Electron capture into excited states of helium by helium-ion impact on helium

Cross sections for electron capture into each excited state of He up to $4{}_{}{}^{1,3}{}_{}{}^{}D$ by ${\mathrm{He}}^{+}$ impact on He in the energy range 100-10 000 keV have been calculated by means of the first Born approximation (Bates's version). A Gaussian technique previously developed for evaluating two-center integrals occurring in the Born amplitude has been used. One-parameter, variational wave functions are derived for each excited state of helium up to $4{}_{}{}^{1,3}{}_{}{}^{}D$. Some of the excited ${}_{}{}^1{}_{}{}^{}S$ cross sections are found to be affected by almost a factor of 2 by the choice of 1 ${}_{}{}^1{}_{}{}^{}S$ helium wave function and orthogonality of the excited state ${}_{}{}^1{}_{}{}^{}S$ functions to this function. The observed departure of the ratio of triplet to singlet cross sections from the statistical weight of three is related partly to the interference between a one-electron process of capture into an excited state of helium and a two-electron process of capture into the ground state with the original ${\mathrm{He}}^{+}$ electron excited, and is related partly to the difference between the variational singlet and triplet excited one-electron wave functions. At energies of about 100 keV, agreement with available experimental results is generally good; however, for the $3{}_{}{}^1{}_{}{}^{}P$, $4{}_{}{}^1{}_{}{}^{}P$, and $4{}_{}{}^1{}_{}{}^{}D$ states, the disagreement exceeds the estimated experimental uncertainty.