{He}}^{+}$ by single-electron impact, and no evidence is found for any indirect excitation mechanism which is responsible for a significant portion of the population of the $4S$ state of ${\mathrm{He}}^{+}$.

• Received 16 November 1964

DOI:https://doi.org/10.1103/PhysRev.138.A301